asm - tensile testing

Tensile TestingSecond Edition

Edited byJ.R. Davis

Davis & Associates

Materials Park, Ohio 44073-0002www.asminternational.org

© 2004 ASM International. All Rights Reserved.Tensile Testing, Second Edition (#05106G)

www.asminternational.org

Copyright � 2004by

ASM International�All rights reserved

No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any formor by any means, electronic, mechanical, photocopying, recording, or otherwise, without thewritten permission of the copyright owner.

First printing, December 2004

Great care is taken in the compilation and production of this book, but it should be made clearthat NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING, WITHOUT LIMITATION,WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE,ARE GIVEN IN CONNECTION WITH THIS PUBLICATION. Although this information isbelieved to be accurate by ASM, ASM cannot guarantee that favorable results will be obtainedfrom the use of this publication alone. This publication is intended for use by persons havingtechnical skill, at their sole discretion and risk. Since the conditions of product or material useare outside of ASM’s control, ASM assumes no liability or obligation in connection with anyuse of this information. No claim of any kind, whether as to products or information in thispublication, and whether or not based on negligence, shall be greater in amount than the purchaseprice of this product or publication in respect of which damages are claimed. THE REMEDYHEREBY PROVIDED SHALL BE THE EXCLUSIVE AND SOLE REMEDY OF BUYER,AND IN NO EVENT SHALL EITHER PARTY BE LIABLE FOR SPECIAL, INDIRECT ORCONSEQUENTIAL DAMAGES WHETHER OR NOT CAUSED BY OR RESULTING FROMTHE NEGLIGENCE OF SUCH PARTY. As with any material, evaluation of the material underend-use conditions prior to specification is essential. Therefore, specific testing under actualconditions is recommended.

Nothing contained in this book shall be construed as a grant of any right of manufacture, sale,use, or reproduction, in connection with any method, process, apparatus, product, composition,or system, whether or not covered by letters patent, copyright, or trademark, and nothing con-tained in this book shall be construed as a defense against any alleged infringement of letterspatent, copyright, or trademark, or as a defense against liability for such infringement.

Comments, criticisms, and suggestions are invited, and should be forwarded to ASM Interna-tional.

Prepared under the direction of the ASM International Technical Book Committee (2004–2005),Yip-Wah Chung, Chair (FASM).

ASM International staff who worked on this project include Scott Henry, Senior Manager ofProduct and Service Development; Bonnie Sanders, Manager of Production; Carol Polakowski,Production Supervisor; and Pattie Pace, Production Coordinator.

Library of Congress Cataloging-in-Publication Data

Tensile testing / edited by J.R. Davis.—2nd ed.p. cm.

Includes bibliographical references and index.ISBN 0-87170-806-X1. Materials—Testing. 2. Brittleness. 3. Tensiometers. I. Davis, J. R. (Joseph R.)

TA418.16.T46 2004620.1�126—dc22 2004057353

ISBN: 0-87170-806-XSAN: 204-7586

ASM International�Materials Park, OH 44073-0002


Printed in the United States of America



Contents

Preface ............................................................................................... vii

Section 1 Tensile Testing: Understanding the Basics

Chapter 1 Introduction to Tensile Testing .............................................1Tensile Specimens and Testing Machines ..................................1Stress-Strain Curves ..............................................................3True Stress and Strain ...........................................................7Other Factors Influencing the Stress-Strain Curve ......................7Test Methodology and Data Analysis .......................................8

Chapter 2 Mechanical Behavior of Materials under Tensile Loads ........ 13Engineering Stress-Strain Curve ............................................ 13True Stress-True Strain Curve ............................................... 18Mathematical Expressions for the Flow Curve ......................... 20Effect of Strain Rate and Temperature .................................... 21Instability in Tension .......................................................... 22Stress Distribution at the Neck .............................................. 23Ductility Measurement in Tensile Testing ............................... 24Sheet Anisotropy ................................................................ 25Notch Tensile Test .............................................................. 28Tensile Test Fractures .......................................................... 28

Chapter 3 Uniaxial Tensile Testing ..................................................... 33Definitions and Terminology ................................................ 34Stress-Strain Behavior ......................................................... 36Properties from Test Results ................................................. 40General Procedures ............................................................. 47The Test Piece ................................................................... 47Test Setup ......................................................................... 54Test Procedures .................................................................. 56Post-Test Measurements ...................................................... 58Variability of Tensile Properties ............................................ 59

Chapter 4 Tensile Testing Equipment and Strain Sensors ..................... 65Testing Machines ............................................................... 66Principles of Operation ........................................................ 68Load-Measurement Systems ................................................. 74Strain-Measurement Systems ................................................ 77Gripping Techniques ........................................................... 83Environmental Chambers ..................................................... 84

iii



Force Verification of Universal Testing Machines ..................... 85Tensile Testing Requirements and Standards ........................... 87

Chapter 5 Tensile Testing for Design .................................................. 91Product Design .................................................................. 91Design for Strength in Tension ............................................. 92Design for Strength, Weight, and Cost ................................... 93Design for Stiffness in Tension ............................................. 95Mechanical Testing for Stress at Failure and Elastic Modulus ..... 97Hardness-Strength Correlation .............................................. 99

Chapter 6 Tensile Testing for Determining Sheet Formability ..............101Effect of Material Properties on Formability ..........................101Effect of Temperature on Formability ...................................106Types of Formability Tests ..................................................107Uniaxial Tensile Testing .....................................................107Plane-Strain Tensile Testing ................................................111

Section 2 Tensile Testing of Engineered Materials and Components

Chapter 7 Tensile Testing of Metals and Alloys ..................................115Elastic Behavior ................................................................115Anelasticity ......................................................................116Damping ..........................................................................118The Proportional Limit .......................................................119Yielding and the Onset of Plasticity ......................................119The Yield Point .................................................................122Grain-Size Effects on Yielding ............................................123Strain Hardening and the Effect of Cold Work ........................124Ultimate Strength ..............................................................126Toughness ........................................................................127Ductility ..........................................................................129True Stress-Strain Relationships ...........................................130Temperature and Strain-Rate Effects .....................................131Special Tests ....................................................................133Fracture Characterization ....................................................134Summary .........................................................................136

Chapter 8 Tensile Testing of Plastics .................................................137Fundamental Factors that Affect Data from Tensile Tests .........138Stipulations in Standardized Tensile Testing ...........................144Utilization of Data from Tensile Tests ...................................150Summary .........................................................................152

Chapter 9 Tensile Testing of Elastomers ............................................155Manufacturing of Elastomers ...............................................155Properties of Interest ..........................................................155Factors Influencing Elastomer Properties ...............................156ASTM Standard D 412 ......................................................158Significance and Use of Tensile-Testing Data .........................159Summary .........................................................................161

Chapter 10 Tensile Testing of Ceramics and Ceramic-MatrixComposites ....................................................................163Rationale for Use of Ceramics ...........................................163Intrinsic Limitations of Ceramics ........................................163

iv



Overview of Important Considerations for Tensile Testing ofAdvanced Ceramics .........................................................164Tensile Testing Techniques ................................................165Summary .......................................................................179

Chapter 11 Tensile Testing of Fiber-Reinforced Composites .................183Fundamentals of Tensile Testing of Composite Materials ........183Tensile Testing of Single Filaments and Tows .......................185Tensile Testing of Laminates .............................................185Data Reduction ...............................................................191Application of Tensile Tests to Design .................................192

Chapter 12 Tensile Testing of Components .........................................195Testing of Threaded Fasteners and Bolted Joints ...................195Testing of Adhesive Joints ................................................204Testing of Welded Joints ...................................................206

Section 3 Tensile Testing at Extreme Temperatures or High-StrainRates

Chapter 13 Hot Tensile Testing .........................................................209Equipment and Testing Procedures .....................................210Hot Ductility and Strength Data from the Gleeble Test ...........215Isothermal Hot Tensile Test Data ........................................220Modeling of the Isothermal Hot Tensile Test ........................226Cavitation during Hot Tensile Testing .................................230

Chapter 14 Tensile Testing at Low Temperatures ...............................239Mechanical Properties at Low Temperatures .........................239Test Selection Factors: Tensile versus Compression Tests .......241Equipment ......................................................................243Tensile Testing Parameters and Standards ............................246Temperature Control ........................................................248Safety ............................................................................248

Chapter 15 High Strain Rate Tensile Testing ......................................251Conventional Load Frames ................................................251Expanding Ring Test ........................................................254Flyer Plate and Short Duration Pulse Loading .......................255The Split-Hopkinson Pressure Bar Technique .......................257Rotating Wheel Test .........................................................260

Section 4 Reference Information

Glossary of Terms ...............................................................................265Reference Tables .................................................................................273

Room-temperature tensile yield strength comparisons ofmetals and plastics ........................................................273

Room-temperature tensile modulus of elasticity comparisonsof various materials ......................................................275

Index ................................................................................................279

v



Preface

In the preface to the first edition of Tensile Testing, editor Patricia Han wrote “Ourvision for this book was to provide a volume that could serve not only as an introductionfor those who are just starting to perform tensile tests and use tensile data, but also asa source of more detailed information for those who are better acquainted with thesubject. We have written this reference book to appeal to laboratory managers, tech-nicians, students, designers, and materials engineers.” This vision has been preservedin the current edition, with some very important new topics added.

As in the first edition, section one opens with an introduction that discusses thefundamentals and language of tensile testing. Subsequent chapters describe test meth-odology and equipment, the use of tensile testing for design, and the use of tensiletesting for determining the formability of sheet metals.

The second section consists of five chapters that deal with tensile testing of the majorclasses of engineering materials—metals, plastics, elastomers, ceramics, and compos-ites. New material on testing of adhesively bonded joints, welded joints, and threadedfasteners has been added.

The third section contains chapters that review testing at elevated and low tempera-tures and special tests carried out at very high strain rates. Although these subjects wereintroduced in the first edition, they have been substantially expanded in this book.

In the fourth and final section, a glossary of terms related to tensile testing andproperties has been compiled. Comprehensive tables provide tensile yield strengths ofvarious materials and compare the elastic modulus of engineering materials.

In summary, this edition retains much of the flavor of the first edition while intro-ducing readers to a number of additional topics that will extend their knowledge andappreciation of the tensile test.

Joseph R. DavisDavis & AssociatesChagrin Falls, Ohio

vii



ASM International is the society for materials engineers and scientists, a worldwide network dedicated to advancing industry, technology, and applications of metals and materials. ASM International, Materials Park, Ohio, USA www.asminternational.org

This publication is copyright © ASM International®. All rights reserved.

Publication title Product code Tensile Testing #05106G

To order products from ASM International:

Online Visit www.asminternational.org/bookstore

Telephone 1-800-336-5152 (US) or 1-440-338-5151 (Outside US) Fax 1-440-338-4634

Mail Customer Service, ASM International 9639 Kinsman Rd, Materials Park, Ohio 44073-0002, USA

Email [email protected]

In Europe

American Technical Publishers Ltd. 27-29 Knowl Piece, Wilbury Way, Hitchin Hertfordshire SG4 0SX, United Kingdom Telephone: 01462 437933 (account holders), 01462 431525 (credit card) www.ameritech.co.uk

In Japan Neutrino Inc. Takahashi Bldg., 44-3 Fuda 1-chome, Chofu-Shi, Tokyo 182 Japan Telephone: 81 (0) 424 84 5550

Terms of Use. This publication is being made available in PDF format as a benefit to members and customers of ASM International. You may download and print a copy of this publication for your personal use only. Other use and distribution is prohibited without the express written permission of ASM International. No warranties, express or implied, including, without limitation, warranties of merchantability or fitness for a particular purpose, are given in connection with this publication. Although this information is believed to be accurate by ASM, ASM cannot guarantee that favorable results will be obtained from the use of this publication alone. This publication is intended for use by persons having technical skill, at their sole discretion and risk. Since the conditions of product or material use are outside of ASM's control, ASM assumes no liability or obligation in connection with any use of this information. As with any material, evaluation of the material under end-use conditions prior to specification is essential. Therefore, specific testing under actual conditions is recommended. Nothing contained in this publication shall be construed as a grant of any right of manufacture, sale, use, or reproduction, in connection with any method, process, apparatus, product, composition, or system, whether or not covered by letters patent, copyright, or trademark, and nothing contained in this publication shall be construed as a defense against any alleged infringement of letters patent, copyright, or trademark, or as a defense against liability for such infringement.

CHAPTER 1

Introduction to Tensile Testing

Fig. 1 Typical tensile specimen, showing a reduced gage section and enlarged shoulders. To avoid end effects from the shoulders,the length of the transition region should be at least as great as the diameter, and the total length of the reduced section should

be at least four times the diameter.

TENSILE TESTS are performed for severalreasons. The results of tensile tests are used inselecting materials for engineering applications.Tensile properties frequently are included in ma-terial specifications to ensure quality. Tensileproperties often are measured during develop-ment of new materials and processes, so that dif-ferent materials and processes can be compared.Finally, tensile properties often are used to pre-dict the behavior of a material under forms ofloading other than uniaxial tension.

The strength of a material often is the primaryconcern. The strength of interest may be mea-sured in terms of either the stress necessary tocause appreciable plastic deformation or themaximum stress that the material can withstand.These measures of strength are used, with ap-propriate caution (in the form of safety factors),in engineering design. Also of interest is the ma-terial’s ductility, which is a measure of howmuch it can be deformed before it fractures.Rarely is ductility incorporated directly in de-sign; rather, it is included in material specifica-tions to ensure quality and toughness. Low duc-tility in a tensile test often is accompanied bylow resistance to fracture under other forms ofloading. Elastic properties also may be of inter-est, but special techniques must be used to mea-sure these properties during tensile testing, andmore accurate measurements can be made byultrasonic techniques.

This chapter provides a brief overview ofsome of the more important topics associatedwith tensile testing. These include:

● Tensile specimens and test machines● Stress-strain curves, including discussions of

elastic versus plastic deformation, yieldpoints, and ductility

● True stress and strain● Test methodology and data analysis

It should be noted that subsequent chapters con-tain more detailed information on these topics.Most notably, the following chapters should bereferred to:

● Chapter 2, “Mechanical Behavior of Mate-rials Under Tensile Loads”

● Chapter 3, “Uniaxial Tensile Testing”● Chapter 4, “Tensile Testing Equipment and

Strain Sensors”

Tensile Specimens andTesting Machines

Tensile Specimens. Consider the typical ten-sile specimen shown in Fig. 1. It has enlargedends or shoulders for gripping. The importantpart of the specimen is the gage section. Thecross-sectional area of the gage section is re-duced relative to that of the remainder of thespecimen so that deformation and failure will be

Tensile Testing, Second EditionJ.R. Davis, editor, p1-12 DOI:10.1361/ttse2004p001

Copyright © 2004 ASM International® All rights reserved. www.asminternational.org

2 / Tensile Testing, Second Edition

Fig. 2 Systems for gripping tensile specimens. For round specimens, these include threaded grips (a), serrated wedges (b), and, forbutt end specimens, split collars constrained by a solid collar (c). Sheet specimens may be gripped with pins (d) or serrated

wedges (e).

localized in this region. The gage length is theregion over which measurements are made andis centered within the reduced section. The dis-tances between the ends of the gage section andthe shoulders should be great enough so that thelarger ends do not constrain deformation withinthe gage section, and the gage length should begreat relative to its diameter. Otherwise, thestress state will be more complex than simpletension. Detailed descriptions of standard spec-imen shapes are given in Chapter 3 and in sub-sequent chapters on tensile testing of specificmaterials.

There are various ways of gripping the spec-imen, some of which are illustrated in Fig. 2.The end may be screwed into a threaded grip, orit may be pinned; butt ends may be used, or thegrip section may be held between wedges. Thereare still other methods (see, for example, Fig. 24in Chapter 3). The most important concern inthe selection of a gripping method is to ensurethat the specimen can be held at the maximumload without slippage or failure in the grip sec-tion. Bending should be minimized.

Testing Machines. The most common testingmachines are universal testers, which test ma-

terials in tension, compression, or bending.Their primary function is to create the stress-strain curve described in the following sectionin this chapter.

Testing machines are either electromechanicalor hydraulic. The principal difference is themethod by which the load is applied.

Electromechanical machines are based on avariable-speed electric motor; a gear reductionsystem; and one, two, or four screws that movethe crosshead up or down. This motion loads thespecimen in tension or compression. Crossheadspeeds can be changed by changing the speed ofthe motor. A microprocessor-based closed-loopservo system can be implemented to accuratelycontrol the speed of the crosshead.

Hydraulic testing machines (Fig. 3) are basedon either a single or dual-acting piston thatmoves the crosshead up or down. However,most static hydraulic testing machines have asingle acting piston or ram. In a manually op-erated machine, the operator adjusts the orificeof a pressure-compensated needle valve to con-trol the rate of loading. In a closed-loop hydrau-lic servo system, the needle valve is replaced byan electrically operated servo valve for precisecontrol.

Introduction to Tensile Testing / 3

Fig. 3 Components of a hydraulic universal testing machine

In general, electromechanical machines arecapable of a wider range of test speeds andlonger crosshead displacements, whereas hy-draulic machines are more cost-effective forgenerating higher forces.

Stress-Strain Curves

A tensile test involves mounting the specimenin a machine, such as those described in the pre-vious section, and subjecting it to tension. Thetensile force is recorded as a function of the in-crease in gage length. Figure 4(a) shows a typ-ical curve for a ductile material. Such plots oftensile force versus tensile elongation would beof little value if they were not normalized withrespect to specimen dimensions.

Engineering stress, or nominal stress, s, is de-fined as

s � F/A (Eq 1)0

where F is the tensile force and A0 is the initialcross-sectional area of the gage section.

Engineering strain, or nominal strain, e, is de-fined as

e � DL/L (Eq 2)0

where L0 is the initial gage length and DL is thechange in gage length (L � L0).

When force-elongation data are converted toengineering stress and strain, a stress-straincurve (Fig. 4b) that is identical in shape to theforce-elongation curve can be plotted. The ad-vantage of dealing with stress versus strainrather than load versus elongation is that thestress-strain curve is virtually independent ofspecimen dimensions.

Elastic versus Plastic Deformation. Whena solid material is subjected to small stresses, thebonds between the atoms are stretched. Whenthe stress is removed, the bonds relax and thematerial returns to its original shape. This re-


Fig. 4 (a) Load-elongation curve from a tensile test and (b) corresponding engineering stress-strain curve. Specimen diameter, 12.5mm; gage length, 50 mm.

versible deformation is called elastic deforma-tion. (The deformation of a rubber band is en-tirely elastic). At higher stresses, planes of atomsslide over one another. This deformation, whichis not recovered when the stress is removed, istermed plastic deformation. Note that the term“plastic deformation” does not mean that the de-formed material is a plastic (a polymeric mate-rial). Bending of a wire (such as paper-clip wire)with the fingers (Fig. 5) illustrates the difference.If the wire is bent a little bit, it will snap backwhen released (top). With larger bends, it willunbend elastically to some extent on release, butthere will be a permanent bend because of theplastic deformation (bottom).

For most materials, the initial portion of thecurve is linear. The slope of this linear region iscalled the elastic modulus or Young’s modulus:

E � s/e (Eq 3)

In the elastic range, the ratio, t, of the mag-nitude of the lateral contraction strain to the ax-ial strain is called Poisson’s ratio:

t � �e /e (in an x-direction tensile test)y x (Eq 4)

Because elastic strains are usually very small,reasonably accurate measurement of Young’smodulus and Poisson’s ratio in a tensile test re-quires that strain be measured with a very sen-sitive extensometer. (Strain gages should beused for lateral strains.) Accurate results can alsobe obtained by velocity-of-sound measurements(unless the modulus is very low or the dampingis high, as with polymers).

When the stress rises high enough, the stress-strain behavior will cease to be linear and thestrain will not disappear completely on unload-ing. The strain that remains is called plasticstrain. The first plastic strain usually corre-sponds to the first deviation from linearity. (Forsome materials, the elastic deformation may benonlinear, and so there is not always this corre-spondence). Once plastic deformation has be-gun, there will be both elastic and plastic con-tributions to the total strain, eT. This can beexpressed as eT � ee � ep, where ep is the plas-

Fig. 5 Elastic and plastic deformation of a wire with the fin-gers. With small forces (top), all of the bending is elastic

and disappears when the force is released. With greater forces(below), some of the bending is recoverable (elastic), but most ofthe bending is not recovered (is plastic) when the force is re-moved.


Fig. 6 The low-strain region of the stress-strain curve for aductile material

tic contribution and ee is the elastic contribution(and still related to the stress by Eq 3).

It is tempting to define an elastic limit as thestress at which plastic deformation first occursand a proportional limit as the stress at whichthe stress-strain curve first deviates from linear-ity. However, neither definition is very useful,because measurement of the stress at which plas-tic deformation first occurs or the first deviationfrom linearity is observed depends on how ac-curately strain can be measured. The smaller theplastic strains that can be sensed and the smallerthe deviations from linearity can be detected, thesmaller the elastic and proportional limits.

To avoid this problem, the onset of the plas-ticity is usually described by an offset yieldstrength, which can be measured with greaterreproducibility. It can be found by constructinga straight line parallel to the initial linear portionof the stress-strain curve, but offset by e �0.002 or 0.2%. The yield strength is the stress atwhich this line intersects the stress-strain curve(Fig. 6). The rationale is that if the material hadbeen loaded to this stress and then unloaded, theunloading path would have been along this off-set line and would have resulted in a plasticstrain of e � 0.2%. Other offset strains are

sometimes used. The advantage of defining yieldstrength in this way is that such a parameter iseasily reproduced and does not depend heavilyon the sensitivity of measurement.

Sometimes, for convenience, yielding in met-als is defined by the stress required to achieve aspecified total strain (e.g., eT � 0.005 or 0.5%elongation) instead of a specified offset strain.In any case, the criterion should be made clearto the user of the data.

Yield Points. For some materials (e.g., low-carbon steels and many linear polymers), thestress-strain curves have initial maxima fol-lowed by lower stresses, as shown in Fig. 7(a)and (b). After the initial maximum, all the de-formation at any instant is occurring within arelatively small region of the specimen. Contin-ued elongation of the specimen occurs by prop-agation of the deforming region (Luders band inthe case of steels) along the gage section ratherthan by increased strain within the deformingregion. Only after the entire gage section hasbeen traversed by the band does the stress riseagain. In the case of linear polymers, a yieldstrength is often defined as the initial maximumstress. For steels, the subsequent lower yieldstrength is used to describe yielding. This is be-cause measurements of the initial maximum orupper yield strength are extremely sensitive tohow axially the load is applied during the tensiletest. Some laboratories cite the minimum,whereas others cite a mean stress during this dis-continuous yielding.

The tensile strength (ultimate strength) is de-fined as the highest value of engineering stress*(Fig. 8). Up to the maximum load, the defor-mation should be uniform along the gage sec-tion. With ductile materials, the tensile strengthcorresponds to the point at which the deforma-tion starts to localize, forming a neck (Fig. 8a).Less ductile materials fracture before they neck(Fig. 8b). In this case, the fracture strength is thetensile strength. Indeed, very brittle materials(e.g., glass at room temperature) do not yieldbefore fracture (Fig. 8c). Such materials havetensile strengths but not yield strengths.

Ductility. There are two common measuresused to describe the ductility of a material. One

*Sometimes the upper yield strength of low-carbon steel ishigher than the subsequent maximum. In such cases, someprefer to define the tensile strength as the subsequent max-imum instead of the initial maximum, which is higher. Insuch cases, the definition of tensile strength should be madeclear to the user.


Fig. 8 Stress-strain curves showing that the tensile strength is the maximum engineering stress regardless of whether the specimennecks (a) or fractures before necking (b and c).

Fig. 7 Inhomogeneous yielding of a low-carbon steel (a) and a linear polymer (b). After the initial stress maxima, the deformationoccurs within a narrow band, which propagates along the entire length of the gage section before the stress rises again.

is the percent elongation, which is defined sim-ply as

%El � [(L � L )/L ] � 100 (Eq 5)f 0 0

where L0 is the initial gage length and Lf is thelength of the gage section at fracture. Measure-ments may be made on the broken pieces or un-der load. For most materials, the amount of elas-tic elongation is so small that the two areequivalent. When this is not so (as with brittlemetals or rubber), the results should statewhether or not the elongation includes an elasticcontribution. The other common measure ofductility is percent reduction of area, which isdefined as

%RA � [(A � A )/A ] � 100 (Eq 6)0 f 0

where A0 and Af are the initial cross-sectionalarea and the cross-sectional area at fracture, re-spectively. If failure occurs without necking, onecan be calculated from the other:

%El � %RA/(100 � %RA) (Eq 7)

After a neck has developed, the two are nolonger related. Percent elongation, as a measureof ductility, has the disadvantage that it is reallycomposed of two parts: the uniform elongationthat occurs before necking, and the localizedelongation that occurs during necking. The sec-ond part is sensitive to the specimen shape.When a gage section that is very long (relativeto its diameter), the necking elongation con-verted to percent is very small. In contrast, witha gage section that is short (relative to its di-


ameter), the necking elongation can account formost of the total elongation.

For round bars, this problem has been reme-died by standardizing the ratio of gage length todiameter to 4:1. Within a series of bars, all withthe same gage-length-to-diameter ratio, thenecking elongation will be the same fraction ofthe total elongation. However, there is no simpleway to make meaningful comparisons of percentelongation from such standardized bars with thatmeasured on sheet tensile specimens or wire.With sheet tensile specimens, a portion of theelongation occurs during diffuse necking, andthis could be standardized by maintaining thesame ratio of width to gage length. However, aportion of the elongation also occurs duringwhat is called localized necking, and this de-pends on the sheet thickness. For tensile testingof wire, it is impractical to have a reduced sec-tion, and so the ratio of gage length to diameteris necessarily very large. Necking elongationcontributes very little to the total elongation.

Percent reduction of area, as a measure ofductility, has the disadvantage that with veryductile materials it is often difficult to measurethe final cross-sectional area at fracture. This isparticularly true of sheet specimens.

True Stress and Strain

If the results of tensile testing are to be usedto predict how a metal will behave under otherforms of loading, it is desirable to plot the datain terms of true stress and true strain. True stress,r, is defined as

r � F/A (Eq 8)

where A is the cross-sectional area at the timethat the applied force is F. Up to the point atwhich necking starts, true strain, e, is defined as

e � ln(L/L ) (Eq 9)0

This definition arises from taking an incrementof true strain, de, as the incremental change inlength, dL, divided by the length, L, at the time,de � dL/L, and integrating. As long as the de-formation is uniform along the gage section, thetrue stress and strain can be calculated from theengineering quantities. With constant volumeand uniform deformation, LA � L0A0:

A /A � L/L (Eq 10)0 0

Thus, according to Eq 2, A0/A � 1 � e. Equa-tion 8 can be rewritten as

r � (F/A )(A /A)0 0

and, with substitution for A0/A and F/A0, as

r � s(1 � e) (Eq 11)

Substitution of L/L0 � 1 � e into the expressionfor true strain (Eq 9) gives

e � ln(1 � e) (Eq 12)

At very low strains, the differences betweentrue and engineering stress and strain are verysmall. It does not really matter whether Young’smodulus is defined in terms of engineering ortrue stress strain.

It must be emphasized that these expressionsare valid only as long as the deformation is uni-form. Once necking starts, Eq 8 for true stressis still valid, but the cross-sectional area at thebase of the neck must be measured directlyrather than being inferred from the length mea-surements. Because the true stress, thus calcu-lated, is the true stress at the base of the neck,the corresponding true strain should also be atthe base of the neck. Equation 9 could still beused if the L and L0 values were known for anextremely short gage section centered on themiddle of the neck (one so short that variationsof area along it would be negligible). Of course,there will be no such gage section, but if therewere, Eq 10 would be valid. Thus the true straincan be calculated as

e � ln(A /A) (Eq 13)0

Figure 9 shows a comparison of engineering andtrue stress-strain curves for the same material.

Other FactorsInfluencing the Stress-Strain Curve

There are a number of factors not previouslydiscussed in this chapter that have an effect onthe shape of the stress-strain curve. These in-clude strain rate, temperature, and anisotropy.For information on these subjects, the readershould refer to Chapters 2 and 3 listed in theintroduction to this chapter as well as Chapter12, “Hot Tensile Testing” and Chapter 15, “HighStrain Rate Tensile Testing.”


Fig. 9 Comparison of engineering and true stress-straincurves. Prior to necking, a point on the r-e curve can

be constructed from a point on the s-e curve using Eq 11 and 12.Subsequently, the cross section must be measured to find truestress and strain.

Test Methodology and Data Analysis

This section reviews some of the more im-portant considerations involved in tensile test-ing. These include:

● Sample selection● Sample preparation● Test set-up● Test procedure● Data recording and analysis● Reporting

Sample Selection. When a material is tested,the objective usually is to determine whether ornot the material is suitable for its intended use.

The sample to be tested must fairly representthe body of material in question. In other words,it must be from the same source and have un-dergone the same processing steps.

It is often difficult to match exactly the testsamples to the structure made from the material.A common practice for testing of large castings,forgings, and composite layups is to add extramaterial to the part for use as “built-in” test sam-ples. This material is cut from the completed partafter processing and is made into test specimensthat have been subjected to the same processingsteps as the bulk of the part.

In practice, these specimens may not exactlymatch the bulk of the part in certain importantdetails, such as the grain patterns in critical areasof a forging. One or more complete parts maybe sacrificed to obtain test samples from themost critical areas for comparison with the“built-in” samples. Thus, it may be determined

how closely the “built-in” samples represent thematerial in question.

There is a special case in which the object ofthe test is to evaluate not the material, but thetest itself. Here, the test specimens must be asnearly identical as possible so the differences inthe test results represent, as far as possible, onlythe variability in the testing process.

Sample Preparation. It should be remem-bered that a “sample” is a quantity of materialthat represents a larger lot. The sample usuallyis made into multiple “specimens” for testing.Test samples must be prepared properly toachieve accurate results. The following rules aresuggested for general guidance.

First, as each sample is obtained, it should beidentified as to material description, source, lo-cation and orientation with respect to the bodyof material, processing status at the time of sam-pling, and the data and time of day that the sam-ple was obtained.

Second, test specimens must be made care-fully, with attention to several details. The spec-imen axis must be properly aligned with the ma-terial rolling direction, forging grain pattern, orcomposite layup. Cold working of the test sec-tion must be minimized. The dimensions of thespecimen must be held within the allowable tol-erances established by the test procedure. Theattachment areas at each end of the specimenmust be aligned with the axis of the bar (see Fig.10). Each specimen must be identified as be-longing to the original sample. If total elonga-tion is to be measured after the specimen breaks,the gage length must be marked on the reducedsection of the bar prior to testing.

The test set-up requires that equipment beproperly matched to the test at hand. There are

Fig. 10 Improper (left) and proper (right) alignment of speci-men attachment areas with axis of specimen


three requirements of the testing machine: forcecapacity sufficient to break the specimens to betested; control of test speed (or strain rate or loadrate), as required by the test specification; andprecision and accuracy sufficient to obtain andrecord properly the load and extension infor-mation generated by the test. This precision andaccuracy should be ensured by current calibra-tion certification.

For grips, of which many types are in com-mon use in tensile testing, only two rules apply:the grips must properly fit the specimens (or viceversa), and they must have sufficient force ca-pacity so that they are not damaged during test-ing.

As described earlier in the section “TensileSpecimens and Testing Machines,” there areseveral techniques for installing the specimen inthe grips. With wedge grips, placement of thespecimen in the grips is critical to proper align-ment (see Fig. 11). Ideally, the grip faces shouldbe of the same width as the tab ends of the testbar; otherwise, lateral alignment is dependentonly on the skill of the technician. The wedgegrip inserts should be contained within the gripbody or crosshead, and the specimen tabs shouldbe fully engaged by the grips (see Fig. 12).

Other types of grips have perhaps fewer trapsfor the inexperienced technician, but an obviousone is that, with threaded grips, a length of

threads on the specimen equal to at least onediameter should be engaged in the threadedgrips.

There are several potential problems that mustbe watched for during the test set-up, includingspecimen misalignment and worn grips. Thephysical alignment of the two points of attach-ment of the specimen is important, because anyoff-center loading will exert bending loads onthe specimen. This is critical in testing of brittlematerials, and may cause problems even for duc-tile materials. Alignment will be affected by thetesting-machine loadframe, any grips and fix-tures used, and the specimen itself. Misalign-ment may also induce load-measurement errorsdue to the passage of bending forces through theload-measuring apparatus. Such errors may bereduced by the use of spherical seats or “U-joints” in the set-up.

Worn grips may contribute to off-center load-ing. Uneven tooth marks across the width of thespecimen tab are an indication of trouble inwedge grips. Split-collar grips may also causeoff-center loading. Uneven wear of grips andmismatching of split-shell insert pairs are poten-tial problem areas.

Strain measurements are required for manytests. They are commonly made with extensom-eters, but strain gages are frequently used—especially on small specimens or where Pois-

Fig. 11 Improper (left, center) and proper (right) alignment of specimen in wedge grips


son’s ratio is to be measured. If strainmeasurements are required, appropriate strain-measuring instruments must be properly in-stalled. The technician should pay particular at-tention to setting of the extensometer gagelength (mechanical zero). The zero of the strainreadout should repeat consistently if the me-chanical zero is set properly. In other words,once the extensometer has been installed and ze-roed, subsequent installations should requireminimal readjustment of the zero.

Test Procedure. The following general rulesfor test procedure may be applied to almostevery tensile test.

Load and strain ranges should be selected sothat the test will fit the range. The maximumvalues to be recorded should be as close to thetop of the selected scale as convenient withoutrunning the risk of going past full scale. Rangesmay be selected using past experience for a par-ticular test, or specification data for the material(if available). Note that many computer-basedtesting systems have automatic range selectionand will capture data even if the range initiallyselected is too small.

The identity of each specimen should be ver-ified, and pertinent identification should be ac-curately recorded for the test records and report.

The dimensions needed to calculate the cross-sectional area of the reduced section should bemeasured and recorded. These measurementsshould be repeated for every specimen; it shouldnot be assumed that sample preparation is per-fectly consistent.

The load-indicator zero and the plot-load-axiszero, if applicable, should be set before the spec-imen is placed in the grips. Zeroes should neverbe reset after the specimen is in place.

The specimen is placed in the grips and issecured by closing the grips. If preload is to beremoved before the test is started, it should bephysically unloaded by moving the loadingmechanism. The zero adjustment should neverbe used for this purpose. Note that, in somecases, preload may be desirable and may be de-liberately introduced. For materials for whichthe initial portion of the curve is linear, the strainzero may be corrected for preload by extendingthe initial straight portion of the stress-straincurve to zero load and measuring strain fromthat point. The strain valve at the zero-load in-tercept is commonly called the “foot correction”and is subtracted from readings taken from strainscale (see Fig. 10 in Chapter 3, “Uniaxial TensileTesting”).

When the extensometer, if applicable, is in-stalled, the technician should be sure to set themechanical zero correctly. The strain-readoutzero should be set after the extensometer is inplace on the specimen.

The test procedure should be in conformancewith the published test specification and should

Fig. 12 Proper and improper engagement of a specimen inwedge grips


be repeated consistently for every test. It is im-portant that the test specification be followed forspeed of testing. Some materials are sensitive totest speed, and different speeds will give differ-ent results. Also, many testing machine load-and strain-measuring instruments are not capa-ble of responding fast enough for accuraterecording of test results if an excessive test speedis used.

The technician should monitor the test closelyand be alert for problems. One common sign oftrouble is a load-versus-strain plot in which theinitial portion of the curve is not straight. Thismay indicate off-center loading of the specimen,improper installation of the extensometer, or thespecimen was not straight to begin with.

Another potential trouble sign is a sharp dropin indicated load during the test. Such a dropmay be characteristic of the material, but it alsocan indicate problems such as slippage betweenthe specimen and the grips or stick-slip move-ment of the wedge grip inserts in the grip body.Slippage may be caused by worn inserts withdull teeth, particularly for hard, smooth speci-mens.

The stick-slip action in wedge grips is morecommon in testing of resilient materials, but italso can occur in testing of metals. Specimenscut from the wall of a pipe or tube may havecurved tab ends that flatten with increasingforce, allowing the inserts to move relative tothe grip body. Short tab ends on round speci-mens also may be crushed by the wedge grips,with the same result. If the sliding faces are notlubricated, they may move in unpredictablesteps accompanied by drops in the load reading.Dry-film molybdenum disulfide lubricants areeffective in solving stick-slip problems in wedgegrips, particularly when testing is done at ele-vated temperature.

When wedge grips are used, the specimenmust be installed so that the clamping force iscontained within the grip body. Placing the spec-imen too near the open end of the grip bodyresults in excessive stress on the grip body andinserts and is a common cause of grip failure.WARNING: Grip failures are dangerous andmay cause injury to personnel and damage toequipment.

Data generally may be grouped into “rawdata,” meaning the observed readings of themeasuring instruments, and “calculated data,”meaning the test results obtained after the firststep of analysis.

In the most simple tensile test, the raw datacomprise a single measurement of peak force

and the dimensional measurements taken to de-termine the cross-sectional area of the test spec-imen. The first analysis step is to calculate the“tensile strength,” defined as the force per unitarea required to fracture the specimen. Morecomplicated tests will require more information,which typically takes the form of a graph offorce versus extension. Computer-based testingmachines can display the graph without paper,and can save the measurements associated withthe graph by electronic means.

A permanent record of the raw test data isimportant, because it allows additional analysesto be performed later, if desired, and because itallows errors in analysis to be found and cor-rected by reference to the original data.

Data Recording. Test records may be neededby many departments within an organization, in-cluding metallurgy, engineering, commercial,and legal departments.

Engineering and metallurgy departments typ-ically are most interested in material properties,but may use raw data for error checking or ad-ditional analyses. The metallurgy departmentwants to know how variations in raw materialsor processing change the properties of the prod-uct being produced and tested, and the engi-neering department wants to know the propertiesof the material for design purposes.

Shipping, receiving, and accounting depart-ments need to know whether or not the materialmeets the specifications for shipping, accep-tance, and payment. The sales department needsinformation for advertising and for advising pro-spective customers.

If a product incorporating the tested materiallater fails—particularly if persons are injured—the legal department may need test data as evi-dence in legal proceedings. In this case, a recordof the raw data will be important for support ofthe original analysis and test report.

Analysis of test data is done at several levels.First, the technician observes the test in pro-gress, and may see that a grip is slipping or thatthe specimen fractures outside the gage section.These observations may be sufficient to deter-mine that a test is invalid.

Immediately after the test, a first-level anal-ysis is performed according to the calculationrequirements of the test procedure. ASTM testspecifications typically show the necessaryequations with an explanation and perhaps anexample. This analysis may be as simple asdividing peak force by cross-sectional area, orit may require more complex calculations. The


outputs of this first level of analysis are themechanical properties of the material beingtested.

Upon completion of the group of tests per-formed on the sample, a statistical analysis maybe made. The statistical analysis produces av-erage (mean or median) values for representa-tion of the sample in the subsequent databaseand also provides information about the unifor-mity of the material and the repeatability of thetest.

The results of tests on each sample of materialmay be stored in a database for future use. Thedatabase allows a wide range of analyses to beperformed using statistical methods to correlatethe mechanical-properties data with other infor-mation about the material. For example, it mayallow determination of whether or not there is asignificant difference between the materialtested and similar material obtained from a dif-ferent supplier or through a different productionpath.

Reporting. The test report usually containsthe results of tests performed on one samplecomposed of several specimens.

When ASTM specifications are used for test-ing, the requirements for reporting are definedby the specification. The needs of a particularuser probably will determine the form for iden-tification of the material, but the reported resultswill most likely be as given in the ASTM testspecification.

The information contained in the test reportgenerally should include identification of thetesting equipment, the material tested, and thetest procedure; the raw and calculated data foreach specimen; and a brief statistical summaryfor the sample.

Each piece of test equipment used for the testshould be identified, including serial numbers,capacity or range used, and date of certificationor date due for certification.

Identification of the material tested should in-clude the type of material (alloy, part number,etc.); the specific batch, lot, order, heat, or coilfrom which the sample was taken; the point inthe processing sequence (condition, temper, etc.)at which the sample was taken; and any test orpretest conditions (test temperature, aging, etc.).

Identification of the test procedure usuallywill be reported by reference to a standard testprocedure such as those published by ASTM orperhaps to a proprietary specification originatingwithin the testing organization.

The raw data for each specimen are recorded,or a reference to the raw data is included so that

the data can be obtained from a file if and whenthey are needed. Frequently, only a portion ofthe raw data—dimensions, for example—is re-corded, and information on the force-versus-ex-tension graph is referenced.

A tabulation of the properties calculated foreach specimen is recorded. The calculations atthis stage are the first level of data analysis. Thecalculations required usually are defined in thetest procedure or specification.

A brief statistical summary for the sample isa feature that is becoming more common withthe proliferation of computerized testing sys-tems, because the computations required can bedone automatically without added operatorworkload. The statistical summary may includethe average (mean) value, median value, stan-dard deviation, highest value, lowest value,range, etc. The average or median value wouldbe used to represent this sample at the next levelof analysis, which is the material database.

Examination of this initial statistical infor-mation can tell a great deal about the test as wellas the material. A low standard deviation orrange indicates that the material in the samplehas uniform properties (each of several speci-mens has nearly the same values for the mea-sured properties) and that the test is producingconsistent results. Conversely, a high standarddeviation or range indicates that a problem ofinconsistent material or testing exists and needsto be investigated.

A continuing record of the average propertiesand the associated standard deviation and rangeinformation is the basis for statistical processcontrol, which systematically interprets this in-formation so as to provide the maximum infor-mation about both the material and the test pro-cess.

ACKNOWLEDGMENTS

This chapter was adapted from:

● W.F. Hosford, Overview of Tensile Testing,Tensile Testing, P. Han, Ed., ASM Interna-tional, 1992, p 1–24

● P.M. Mumford, Test Methodology and DataAnalysis, Tensile Testing, P. Han, Ed., ASMInternational, 1992, p 49–60

● R. Gedney, Guide To Testing Metals UnderTension, Advanced Materials & Processes,February, 2002, p 29–31

CHAPTER 2

Mechanical Behavior ofMaterials under Tensile Loads

THE MECHANICAL BEHAVIOR OF MA-TERIALS is described by their deformation andfracture characteristics under applied stresses(for example, tensile, compressive, or multiaxialstresses). Determination of this mechanical be-havior is influenced by several factors that in-clude metallurgical/material variables, testmethods, and the nature of the applied stresses.

This chapter focuses on mechanical behaviorunder conditions of uniaxial tension during ten-sile testing. As stated in other chapters, the en-gineering tensile test is widely used to providebasic design information on the strength of ma-terials and as an acceptance test for the specifi-cation of materials. In this test procedure, a spec-imen is subjected to a continually increasinguniaxial load (force), while simultaneous obser-vations are made of the elongation of the spec-imen. In this chapter, emphasis is placed on theinterpretation of these observations rather thanon the procedures for conducting the tests. Testprocedures are described in Chapter 3, “UniaxialTensile Testing.”

Emphasis has also been placed in this chapteron the response of metallic materials to tensilestresses. Additional information can be found inChapter 7, “Tensile Testing of Metals and Al-loys.” The mechanical behaviors of nonmetallicmaterials under tension are discussed in Chap-ters 8 (plastics), 9 (elastomers), 10 (ceramics andceramic-matrix composites), and 11 (fiber-re-inforced composites).

Engineering Stress-Strain Curve

In the conventional engineering tensile test,an engineering stress-strain curve is constructedfrom the load-elongation measurements made

on the test specimen (Fig. 1). The engineeringstress (s) used in this stress-strain curve is theaverage longitudinal stress in the tensile speci-men. It is obtained by dividing the load (P) bythe original area of the cross section of the spec-imen (A0):

Ps � (Eq 1)

A0

The strain, e, used for the engineering stress-strain curve is the average linear strain, which isobtained by dividing the elongation of the gagelength of the specimen (d) by its original length(L0):

d DL L � L0e � � � (Eq 2)L L L0 0 0

Because both the stress and the strain are ob-tained by dividing the load and elongation byconstant factors, the load-elongation curve hasthe same shape as the engineering stress-straincurve. The two curves frequently are used inter-changeably.

The shape and magnitude of the stress-straincurve of a metal depend on its composition, heattreatment, prior history of plastic deformation,and the strain rate, temperature, and state ofstress imposed during the testing. The parame-ters that are used to describe the stress-straincurve of a metal are the tensile strength, yieldstrength or yield point, percent elongation, andreduction in area. The first two are strength pa-rameters; the last two indicate ductility.

The general shape of the engineering stress-strain curve (Fig. 1) requires further explanation.In the elastic region, stress is linearly propor-tional to strain. When the stress exceeds a valuecorresponding to the yield strength, the speci-




Fig. 1 Engineering stress-strain curve. Intersection of the dashed line with the curve determines the offset yield strength. See alsoFig. 2 and corresponding text.

men undergoes gross plastic deformation. If theload is subsequently reduced to zero, the speci-men will remain permanently deformed. Thestress required to produce continued plastic de-formation increases with increasing plasticstrain; that is, the metal strain hardens. The vol-ume of the specimen (area � length) remainsconstant during plastic deformation, AL � A0L0,and as the specimen elongates, its cross-sec-tional area decreases uniformly along the gagelength.

Initially, the strain hardening more than com-pensates for this decrease in area, and the engi-neering stress (proportional to load P) continuesto rise with increasing strain. Eventually, a pointis reached where the decrease in specimen cross-sectional area is greater than the increase in de-formation load arising from strain hardening.This condition will be reached first at some pointin the specimen that is slightly weaker than therest. All further plastic deformation is concen-trated in this region, and the specimen begins toneck or thin down locally. Because the cross-sectional area now is decreasing far more rapidlythan the deformation load is increased by strainhardening, the actual load required to deform thespecimen falls off, and the engineering stress de-fined in Eq 1 continues to decrease until fractureoccurs.

The tensile strength, or ultimate tensilestrength (su) is the maximum load divided by theoriginal cross-sectional area of the specimen:

Pmaxs � (Eq 3)u A0

The tensile strength is the value most frequentlyquoted from the results of a tension test. Actu-ally, however, it is a value of little fundamentalsignificance with regard to the strength of ametal. For ductile metals, the tensile strengthshould be regarded as a measure of the maxi-mum load that a metal can withstand under thevery restrictive conditions of uniaxial loading.This value bears little relation to the usefulstrength of the metal under the more complexconditions of stress that usually are encountered.

For many years, it was customary to base thestrength of members on the tensile strength, suit-ably reduced by a factor of safety. The currenttrend is to use the more rational approach of bas-ing the static design of ductile metals on theyield strength. However, due to the long practiceof using the tensile strength to describe thestrength of materials, it has become a familiarproperty, and as such, it is a useful identificationof a material in the same sense that the chemicalcomposition serves to identify a metal or alloy.Furthermore, because the tensile strength is easyto determine and is a reproducible property, it isuseful for the purposes of specification and forquality control of a product. Extensive empiricalcorrelations between tensile strength and prop-erties such as hardness and fatigue strength are

Mechanical Behavior of Materials under Tensile Loads / 15

Fig. 3 Typical yield-point behavior of low-carbon steel. Theslope of the initial linear portion of the stress-strain

curve, designated by E, is the modulus of elasticity.

Fig. 2 Typical tensile stress-strain curve for ductile metal in-dicating yielding criteria. Point A, elastic limit; point

A�, proportional limit; point B, yield strength or offset (0 to C)yield strength; 0, intersection of the stress-strain curve with thestrain axis

often useful. For brittle materials, the tensilestrength is a valid design criterion.

Measures of Yielding. The stress at whichplastic deformation or yielding is observed tobegin depends on the sensitivity of the strainmeasurements. With most materials, there is agradual transition from elastic to plastic behav-ior, and the point at which plastic deformationbegins is difficult to define with precision. Intests of materials under uniaxial loading, threecriteria for the initiation of yielding have beenused: the elastic limit, the proportional limit, andthe yield strength.

Elastic limit, shown at point A in Fig. 2, isthe greatest stress the material can withstandwithout any measurable permanent strain re-maining after the complete release of load. Withincreasing sensitivity of strain measurement, thevalue of the elastic limit is decreased until itequals the true elastic limit determined from mi-crostrain measurements. With the sensitivity ofstrain typically used in engineering studies(10�4 in./in.), the elastic limit is greater than theproportional limit. Determination of the elasticlimit requires a tedious incremental loading-un-loading test procedure. For this reason, it is oftenreplaced by the proportional limit.

Proportional limit, shown at point A� in Fig.2, is the highest stress at which stress is directlyproportional to strain. It is obtained by observingthe deviation from the straight-line portion of thestress-strain curve.

The yield strength, shown at point B in Fig.2, is the stress required to produce a small spec-ified amount of plastic deformation. The usualdefinition of this property is the offset yieldstrength determined by the stress correspondingto the intersection of the stress-strain curve off-set by a specified strain (see Fig. 1 and 2). In the

United States, the offset is usually specified asa strain of 0.2 or 0.1% (e � 0.002 or 0.001):

P(strain offset�0.002)s � (Eq 4)0 A0

Offset yield strength determination requires aspecimen that has been loaded to its 0.2% offsetyield strength and unloaded so that it is 0.2%longer than before the test. The offset yieldstrength is often referred to in Great Britain asthe proof stress, where offset values are either0.1 or 0.5%. The yield strength obtained by anoffset method is commonly used for design andspecification purposes, because it avoids thepractical difficulties of measuring the elasticlimit or proportional limit.

Some materials have essentially no linear por-tion to their stress-strain curve, for example, softcopper, gray cast iron, and many polymers. Forthese materials, the offset method cannot beused, and the usual practice is to define the yieldstrength as the stress to produce some totalstrain, for example, e � 0.005.

Some metals, particularly annealed low-car-bon steel, show a localized, heterogeneous typeof transition from elastic to plastic deformationthat produces a yield point in the stress-straincurve. Rather than having a flow curve with agradual transition from elastic to plastic behav-ior, such as Fig. 1 and 2, metals with a yieldpoint produce a flow curve or a load-elongationdiagram similar to Fig. 3. The load increasessteadily with elastic strain, drops suddenly, fluc-tuates about some approximately constant valueof load, and then rises with further strain.


Fig. 4 Rimmed 1008 steel with Luders bands on the surfaceas a result of stretching the sheet just beyond the yield

point during forming

The load at which the sudden drop occurs iscalled the upper yield point. The constant loadis called the lower yield point, and the elonga-tion that occurs at constant load is called theyield-point elongation. The deformation occur-ring throughout the yield-point elongation is het-erogeneous. At the upper yield point, a discreteband of deformed metal, often readily visible,appears at a stress concentration, such as a fillet.Coincident with the formation of the band, theload drops to the lower yield point. The bandthen propagates along the length of the speci-men, causing the yield-point elongation. A simi-lar behavior occurs with some polymers and su-perplastic metal alloys, where a neck forms butgrows in a stable manner, with material beingfed into the necked region from the thicker ad-jacent regions. This type of deformation in poly-mers is called “drawing.”

In typical cases, several bands form at severalpoints of stress concentration. These bands aregenerally at approximately 45� to the tensileaxis. They are usually called Luders bands orstretcher strains, and this type of deformation issometimes referred to as the Piobert effect.When several Luders bands are formed, the flowcurve during the yield-point elongation is irreg-ular, each jog corresponding to the formation ofa new Luders band. After the Luders bands havepropagated to cover the entire length of the spec-imen test section, the flow will increase withstrain in the typical manner. This marks the endof the yield-point elongation. Luders bandsformed on a rimmed 1008 steel are shown inFig. 4.

Measures of Ductility. Currently, ductility isconsidered a qualitative, subjective property ofa material. In general, measurements of ductilityare of interest in three respects (Ref 1):

● To indicate the extent to which a metal canbe deformed without fracture in metalwork-ing operations, such as rolling and extrusion

● To indicate to the designer the ability of themetal to flow plastically before fracture. Ahigh ductility indicates that the material is“forgiving” and likely to deform locallywithout fracture should the designer err inthe stress calculation or the prediction of se-vere loads.

● To serve as an indicator of changes in im-purity level or processing conditions. Duc-tility measurements may be specified to as-sess material quality, even though no directrelationship exists between the ductilitymeasurement and performance in service.

The conventional measures of ductility thatare obtained from the tension test are the engi-neering strain at fracture (ef) (usually called theelongation) and the reduction in area at fracture(q). Elongation and reduction in area usually areexpressed as a percentage. Both of these prop-erties are obtained after fracture by putting thespecimen back together and taking measure-ments of the final length, Lf, and final specimencross section, Af :

L � Lf 0e � (Eq 5)f L0

A � A0 fq � (Eq 6)A0

Because an appreciable fraction of the plasticdeformation will be concentrated in the neckedregion of the tension specimen, the value of efwill depend on the gage length (L0) over whichthe measurement was taken (see the section ofthis article on ductility measurement in tensiontesting). The smaller the gage length, the greaterthe contribution to the overall elongation fromthe necked region and the higher the value of ef.Therefore, when reporting values of percentageelongation, the gage length should always begiven.

Reduction in area does not suffer from thisdifficulty. These values can be converted into anequivalent zero-gage-length elongation (e0).


Fig. 5 Comparison of stress-strain curves for high- and low-toughness steels. Cross-hatched regions in this curve

represent the modulus of resilience (UR) of the two materials. TheUR is determined by measuring the area under the stress-straincurve up to the elastic limit of the material. Point A representsthe elastic limit of the spring steel; point B represents that of thestructural steel.

Table 1 Typical values of modulus of elasticity at different temperatures

Modulus of elasticity GPa (106 psi), at:

Material Room temperature 250 �C (400 �F) 425 �C (800 �F) 540 �C (1000 �F) 650 �C (1200 �F)

Carbon steel 207 (30.0) 186 (27.0) 155 (22.5) 134 (19.5) 124 (18.0)Austenitic stainless steel 193 (28.0) 176 (25.5) 159 (23.0) 155 (22.5) 145 (21.0)Titanium alloys 114 (16.5) 96.5 (14.0) 74 (10.7) 70 (10.0) . . .Aluminum alloys 72 (10.5) 65.5 (9.5) 54 (7.8) . . . . . .

From the constancy of volume relationship forplastic deformation, AL � A0L0:

L A 10� �

L A 1 � q0

L � L A 10 0e � � � 1 � � 10 L A 1 � q0

q�

1 � q (Eq 7)

This represents the elongation based on a veryshort gage length near the fracture.

Another way to avoid the complications re-sulting from necking is to base the percentageelongation on the uniform strain out to the pointat which necking begins. The uniform elonga-tion (eu), correlates well with stretch-formingoperations. Because the engineering stress-straincurve often is quite flat in the vicinity of neck-ing, it may be difficult to establish the strain atmaximum load without ambiguity. In this case,the method suggested in Ref 2 is useful.

Modulus of Elasticity. The slope of the initiallinear portion of the stress-strain curve is themodulus of elasticity, or Young’s modulus, asshown in Fig. 3. The modulus of elasticity (E)is a measure of the stiffness of the material. Thegreater the modulus, the smaller the elastic strainresulting from the application of a given stress.

Because the modulus of elasticity is needed forcomputing deflections of beams and other mem-bers, it is an important design value.

The modulus of elasticity is determined by thebinding forces between atoms. Because theseforces cannot be changed without changing thebasic nature of the material, the modulus of elas-ticity is one of the most structure-insensitive ofthe mechanical properties. Generally, it is onlyslightly affected by alloying additions, heattreatment, or cold work (Ref 3). However, in-creasing the temperature decreases the modulusof elasticity. At elevated temperatures, the mod-ulus is often measured by a dynamic method(Ref 4). Typical values of the modulus of elas-ticity for common engineering metals at differ-ent temperatures are given in Table 1.

Resilience. The ability of a material to absorbenergy when deformed elastically and to returnit when unloaded is called resilience. This prop-erty usually is measured by the modulus of re-silience, which is the strain energy per unit vol-ume (U0) required to stress the material fromzero stress to the yield stress (r0). The strainenergy per unit volume for uniaxial tension is:

1U � r e (Eq 8)0 x x2

From the above definition, the modulus of resil-ience (UR) is:

21 1 s s0 0U � s e � s � (Eq 9)R 0 0 02 2 E 2E

This equation indicates that the ideal material forresisting energy loads in applications where thematerial must not undergo permanent distortion,such as in mechanical springs, is one having ahigh yield stress and a low modulus of elasticity.

For various grades of steel, the modulus ofresilience ranges from 100 to 4500 kJ/m3 (14.5–650 lbf • in./in.3), with the higher values repre-senting steels with higher carbon or alloy con-tents (Ref 5). The cross-hatched regions in Fig.5 indicate the modulus of resilience for two


Fig. 6 Typical engineering stress-strain curves

steels. Due to its higher yield strength, the high-carbon spring steel has the greater resilience.

The toughness of a material is its ability toabsorb energy in the plastic range. The ability towithstand occasional stresses above the yieldstress without fracturing is particularly desirablein parts such as freight-car couplings, gears,chains, and crane hooks. Toughness is a com-monly used concept that is difficult to preciselydefine. Toughness may be considered to be thetotal area under the stress-strain curve. This area,which is referred to as the modulus of toughness(UT) is an indication of the amount of work perunit volume that can be done on the materialwithout causing it to rupture.

Figure 5 shows the stress-strain curves forhigh- and low-toughness materials. The high-carbon spring steel has a higher yield strengthand tensile strength than the medium-carbonstructural steel. However, the structural steel ismore ductile and has a greater total elongation.The total area under the stress-strain curve isgreater for the structural steel; therefore, it is atougher material. This illustrates that toughnessis a parameter that comprises both strength andductility.

Several mathematical approximations for thearea under the stress-strain curve have been sug-gested. For ductile metals that have a stress-strain curve like that of the structural steel, thearea under the curve can be approximated by:

U � s e (Eq 10)T u f

or

s � s0 uU � e (Eq 11)T f2

For brittle materials, the stress-strain curve issometimes assumed to be a parabola, and thearea under the curve is given by:

2U � s e (Eq 12)T u f3

Typical Stress-Strain Curves. Figure 6 com-pares the engineering stress-strain curves in ten-sion for three materials. The 0.8% carbon eutec-toid steel is representative of a material with lowductility. The annealed 0.2% carbon mild steelshows a pronounced upper and lower yieldpoint. The polycarbonate engineered polymerhas no well-defined linear modulus, and a large

strain to fracture. Note the pronounced differ-ence in stress level at which yielding is defined,as well as the quite different shape of the stress-strain curves.

True Stress-True Strain Curve

The engineering stress-strain curve does notgive a true indication of the deformation char-acteristics of a metal because it is based entirelyon the original dimensions of the specimen, andthese dimensions change continuously duringthe test. Also, ductile metal that is pulled in ten-sion becomes unstable and necks down duringthe course of the test. Because the cross-sec-tional area of the specimen is decreasing rapidlyat this stage in the test, the load required to con-tinue deformation falls off.

The average stress based on the original arealikewise decreases, and this produces the fall-offin the engineering stress-strain curve beyond thepoint of maximum load. Actually, the metal con-tinues to strain harden to fracture, so that thestress required to produce further deformationshould also increase. If the true stress, based onthe actual cross-sectional area of the specimen,is used, the stress-strain curve increases contin-uously to fracture. If the strain measurement isalso based on instantaneous measurement, thecurve that is obtained is known as true stress-true strain curve. This is also known as a flowcurve because it represents the basic plastic-flowcharacteristics of the material.

Any point on the flow curve can be consideredthe yield stress for a metal strained in tension bythe amount shown on the curve. Thus, if the loadis removed at this point and then reapplied, thematerial will behave elastically throughout theentire range of reloading.


Fig. 7 Comparison of engineering and true stress-true straincurves

The true stress (r) is expressed in terms ofengineering stress (s) by:

Pr � (e � 1) � s(e � 1) (Eq 13)

A0

The derivation of Eq 13 assumes both constancyof volume and a homogeneous distribution ofstrain along the gage length of the tension spec-imen. Thus, Eq 13 should be used only until theonset of necking. Beyond the maximum load,the true stress should be determined from actualmeasurements of load and cross-sectional area.

Pr � (Eq 14)

A

The true strain, e, may be determined fromthe engineering or conventional strain (e) by:

Le � ln(e � 1) � ln (Eq 15)

L0

This equation is applicable only to the onset ofnecking for the reasons discussed above. Be-yond maximum load, the true strain should bebased on actual area or diameter (D) measure-ments:

p 2D0� �4A D0 0e � ln � ln � 2 ln (Eq 16)A Dp 2D� �4

Figure 7 compares the true stress-true straincurve with its corresponding engineering stress-strain curve. Note that because of the relativelylarge plastic strains, the elastic region has been

compressed into the y-axis. In agreement withEq 13 and 15; the true stress-true strain curve isalways to the left of the engineering curve untilthe maximum load is reached.

However, beyond maximum load, the high,localized strains in the necked region that areused in Eq 16 far exceed the engineering straincalculated from Eq 2. Frequently, the flow curveis linear from maximum load to fracture, whilein other cases its slope continuously decreasesto fracture. The formation of a necked region ormild notch introduces triaxial stresses that makeit difficult to determine accurately the longitu-dinal tensile stress from the onset of necking un-til fracture occurs. This concept is discussed ingreater detail in the section “Instability in Ten-sion” later in this chapter. The following param-eters usually are determined from the true stress-true strain curve.

The true stress at maximum load corre-sponds to the true tensile strength. For most ma-terials, necking begins at maximum load at avalue of strain where the true stress equals theslope of the flow curve. Let ru and eu denote thetrue stress and true strain at maximum load whenthe cross-sectional area of the specimen is Au.The ultimate tensile strength can be defined as:

Pmaxs � (Eq 17)u A0

and

Pmaxr � (Eq 18)u Au

Eliminating Pmax yields:

A0r � s (Eq 19)u u Au

and

eur � s e (Eq 20)u u

The true fracture stress is the load at frac-ture divided by the cross-sectional area at frac-ture. This stress should be corrected for the tri-axial state of stress existing in the tensilespecimen at fracture. Because the data requiredfor this correction frequently are not available,true fracture stress values are frequently in error.

The true fracture strain, ef, is the true strainbased on the original area (A0) and the area afterfracture (Af):


Fig. 9 Various forms of power curve r � KenFig. 8 Log-log plot of true stress-true strain curve n is the

strain-hardening exponent; K is the strength coefficient.

A0e � ln (Eq 21)f Af

This parameter represents the maximum truestrain that the material can withstand beforefracture and is analogous to the total strain tofracture of the engineering stress-strain curve.Because Eq 15 is not valid beyond the onset ofnecking, it is not possible to calculate ef frommeasured values of ef. However, for cylindricaltensile specimens, the reduction in area (q) isrelated to the true fracture strain by:

1e � ln (Eq 22)f 1�q

The true uniform strain eu, is the true strainbased only on the strain up to maximum load. Itmay be calculated from either the specimencross-sectional area (Au) or the gage length (Lu)at maximum load. Equation 15 may be used toconvert conventional uniform strain to true uni-form strain. The uniform strain frequently is use-ful in estimating the formability of metals fromthe results of a tension test:

A0e � ln (Eq 23)u Au

The true local necking strain (en) is thestrain required to deform the specimen frommaximum load to fracture:

Aue � ln (Eq 24)n Af

Mathematical Expressions forthe Flow Curve

The flow curve of many metals in the regionof uniform plastic deformation can be expressedby the simple power curve relation:

nr � Ke (Eq 25)

where n is the strain-hardening exponent, and Kis the strength coefficient. A log-log plot of truestress and true strain up to maximum load willresult in a straight line if Eq 25 is satisfied bythe data (Fig. 8).

The linear slope of this line is n, and K is thetrue stress at e � 1.0 (corresponds to q � 0.63).As shown in Fig. 9, the strain-hardening expo-nent may have values from n � 0 (perfectlyplastic solid) to n � 1 (elastic solid). For mostmetals, n has values between 0.10 and 0.50 (seeTable 2).

The rate of strain hardening dr/de is not iden-tical to the strain-hardening exponent. From thedefinition of n:

d(log r) d(ln r) e drn � � �

d(log e) d(ln e) r de

Table 2 Values for n and K for metals at room temperature

K

Metals Condition n MPa ksi Ref

0.05% carbon steel Annealed 0.26 530 77 6SAE 4340 steel Annealed 0.15 641 93 60.6% carbon steel Quenched and tempered at 540 �C (1000 �F) 0.10 1572 228 70.6% carbon steel Quenched and tempered at 705 �C (1300 �F) 0.19 1227 178 7Copper Annealed 0.54 320 46.4 670/30 brass Annealed 0.49 896 130 7


Table 3 Range of strain rates in commonmechanical property tests

Range of strain rate Type of test

10�8 to 10�5 s�1 Creep test at constant load or stress10�5 to 10�1 s�1 Tension test with hydraulic or screw driven

machines10�1 to 102 s�1 Dynamic tension or compression tests102 to 104 s�1 High-speed testing using impact bars104 to 108 s�1 Hypervelocity impact using gas guns or

explosively driven projectiles

or

dr r� n (Eq 26)

de e

Deviations from Eq 25 frequently are ob-served, often at low strains (10�3) or high strains(e � 1.0). One common type of deviation is fora log-log plot of Eq 25 to result in two straightlines with different slopes. Sometimes data thatdo not plot according to Eq 25 will yield astraight line according to the relationship:

nr � K(e � e) (Eq 27)0

e0 can be considered to be the amount of strainthat the material received prior to the tensile test(Ref 8). Another common variation on Eq 25 isthe Ludwik equation:

nr � r � Ke (Eq 28)0

where r0 is the yield stress, and K and n are thesame constants as in Eq 25. This equation maybe more satisfying than Eq 25, because the latterimplies that at zero true strain the stress is zero.It has been shown that r0 can be obtained fromthe intercept of the strain-hardening portion ofthe stress-strain curve and the elastic modulusline by (Ref 9):

1/(1�n)Kr � (Eq 29)0 � n�E

The true stress-true strain curve of metalssuch as austenitic stainless steel, which deviatemarkedly from Eq 25 at low strains (Ref 10),can be expressed by:

n K K n e1 1 1r � Ke � e � e e (Eq 30)

where is approximately equal to the propor-K1etional limit, and n1 is the slope of the deviationof stress from Eq 25 plotted against e. Otherexpressions for the flow curve are available (Ref11, 12). The true strain term in Eq 25 to 28 prop-erly should be the plastic strain, ep � etotal �eE � etotal � r/E, where eE represents elasticstrain.

Effect of Strain Rate and Temperature

The rate at which strain is applied to the ten-sile specimen has an important influence on the

stress-strain curve. Strain rate is defined as �ede/dt. It is expressed in units of s�1. The rangeof strain rates encompassed by various tests isshown in Table 3.

Increasing strain rate increases the flow stress.Moreover, the strain-rate dependence of strengthincreases with increasing temperature. The yieldstress and the flow stress at lower values of plas-tic strain are more affected by strain rate thanthe tensile strength.

If the crosshead velocity of the testing ma-chine is v � dL/dt, then the strain rate expressedin terms of conventional engineering strain is:

de d(L � L )/L 1 dL0 0e � � �dt dt L dt0

v� (Eq 31)

L0

The engineering strain rate is proportional to thecrosshead velocity. In a modern testing machine,in which the crosshead velocity can be set ac-curately and controlled, it is a simple matter tocarry out tensile tests at a constant engineeringstrain rate.

The true strain rate is given by:

de d[ln(L/L )] 1 dL v0e � � � � (Eq 32)dt dt L dt L

Equation 32 shows that for a constant crossheadvelocity the true strain rate will decrease as thespecimen elongates or cross-sectional areashrinks. To run tensile tests at a constant truestrain rate requires monitoring the instantaneouscross section of the deforming region, withclosed-loop control feed back to increase thecrosshead velocity as the area decreases. Thetrue strain rate is related to the engineering strainrate by the following equation:

v L de 1 de e0e � � � � (Eq 33)L L dt 1 � e dt 1 � e


Fig. 10 Strain-rate change test, used to determine strain-ratesensitivity, m. See text for discussion.

The strain-rate dependence of flow stressat constant strain and temperature is given by:

mr � C(e) |e,T (Eq 34)

The exponent in Eq 34, m, is known as thestrain-rate sensitivity, and C is the strain hard-ening coefficient. It can be obtained from theslope of a plot of log r versus log . However,ea more sensitive way to determine m is with arate-change test (Fig. 10). A tensile test is carriedout at strain rate and at a certain flow stress,e1r1, the strain rate is suddenly increased to e .2The flow stress quickly increases to r2. Thestrain-rate sensitivity, at constant strain and tem-perature, can be determined from:

� ln r e �r D log rm � � �� ln e r �e D log ee,T

log r � log r log(r /r )2 1 2 1� � (Eq 35)

log e � log e log(e /e )2 2 1

The strain-rate sensitivity of metals is quite low(�0.1) at room temperature, but m increaseswith temperature. At hot-working temperatures,T/Tm � 0.5, m values of 0.1 to 0.2 are commonin metals. Polymers have much higher values ofm, and may approach m � 1 in room-tempera-ture tests for some polymers.

The temperature dependence of flowstress can be represented by:

Q/RTr � C e | (Eq 36)˙2 e,e

where Q is an activation energy for plastic flow,cal/g • mol; R is universal gas constant, 1.987cal/K • mol; and T is testing temperature in kel-vin. From Eq 36, a plot of ln r versus 1/T willgive a straight line with a slope Q/R.

Instability in Tension

Necking generally begins at maximum loadduring the tensile deformation of a ductile metal.An exception to this is the behavior of cold-rolled zirconium tested at 200 to 370 �C (390–700 �F), where necking occurs at a strain oftwice the strain at maximum load (Ref 13). Anideal plastic material in which no strain hard-ening occurs would become unstable in tensionand begin to neck as soon as yielding occurred.However, an actual metal undergoes strain hard-ening, which tends to increase the load-carrying

capacity of the specimen as deformation in-creases.

This effect is opposed by the gradual decreasein the cross-sectional area of the specimen as itelongates. Necking or localized deformation be-gins at maximum load, where the increase instress due to decrease in the cross-sectional areaof the specimen becomes greater than the in-crease in the load-carrying ability of the metaldue to strain hardening. This condition of insta-bility leading to localized deformation is definedby the condition dP � 0:

P � rA (Eq 37)

dP � rdA � Adr � 0 (Eq 38)

From the constancy-of-volume relationship:

dL dA� � � de (Eq 39)

L A

and from the instability condition, Eq 38:

dA dr� � (Eq 40)

A r

so that at a point of tensile instability:

dr� r (Eq 41)

de

Therefore, the point of necking at maximumload can be obtained from the true stress-truestrain curve by finding the point on the curvehaving a subtangent of unity (Fig. 11a), or thepoint where the rate of strain hardening equalsthe stress (Fig. 11b). The necking criterion can


Fig. 12 Considere’s construction for the determination of thepoint of maximum load. Source: Ref 14

Fig. 11 Graphical interpretation of necking criterion. The point of necking at maximum load can be obtained from the true stress-true strain curve by finding (a) the point on the curve having a subtangent of unity or (b) the point where dr/de � r.

be expressed more explicitly if engineeringstrain is used. Starting with Eq 41:

dL

dr dr de dr L dr L0� � �

de de de de dL de L0

Ldr

� (1 � e) � rde

dr r� (Eq 42)

de 1 � e

Equation 42 permits an interesting geometri-cal construction for the determination of thepoint of maximum load (Ref 14). In Fig. 12, thestress-strain curve is plotted in terms of truestress against engineering strain. Let point Arepresent a negative strain of 1.0. A line drawnfrom point A, which is tangent to the stress-strain curve, will establish the point of maxi-mum load because, according to Eq 42, the slopeat this point is r/(1 � e).

By substituting the necking criterion given inEq 41 into Eq 26, a simple relationship for thestrain at which necking occurs is obtained:

e � n (Eq 43)u

Although Eq 26 is based on the assumption thatthe flow curve is given by Eq 25, it has beenshown that eu � n does not depend on thispower law behavior (Ref 15).

Stress Distribution at the Neck

The formation of a neck in the tensile speci-men introduces a complex triaxial state of stressin that region. The necked region is in effect amild notch. A notch under tension produces ra-dial stress (rr) and transverse stress (rt ) whichraise the value of longitudinal stress required tocause the plastic flow. Therefore, the averagetrue stress at the neck, which is determined bydividing the axial tensile load by the minimumcross-sectional area of the specimen at the neck,is higher than the stress that would be requiredto cause flow if simple tension prevailed.

Figure 13 illustrates the geometry at thenecked region and the stresses developed by thislocalized deformation. R is the radius of curva-ture of the neck, which can be measured eitherby projecting the contour of the necked regionon a screen or by using a tapered, conical radiusgage.

Bridgman made a mathematical analysis thatprovides a correction to the average axial stressto compensate for the introduction of transversestresses (Ref 16). This analysis was based on thefollowing assumptions:


Fig. 14 Relationship between Bridgman correction factor r/(rx)avg and true tensile strain. Source: Ref 19

Fig. 13 Stress distribution at the neck of a tensile specimen.(a) Geometry of necked region. R is the radius of cur-

vature of the neck; a is the minimum radius at the neck. (b)Stresses acting on element at point O. rx is the stress in the axialdirection; rr is the radial stress; rt is the transverse stress.

● The contour of the neck is approximated bythe arc of a circle.

● The cross section of the necked region re-mains circular throughout the test.

● The von Mises criterion for yielding applies.● The strains are constant over the cross sec-

tion of the neck.

According to this analysis, the uniaxial flowstress corresponding to that which would existin the tensile test if necking had not introducedtriaxial stresses is:

(r )x avgr � (Eq 44)1 � 2R a

ln 1 �� a 2R

where (rx)avg is the measured stress in the axialdirection (load divided by minimum cross sec-tion) and a is the minimum radius at the neck.Figure 7 shows how the application of the Bridg-man correction changes the true stress-true straincurve. A correction for the triaxial stresses in theneck of a flat tensile specimen has been consid-ered (Ref 17). The values of a/R needed for theanalysis can be obtained either by straining aspecimen a given amount beyond necking andunloading to measure a and R directly, or bymeasuring these parameters continuously pastnecking using photography or a tapered ringgage (Ref 18).

To avoid these measurements, Bridgman pre-sented an empirical relation between a/R and thetrue strain in the neck. Figure 14 shows that thisgives close agreement for steel specimens, but

not for other metals with widely different neck-ing strains. A much better correlation is obtainedbetween the Bridgman correction and the truestrain in the neck minus the true strain at neck-ing, eu (Ref 20).

Dowling (Ref 21) has shown that the Bridg-man correction factor B can be estimated from:

B � 0.83 � 0.186 log e (0.15 � e � 3) (Eq 45)

where B � r/(rx)avg.

Ductility Measurement inTensile Testing

The measured elongation from a tensile spec-imen depends on the gage length of the speci-men, or the dimensions of its cross section. Thisis because the total extension consists of twocomponents: the uniform extension up to neck-ing and the localized extension once necking be-gins. The extent of uniform extension dependson the metallurgical condition of the material(through n) and the effect of specimen size andshape on the development of the neck.

Figure 15 illustrates the variation of the localelongation, as defined in Eq 7, along the gagelength of a prominently necked tensile speci-men. The shorter the gage length, the greater theinfluence of localized deformation at the neckon the total elongation of the gage length. Theextension of a specimen at fracture can be ex-pressed by:


Fig. 15 Variation of local elongation with position along gagelength of tensile specimen

L � L � � � e L (Eq 46)f 0 u 0

where � is the local necking extension, and euL0is the uniform extension. The tensile elongationis then:

L � L �f 0e � � � e (Eq 47)f uL L0 0

This clearly indicates that the total elongation isa function of the specimen gage length. Theshorter the gage length, the greater the percentelongation.

Numerous attempts have been made to ration-alize the strain distribution in the tensile test.Perhaps the most general conclusion that can bedrawn is that geometrically similar specimensdevelop geometrically similar necked regions.According to Barba’s law (Ref 22), � � b A ,� 0and the elongation equation becomes:

A� 0e � b � e (Eq 48)f uL0

where b is a coefficient of proportionality.To compare elongation measurements of dif-

ferent sized specimens, the specimens must begeometrically similar. Equation 48 shows thatthe critical geometrical factor for which simili-tude must be maintained is L0/ for sheetA� 0specimens, or L0/D0 for round bars. In theUnited States, the standard round tensile speci-men has a 12.8 mm (0.505 in.) diameter and a50 mm (2 in.) gage length. Subsize specimenshave the following respective diameter and gagelength: 9.06 and 35.6 mm (0.357 and 1.4 in.),6.4 and 25 mm (0.252 and 1.0 in.), and 4.06 and16.1 mm (0.160 and 0.634 in.). Different valuesof L0/ are specified for sheet specimens byA� 0the standardizing agencies in different countries.In the United States, ASTM recommends a

L0/ value of 4.5 for sheet specimens and aA� 0L0/D0 value of 4.0 for round specimens.

Generally, a given elongation will be pro-duced in a material if is maintained con-A /L� 0 0stant as predicted by Eq 48. Thus, at a constantvalue of elongation � where AA /L A /A ,� �1 1 2 2and L are the areas and gage lengths of two dif-ferent specimens, 1 and 2, of the same metal. Topredict elongation using gage length L2 on aspecimen with area A2 by means of measure-ments on a specimen with area A1, it only isnecessary to adjust the gage length of specimen1 to conform with L1 � For example,L A /A .�2 1 2suppose that a 3.2 mm (0.125 in.) thick sheet isavailable, and one wishes to predict the elon-gation with a 50 mm (2 in.) gage length for theidentical material but in 2.0 mm (0.080 in.)thickness. Using 12.7 mm (0.5 in.) wide sheetspecimens, a test specimen with a gage length L� 50 mm (3.2 mm/2.0 mm)1/2 � 63 mm, or 2in. (0.125 in./0.080 in.)1/2 � 2.5 in., made fromthe 3.2 mm (0.125 in.) sheet would be predictedto give the same elongation as a 50 mm (2 in.)gage length in 2.0 mm (0.080 in.) thick sheet.Experimental verification for this procedure hasbeen shown in Ref 23.

The occurrence of necking in the tensile test,however, makes any quantitative conversion be-tween elongation and reduction in area impos-sible. Although elongation and reduction in areausually vary in the same way—for example, asa function of test temperature, tempering tem-perature, or alloy content—this is not always thecase. Generally, elongation and reduction in areameasure different types of material behavior.Provided the gage length is not too short, percentelongation is primarily influenced by uniformelongation, and thus it is dependent on thestrain-hardening capacity of the material.

Reduction in area is more a measure of thedeformation required to produce fracture, and itschief contribution results from the necking pro-cess. Because of the complicated stress state inthe neck, values of reduction in area are depen-dent on specimen geometry and deformation be-havior, and they should not be taken as true ma-terial properties. However, reduction in area isthe most structure-sensitive ductility parameter,and as such, it is useful in detecting qualitychanges in the material.

Sheet Anisotropy (Ref 24)

If the tensile tests are performed on specimenscut from sheet material at different orientations


Fig. 16 Tensile specimen cut from a rolled sheet (left). The r-value is the ratio of ew/et during extension (right). Source: Ref 24

to the prior rolling direction (Fig. 16), there maynot be much difference between the stress-straincurves. However, the lack of variation of thestress-strain curves with direction does not in-dicate that the material is isotropic. The param-eter that is commonly used to characterize theanisotropy of sheet metal is the strain ratio or r-value defined as the ratio of the contractilestrains measured in a tensile test before neckingoccurs:

ewr � (Eq 49)et

where ew is the width strain, ln (w/w0), and et isthe thickness strain, ln (t/t0). The value of rwould be equal to 1 for an isotropic material.Often, however, r is either greater or less than1. For thin sheets, accurate direct measurementof the thickness strain is difficult. Therefore, thethickness strain is often deduced from the con-stant-volume relationship, et � �ew � el,where el is the length strain, ln (l/l0). By substi-tution,

�ewr � (Eq 50)e � ew l

To avoid constraints from the test specimengrips, the strains should be measured on a gage

section that is removed from the enlarged endsby a distance at least equal to the width of thespecimen. Some workers suggest that the strainsbe measured when the elongation is about 15%as long as this is less than the strain at whichnecking starts.

Although the r-value usually does not changemuch during the tensile test, the strains at 15%are large enough to be measured with reasonableaccuracy. The measurement of r is subject togreater error than may at first be apparent. If theaccuracy of measuring strains were �0.01, theerror in r would be �25%. Consider, for ex-ample, a material for which r � 1 (et � ew). Atan elongation strain of 15% (el � 0.14), the val-ues of et and ew should be 0.07. Measurementerrors of �0.01 could lead to r � 0.08/0.06 �1.33 or r � 0.06/0.08 � 0.75. Even if the ac-curacy were �0.002, the limits on r would be0.072/0.068 � 1.06 and 0.068/0.072 � 0.94.Measurements of r at lower elongations are evenless accurate.

The value of r often depends on the angle atwhich the specimen is cut from the sheet (Fig.17). In this case an average r-value, R, is oftenquoted, where r is given by:

r � r � 2r0 90 45r � (Eq 51)4


Table 4 Plastic anisotropy factor r for selected alloys

Material Condition r r0 r90

Aluminum

1100 H14 0.56 0.43 0.895082 H19 1.16 0.39 1.812024 O 0.81 0.81 0.633003 O 0.75 . . . . . .5052 O 0.58 . . . . . .

Copper and copper alloys

Copper Annealed 0.95 . . . . . .65/35 brass Annealed 0.74 . . . . . .70/30 brass Annealed 0.70 . . . . . .

Steel

Rimmed Annealed in hydrogen 1.01–1.11 . . . . . .Killed Annealed 1.4–1.62 . . . . . .Killed, draw quality Annealed 1.79 . . . . . .Killed, draw quality Temper rolled 1.23 . . . . . .Sheet, draw quality . . . 0.7–2.8 . . . . . .

Titanium

Ti-6Al-4V Annealed . . . 2.57 3.0Ti-5Al-2.5Sn Annealed . . . 8.1 9.0

Magnesium

AZ31B-H24 0.004 plastic strain . . . 1.0 2.9AZ31B-H24 0.10 plastic strain . . . 2.0 0.67

Zirconium

Zircaloy-2 Heat treated . . . 0.13 0.13Zircaloy-2 Heat treated and cross rolled . . . 2.29 0.67

Source: Ref 25

Fig. 17 Tensile specimen orientation to determine r0, r45, and r90 in rolled sheet.

The subscripts refer to the angles between thetensile axis and the rolling direction (Fig. 17).The r value describes the degree of normalanisotropy, reflecting the difference betweenplastic properties in and normal to the plane ofthe sheet. Typical r values for metals and alloysare given in Table 4.

Other properties are averaged in an analogousway. For example, for n and K in Eq 25:

n � n � 2n0 90 45n � (Eq 52)4

andK � K � 2K0 90 45K � (Eq 53)

4

The degree of anisotropy in the plane of thesheet (planar anisotropy) can be described bythe parameter:


Fig. 18 Notched and unnotched tensile properties of an alloysteel as a function of tempering temperature. Source:

Ref 26

r � r � 2r0 90 45Dr � (Eq 54)2

The degree of earing in deep drawing correlateswell with Dr.

Notch Tensile Test

Ductility measurements on standard smoothtensile specimens do not always reveal metal-lurgical or environmental changes that lead toreduced local ductility. The tendency for re-duced ductility in the presence of a triaxial stressfield and steep stress gradients (such as occur ata notch) is called notch sensitivity. A commonway of evaluating notch sensitivity is a tensiletest using a notched specimen.

The notch tensile test has been used exten-sively for investigating the properties of high-strength steels, for studying hydrogen embrittle-ment in steels and titanium, and for investigatingthe notch sensitivity of high-temperature alloys.More recently, notched tensile specimens havebeen used for fracture mechanics measurements.Notch sensitivity can also be investigated withthe notched-impact test.

The most common notch tensile specimenuses a 60� notch with a root radius 0.025 mm(0.001 in.) or less introduced into a round (cir-cumferential notch) or flat (double-edge notch)tensile specimen. Usually, the depth of the notchis such that the cross-sectional area at the rootof the notch is one half of the area in the un-notched section. The specimen is aligned care-fully and loaded in tension until fracture occurs.The notch strength is defined as the maximumload divided by the original cross-sectional areaat the notch. Because of the plastic constraint atthe notch, this value will be higher than the ten-sile strength of an unnotched specimen if thematerial possesses some ductility. Therefore, thecommon way of detecting notch brittleness (orhigh notch sensitivity) is by determining thenotch-strength ratio, NSR:

NSRs (for notched specimen at maximum load)net

�s (tensile strength for unnotched specimen)u

(Eq 55)

If the NSR is less than unity, the material isnotch brittle. The other property that is measuredin the notch tensile test is the reduction in areaat the notch.

As strength, hardness, or some metallurgicalvariable restricting plastic flow increases, themetal at the root of the notch is less able to flow,and fracture becomes more likely. Notch brittle-ness may be considered to begin at the strengthlevel where the notch strength begins to fall or,more conventionally, at the strength level wherethe NSR becomes less than unity.

The sensitivity of notch strength for detectingmetallurgical embrittlement is illustrated in Fig.18. Note that the conventional elongation mea-sured on a smooth specimen was unable to de-tect the fall in notch strength produced by tem-pering in the 330 to 480 �C (600–900 �F) range.For a more detailed review of notch tensile test-ing, see Ref 27.

Tensile Test Fractures (Ref 28)

Tensile test specimens can exhibit either duc-tile or brittle types of fracture. Ductile and brittleare terms that describe the amount of macro-scopic plastic deformation that precedes frac-ture. Ductile fractures are characterized by tear-ing of metal accompanied by appreciable grossplastic deformation and expenditure of consid-erable energy. Ductile tensile fractures in mostmaterials have a gray, fibrous appearance and are


classified on a macroscopic scale as either flat(perpendicular to the maximum tensile stress) orshear (at a 45� slant to the maximum tensilestress) fractures.

Brittle fractures are characterized by rapidcrack propagation with less expenditure of en-ergy than with ductile fractures and without ap-preciable gross plastic deformation. Brittle ten-sile fractures have a bright, granular appearanceand exhibit little or no necking. They are gen-erally of the flat type, that is, normal (perpen-dicular) to the direction of the maximum tensilestress. A chevron pattern may be present on thefracture surface, pointing toward the origin of

the crack, especially in brittle fractures in flatplatelike components.

It must be pointed out, however, that theseterms can also be applied, and are applied, tofracture on a microscopic level. Ductile fracturesare those that occur by microvoid formation andcoalescence, whereas brittle fractures may occurby either transgranular (cleavage or quasi-cleav-age) or intergranular cracking.

Clearly, the classic cup-and-cone fractureshown in Fig. 19(a) has occurred as a result ofappreciable plastic deformation and thus is aductile fracture, whereas the fracture shown inFig. 19(b) is a brittle fracture. The cup-and-cone

Fig. 20 Sections of a tensile specimen at various stages of formation during development of a cup-and-cone fracture. Note that thefracture is initiating internally. 7�. Source: Ref 28

Fig. 19 Appearance of ductile (a) and brittle (b) tensile fractures. Source: Ref 28

(a) (b)


tensile fracture exhibits three zones: the innerflat fibrous zone where the fracture begins, anintermediate radial zone, and the outer shear-lipzone where the fracture terminates. Figure 19(a)shows each of these zones; the flat brittle frac-ture shown in Fig. 19(b) exhibits little or noshear-lip zone.

Ductile Fracture. The sequence of eventsthat culminates in a cup-and-cone fracture is il-lustrated in Fig. 20, which shows the develop-ment of voids within the necked region (triaxialtensile stresses) of a tensile specimen and thecoalescence of the voids to produce an internalcrack by normal rupture. Final separation of thecross section occurs by shear rupture, which pro-duces the wall of the cup. Figure 21 shows scan-ning electron microscopy (SEM) fractographs ofthe bottom and the sidewall of the cup. On themicroscopic level, a crack is formed by coales-cence of microvoids that form as a result of par-ticle-matrix decohesion or cracking of second-phase particles; the microvoids and theassociated particles are shown at high magnifi-cation in Fig. 22. The process of microvoid for-mation and coalescence involves considerablelocalized plastic deformation and requires theexpenditure of a large amount of energy, whichis the basis of selection of a material with goodfracture toughness. The reduction of area of ul-trahigh-purity aluminum and copper approaches100% because of the absence within these ma-terials of void-nucleating particles. In their vi-sual appearance, ductile fractures have a matteor silky texture.

Brittle Fracture. Regarding the brittle frac-ture shown in Fig. 19(b), it will be noted thatthe fracture surface is characterized by radial

ridges that emanate from the center of the frac-ture surface. The ridges run parallel to the di-rection of crack propagation, and a ridge is pro-duced when two cracks that are not coplanarbecome connected by tearing of the intermediatematerial. The cracks, which propagate predomi-nantly by quasi-cleavage, move rapidly towardthe periphery of the specimen cross section and,as shown in Fig. 19(b), penetrate the externalsurface of the specimen by shear rupture alonga relatively small shear lip. The shear lip devel-ops as a result of the change in the state of stressfrom one of triaxial tension to one of planestress. The extent or width of the shear lip de-

Fig. 21 Fractographs of a ductile cup-and-cone fracture surface. (a) Bottom of the cup. (b) Sidewall of the cup. SEM. 650�. Source:Ref 28

Fig. 22 Large and small sulfide inclusions in a ductile dimplefracture. SEM. 5000�.


pends on the temperature at which fracture oc-curs, formation of a shear lip being favored byhigher temperatures.

ACKNOWLEDGMENTS


● G.E. Dieter, Mechanical Behavior UnderTensile and Compressive Loads, MechanicalTesting and Evaluation, Vol 8, ASM Hand-book, ASM International, 2000, p 99–108

● W.F. Hosford, Overview of Tensile Testing,Tensile Testing, P. Han, Ed., ASM Interna-tional, 1992, p 2–24

● W.T. Becker, Special Applications of Ten-sion and Compression Testing, Course 12,Lesson 5, Mechanical Testing of Metals,American Society for Metals, 1983, p 19

REFERENCES

1. G.E. Dieter, Introduction to Ductility, inDuctility, American Society for Metals,1968

2. P.G. Nelson and J. Winlock, ASTM Bull.,Vol 156, Jan 1949, p 53

3. D.J. Mack, Trans. AIME, Vol 166, 1946, p68–85

4. P.E. Armstrong, Measurement of ElasticConstants, in Techniques of Metals Re-search, Vol V, R.F. Brunshaw, Ed., Intersci-ence, New York, 1971

5. H.E. Davis, G.E. Troxell, and G.F.W.Hauck, The Testing of Engineering Materi-als, McGraw-Hill, New York, 1964, p 33

6. J.R. Low and F. Garofalo, Proc. Soc. Exp.Stress Anal., Vol 4 (No. 2), 1947, p 16–25

7. J.R. Low, Properties of Metals in MaterialsEngineering, American Society for Metals,1949

8. J. Datsko, Material Properties and Manu-facturing Processes, John Wiley & Sons,New York, 1966, p 18–20

9. W.B. Morrison, Trans. ASM, Vol 59, 1966,p 824

10. D.C. Ludwigson, Metall. Trans., Vol 2,1971, p 2825–2828

11. H.J. Kleemola and M.A. Nieminen, Metall.Trans., Vol 5, 1974, p 1863–1866

12. C. Adams and J.G. Beese, Trans. ASME, Se-ries H, Vol 96, 1974, p 123–126

13. J.H. Keeler, Trans. ASM, Vol 47, 1955, p157–192

14. A. Considere, Ann. Ponts Chaussees, Vol 9,1885, p 574–775

15. G.W. Geil and N.L. Carwile, J. Res. Natl.Bur. Stand., Vol 45, 1950, p 129

16. P.W. Bridgman, Trans. ASM, Vol 32, 1944,p 553

17. J. Aronofsky, J. Appl. Mech., Vol 18, 1951,p 75–84

18. T.A. Trozera, Trans. ASM, Vol 56, 1963, p280–282

19. E.R. Marshall and M.C. Shaw, Trans. ASM,Vol 44, 1952, p 716

20. W.J. McG. Tegart, Elements of MechanicalMetallurgy, Macmillan, New York, 1966, p22

21. N.E. Dowling, Mechanical Behavior of Ma-terials, Prentice-Hall, Englewood Cliffs,NJ, 1993, p 165

22. M.J. Barba, Mem. Soc. Ing. Civils, Part I,1880, p 682

23. E.G. Kula and N.N. Fahey, Mater. Res.Stand., Vol 1, 1961, p 631

24. W.F. Hosford, Overview of Tensile Testing,Tensile Testing, P. Han, Ed., ASM Interna-tional, 1992, p 2–24

25. W.T. Becker, Special Applications of Ten-sion and Compression Testing, Course 12,Lesson 5, Mechanical Testing of Metals,American Society for Metals, 1983, p 19

26. G.B. Espey, M.H. Jones, and W.F. Brown,Jr., ASTM Proc., Vol 59, 1959, p 837

27. J.D. Lubahn, Trans. ASME, Vol 79, 1957, p111–115

28. Ductile and Brittle Fractures, Failure Anal-ysis and Prevention, Vol 11, Metals Hand-book, 9th ed., American Society for Metals,1986, p 82–101

CHAPTER 3

Uniaxial Tensile Testing

Fig. 1 “Fish-bone” diagram of sources of variability in mechanical-test results

THE TENSILE TEST is one of the most com-monly used tests for evaluating materials. In itssimplest form, the tensile test is accomplishedby gripping opposite ends of a test piece (spec-imen) within the load frame of a test machine.A tensile force is applied by the machine, re-sulting in the gradual elongation and eventualfracture of the test piece. During the process,force-extension data, a quantitative measure ofhow the test piece deforms under the appliedtensile force, usually are monitored and re-corded. When properly conducted, the tensiletest provides force-extension data that can quan-tify several important mechanical properties ofa material. These mechanical properties deter-mined from tensile tests include, but are not lim-ited to, the following:● Elastic deformation properties, such as the

modulus of elasticity (Young’s modulus) andPoisson’s ratio

● Yield strength and ultimate tensile strength● Ductility properties, such as elongation and

reduction in area● Strain-hardening characteristics

These material characteristics from tensile testsare used for quality control in production, forranking performance of structural materials, forevaluation of newly developed alloys, and fordealing with the static-strength requirements ofdesign.

The basic principle of the tensile test is quitesimple, but numerous variables affect results.General sources of variation in mechanical-testresults include several factors involving mate-rials, namely, methodology, human factors,equipment, and ambient conditions, as shown inthe “fish-bone” diagram in Fig. 1. This chapterdiscusses the methodology of the tensile test andthe effect of some of the variables on the tensile




properties determined. The following method-ology and variables are discussed:

● Shape of the item being tested● Method of gripping the item● Method of applying the force● Determination of strength properties other

than the maximum force required to fracturethe test item

● Ductility properties to be determined● Speed of force application or speed of elon-

gation (e.g., control of stress rate or strainrate)

● Test temperature

The main focus of this chapter is on the meth-odology of tensile tests as it applies to metallicmaterials. Factors associated with test machinesand their method of force application are de-scribed in more detail in Chapter 4, “TensileTesting Equipment and Strain Sensors.”

This chapter does not address the tensile test-ing of nonmetallic materials, such as plastics,elastomers, or ceramics. Although uniaxial ten-sile testing is used in the mechanical evaluationof these materials, other test methods often areused for mechanical-property evaluation. Thegeneral concept of tensile properties is verysimilar for these nonmetallic materials, but thereare also some very important differences in theirbehavior and the required test procedures forthese materials:

● Tensile-test results for plastics depend morestrongly on the strain rate because plasticsare viscoelastic materials that exhibit time-dependent deformation (i.e., creep) duringforce application. Plastics are also more sen-sitive to temperature than metals. Thus, con-trol of strain rates and temperature are morecritical with plastics, and sometimes tensiletests are run at more than one strain and/ortemperature. The ASTM standard for tensiontesting of plastics is D 638. See Chapter 8,“Tensile Testing of Plastics,” for further de-tails.

● Tensile testing of ceramics requires more at-tention to alignment and gripping of the testpiece in the test machine because ceramicsare brittle materials that are extremely sen-sitive to bending strains and because the hardsurface of ceramics reduces the effectivenessof frictional gripping devices. The need forlarge gripping areas thus requires the use oflarger test pieces (Ref 1). The ASTM stan-dard for tensile testing of monolithic ce-

ramics at room temperature is C 1273. Thestandard for continuous fiber-reinforced ad-vanced ceramics at ambient temperatures isC 1275. See Chapter 10, “Tensile Testing ofCeramics and Ceramic-Matrix Composites,”for further details.

● Tensile testing of elastomers is described inASTM D 412 with specific instructionsabout test-piece preparation, equipment, andtest conditions. Tensile properties of elasto-mers vary widely, depending on the partic-ular formulation, and scatter both within andbetween laboratories is appreciable com-pared with the scatter of tensile-test resultsof metals (Ref 2). The use of tensile-test re-sults of elastomers is limited principally tocomparison of compound formulations. SeeChapter 9, “Tensile Testing of Elastomers,”for further details.

Definitions and Terminology

The basic results of a tensile test and othermechanical tests are quantities of stress andstrain that are measured. These basic terms andtheir units are briefly defined here, along withdiscussions of basic stress-strain behavior andthe differences between related terms, such asstress and force and strain and elongation.

Load (or force) typically refers to the forceacting on a body. However, there is currently aneffort within the technical community to replacethe word load with the more precise term force,which has a distinct meaning for any type offorce applied to a body. Load applies, in a strictsense, only to the gravitational force that acts ona mass. Nonetheless, the two terms are oftenused interchangeably.

Force is usually expressed in units of pounds-force, lbf, in the English system. In the metricsystem, force is expressed in units of newtons(N), where one newton is the force required togive a 1 kg mass an acceleration of 1 m/s2 (1 N� 1 kgm/s2). Although newtons are the pre-ferred metric unit, force is also expressed as kil-ogram force, kgf, which is the gravitational forceon a 1 kg mass on the surface of the earth. Thenumerical conversions between the various unitsof force are as follows:

● 1 lbf � 4.448222 N or 1 N � 0.2248089lbf

● 1 kgf � 9.80665 N

Uniaxial Tensile Testing / 35

In some engineering disciplines, such as civilengineering, the quantity of 1000 lbf is also ex-pressed in units of kip, such that 1 kip � 1000lbf.

Stress is simply the amount of force that actsover a given cross-sectional area. Thus, stress isexpressed in units of force per area units and isobtained by dividing the applied force by thecross-sectional area over which it acts. Stress isan important quantity because it allows strengthcomparison between tests conducted using testpieces of different sizes and/or shapes. Whendiscussing strength values in terms of force, theload (force) carrying capacity of a test piece isa function of the size of the test piece. However,when material strength is defined in terms ofstress, the size or shape of the test piece has littleor no influence on stress measurements ofstrength (provided the cross section contains atleast 10 to 15 metallurgical grains).

Stress is typically denoted by either the Greeksymbol sigma, r, or by s, unless a distinction isbeing made between true stress and nominal (en-gineering) stress as discussed in this article. Theunits of stress are typically lbf/in.2 (psi) or thou-sands of psi (ksi) in the English system and apascal (Pa) in the metric system. Engineeringstresses in metric units are also expressed interms of newtons per area (i.e., N/m2 or N/mm2)or as kilopascals (kPA) and megapascals (MPa).Conversions between these various units ofstress are as follows:

● 1 Pa � 1.45 � 10�4 psi● 1 Pa � 1 N/m2

● 1 kPa � 103 Pa or 1 kPa � 0.145 psi● 1 MPa � 106 Pa or 1 MPa � 0.145 ksi● 1 N/mm2 � 1 MPa

Strain and elongation are similar terms thatdefine the amount of deformation from a givenamount of applied stress. In general terms, strainis defined (by ASTM E 28) as “the change perunit length due to force in an original linear di-mension.” The phrase change per unit lengthmeans that a change in length, DL, is expressedas a ratio of the original length, L0. This changein length can be expressed in general terms as astrain or as elongation of gage length, as de-scribed subsequently in the context of a tensiontest.

Strain is a general term that can be expressedmathematically, either as engineering strain oras true strain. Nominal (or engineering) strain isoften represented by the letter e, and logarithmic(or true) strain is often represented by the Greek

letter e. The equation for engineering strain, e,is based on the nominal change in length (DL)where:

e � DL/L � (L � L )/L0 0 0

The equation for true strain, e, is based on theinstantaneous change in length (dl) where:

L dl Le � � ln� � �

L l L0 0

These two basic expressions for strain are inter-related, such that:

e � ln(1 � e)

In a tensile test, the typical measure of strain isengineering strain, e, and the units are inches perinch (or millimeter per millimeter and so on).Often, however, no units are shown becausestrain is the ratio of length in a given measuringsystem.

This chapter refers to only engineering strainunless otherwise specified. In a tensile test, truestrain is based on the change in the cross-sec-tional area of the test piece as it is loaded. It isnot further discussed herein, but a detailed dis-cussion is found in Chapter 2, “Mechanical Be-havior of Materials under Tensile Loads.”

Elongation is a term that describes the amountthat the test piece stretches during a tensile test.This stretching or elongation can be defined ei-ther as the total amount of stretch, DL, that apart undergoes or the increase in gage length perthe initial gage length, L0.

The latter definition is synonymous with themeaning of engineering strain, DL/L0, while thefirst definition is the total amount of extension.Because two definitions are possible, it is im-perative that the exact meaning of elongation beunderstood each time it is used.

This chapter uses the term elongation, e, tomean nominal or engineering strain (i.e., e �DL/L0). The amount of stretch is expressed asextension, or the symbol DL. In many cases,elongation, e, is also reported as a percentagechange in gage length as a measure of ductility(i.e., percent elongation), (DL/L0) � 100. Thisconvention is used in Chapter 1, “Introductionto Tensile Testing.”

Engineering Stress and True Stress. Alongwith the previous descriptions of engineeringstrain and true strain, it is also possible to definestress in two different ways as engineering stress


and true stress. As is intuitive, when a tensileforce stretches a test piece, the cross-sectionalarea must decrease (because the overall volumeof the test piece remains essentially constant).Hence, because the cross section of the test piecebecomes smaller during a test, the value of stressdepends on whether it is calculated based on thearea of the unloaded test piece (the initial area)or on the area resulting from that applied force(the instantaneous area). Thus, in this context,there are two ways to define stress:

● Engineering stress, s: The force at any timeduring the test divided by the initial area ofthe test piece; s � F/A0 where F is the force,and A0 is the initial cross section of a testpiece.

● True stress, r: The force at any time dividedby the instantaneous area of the test piece; r� F/Ai where F is the force, and Ai is theinstantaneous cross section of a test piece.

Because an increasing force stretches a testpiece, thus decreasing its cross-sectional area,the value of true stress will always be greaterthan the nominal, or engineering, stress.

These two definitions of stress are further re-lated to one another in terms of the strain thatoccurs when the deformation is assumed to oc-cur at a constant volume (as it frequently is). Aspreviously noted, strain can be expressed as ei-ther engineering strain (e) or true strain, wherethe two expressions of strain are related as e �ln(1 � e). When the test-piece volume is con-stant during deformation (i.e., AiLi � A0L0),then the instantaneous cross section, Ai, is re-lated to the initial cross section, A0, where

A � A exp {�e}0

� A /(1 � e)0

If these expressions for instantaneous and initialcross sections are divided into the applied forceto obtain values of true stress (at the instanta-neous cross section, Ai) and engineering stress(at the initial cross section, A0), then:

r � s exp {e} � s(1 � e)

Typically, engineering stress is more commonlyconsidered during uniaxial tension tests. All dis-cussions in this article are based on nominal en-gineering stress and strain unless otherwisenoted. More detailed discussions on true stressand true strain are in Chapter 2, “MechanicalBehavior of Materials under Tensile Loads.”

Stress-Strain Behavior

During a tensile test, the force applied to thetest piece and the amount of elongation of thetest piece are measured simultaneously. The ap-plied force is measured by the test machine orby accessory force-measuring devices. Theamount of stretching (or extension) can be mea-sured with an extensometer. An extensometer isa device used to measure the amount of stretchthat occurs in a test piece. Because the amountof elastic stretch is quite small at or around theonset of yielding (in the order of 0.5% or lessfor steels), some manner of magnifying thestretch is required. An extensometer may be amechanical device, in which case the magnifi-cation occurs by mechanical means. An exten-someter may also be an electrical device, inwhich case the magnification may occur by me-chanical means, electrical means, or by a com-bination of both. Extensometers generally havefixed gage lengths. If an extensometer is usedonly to obtain a portion of the stress-strain curvesufficient to determine the yield properties, thegage length of the extensometer may be shorterthan the gage length required for the elongation-at-fracture measurement. It may also be longer,but in general, the extensometer gage lengthshould not exceed approximately 85 to 90% ofthe length of the reduced section or of the dis-tance between the grips for test pieces withoutreduced sections. This ratio for some of the mostcommon test configurations with a 2 in. gagelength and 21⁄4 in. reduced section is 0.875%.

The applied force, F, and the extension, DL,are measured and recorded simultaneously atregular intervals, and the data pairs can be con-verted into a stress-strain diagram as shown inFig. 2. The conversion from force-extensiondata to stress-strain properties is shown sche-matically in Fig. 2(a). Engineering stress, s, isobtained by dividing the applied force by theoriginal cross-sectional area, A0, of the testpiece, and strain, e, is obtained by dividing theamount of extension, DL, by the original gagelength, L. The basic result is a stress-strain curve(Fig. 2b) with regions of elastic deformation andpermanent (plastic) deformation at stressesgreater than those of the elastic limit (EL in Fig.2b).

Typical stress-strain curves for three types ofsteels, aluminum alloys, and plastics are shownin Fig. 3 (Ref 3). Stress-strain curves for somestructural steels are shown in Fig. 4(a) (Ref 4)for elastic conditions and for small amounts of


Fig. 2 Stress-strain behavior in the region of the elastic limit.(a) Definition of r and e in terms of initial test piece

length, L, and cross-sectional area, A0, before application of atensile force, F. (b) Stress-strain curve for small strains near theelastic limit (EL)

Fig. 3 Typical engineering stress-strain curves from tensiletests on (a) three steels, (b) three aluminum alloys, and

(c) three plastics. PTFE, polytetrafluoroethylene. Source: Ref 3

plastic deformation. The general shape of thestress-strain curves can be described for defor-mation in this region. However, as plastic de-formation occurs, it is more difficult to gener-alize about the shape of the stress-strain curve.Figure 4(b) shows the curves of Fig. 4(a) con-tinued to fracture.

Elastic deformation occurs in the initial por-tion of a stress-strain curve, where the stress-strain relationship is initially linear. In this re-gion, the stress is proportional to strain.Mechanical behavior in this region of stress-

strain curve is defined by a basic physical prop-erty called the modulus of elasticity (often ab-breviated as E). The modulus of elasticity is theslope of the stress-strain line in this linear re-


Fig. 4 Typical stress-strain curves for structural steels having specified minimum tensile properties. (a) Portions of the stress-straincurves in the yield-strength region. (b) Stress-strain curves extended through failure. Source: Ref 4

gion, and it is a basic physical property of allmaterials. It essentially represents the springconstant of a material.

The modulus of elasticity is also calledHooke’s modulus or Young’s modulus after thescientists who discovered and extensively stud-ied the elastic behavior of materials. The behav-ior was first discovered in the late 1600s by theEnglish scientist Robert Hooke. He observed

that a given force would always cause a repeat-able, elastic deformation in all materials. He fur-ther discovered that there was a force abovewhich the deformation was no longer elastic;that is, the material would not return to its origi-nal length after release of the force. This limitingforce is called the elastic limit (EL in Fig. 2b).Later, in the early 1800s, Thomas Young, an En-glish physicist, further investigated and de-


Fig. 5 Effects of prior tensile loading on tensile stress-strainbehavior. Solid line, stress-strain curve based on di-

mensions of unstrained test piece (unloaded and reloaded twice);dotted line, stress-strain curve based on dimensions of test pieceafter first unloading; dashed line, stress-strain curve based on di-mensions of test piece after second unloading. Note: Graph is notto scale.

scribed this elastic phenomenon, and so hisname is associated with it.

The proportional limit (PL) is a point in theelastic region where the linear relationship be-tween stress and strain begins to break down. Atsome point in the stress-strain curve (PL in Fig.2b), linearity ceases, and small increase in stresscauses a proportionally larger increase in strain.This point is referred to as the proportional limit(PL) because up to this point, the stress andstrain are proportional. If an applied force belowthe PL point is removed, the trace of the stressand strain points returns along the original line.If the force is reapplied, the trace of the stressand strain points increases along the originalline. (When an exception to this linearity is ob-served, it usually is due to mechanical hysteresisin the extensometer, the force indicating system,the recording system, or a combination of allthree.)

The elastic limit (EL) is a very importantproperty when performing a tensile test. If theapplied stresses are below the elastic limit, thenthe test can be stopped, the test piece unloaded,and the test restarted without damaging the testpiece or adversely affecting the test results. Forexample, if it is observed that the extensometeris not recording, the force-elongation curveshows an increasing force, but no elongation. Ifthe force has not exceeded the elastic limit, thetest piece can be unloaded, adjustments made,and the test restarted without affecting the re-sults of the test. However, if the test piece hasbeen stressed above the EL, plastic deformation(set) will have occurred (Fig. 2b), and there willbe a permanent change in the stress-strain be-havior of the test piece in subsequent tension (orcompression) tests.

The PL and the EL are considered identicalin most practical instances. In theory, however,the EL is considered to be slightly higher thanthe PL, as illustrated in Fig. 2b. The measuredvalues of EL or PL are highly dependent on themagnification and sensitivity of the extensome-ter used to measure the extension of the testpiece. In addition, the measurement of PL andEL also highly depends on the care with whicha test is performed.

Plastic Deformation (Set) from Stressesabove the Elastic Limit. If a test piece isstressed (or loaded) and then unloaded, any re-test proceeds along the unloading path whetheror not the elastic limit was exceeded. For ex-ample, if the initial stress is less than the elasticlimit, the load-unload-reload paths are identical.However, if a test piece is stressed in tension

beyond the elastic limit, then the unload path isoffset and parallel to the original loading path(Fig. 2b). Moreover, any subsequent tensionmeasurements will follow the previous unloadpath parallel to the original stress-strain line.Thus, the application and removal of stressesabove the elastic limit affect all subsequentstress-strain measurements.

The term set refers to the permanent defor-mation that occurs when stresses exceed theelastic limit (Fig. 2b). ASTM E 6 defines set asthe strain remaining after the complete releaseof a load-producing deformation. Because set ispermanent deformation, it affects subsequentstress-strain measurements whether the reload-ing occurs in tension or compression. Likewise,permanent set also affects all subsequent tests ifthe initial loading exceeds the elastic limit incompression. Discussions of these two situa-tions follow.

Reloading after Exceeding the Elastic Limitin Tension. If a test piece is initially loaded intension beyond the elastic limit and then un-loaded, the unload path is parallel to the initialload path but offset by the set; on reloading intension, the unloading path will be followed.Figure 5 illustrates a series of stress-straincurves obtained using a machined round testpiece of steel. (The strain axis is not to scale.)In this figure, the test piece was loaded first toPoint A and unloaded. The area of the test piecewas again determined (A2) and reloaded to Point


Fig. 6 Example of the Bauschinger effect and hysteresis loopin tension-compression-tension loading. This example

shows initial tension loading to 1% strain, followed by compres-sion loading to 1% strain, and then a second tension loading to1% strain.

B and unloaded. The area of the test piece wasdetermined for a third time (A3) and reloadeduntil fracture occurred. Because during eachloading the stresses at Points A and B were inexcess of the elastic limit, plastic deformationoccurred. As the test piece is elongated in thisseries of tests, the cross-sectional area must de-crease because the volume of the test piece mustremain constant. Therefore, A1 � A2 � A3.

The curve with a solid line in Fig. 5 is ob-tained for engineering stresses calculated usingthe applied forces divided by the original cross-sectional area. The curve with a dotted line isobtained from stresses calculated using the ap-plied forces divided by the cross-sectional area,A2, with the origin of this stress-strain curve lo-cated on the abscissa at the end point of the firstunloading line. The curve represented by thedashed line is obtained from the stresses calcu-lated using the applied forces divided by thecross-sectional area, A3, with the origin of thisstress-strain curve located on the abscissa at theend point of the second unloading line. This fig-ure illustrates what happens if a test is stopped,unloaded, and restarted. It also illustrates one ofthe problems that can occur when testing piecesfrom material that has been formed into a part(or otherwise plastically strained before testing).An example is a test piece that was machinedfrom a failed structure to determine the tensileproperties. If the test piece is from a location thatwas subjected to tensile deformation during thefailure, the properties obtained are probably notrepresentative of the original properties of thematerial.

Bauschinger Effect. The other loading con-dition occurs when the test piece is initiallyloaded in compression beyond the elastic limitand then unloaded. The unload path is parallelto the initial load path but offset by the set; onreloading in tension, the elastic limit is muchlower, and the shape of the stress-strain curve issignificantly different. The same phenomenonoccurs if the initial loading is in tension and thesubsequent loading is in compression. This con-dition is called the Bauschinger effect, namedfor the German scientist who first described itaround 1860. Again, the significance of this phe-nomenon is that if a test piece is machined froma location that has been subjected to plastic de-formation, the stress-strain properties will besignificantly different than if the material hadnot been so strained. This occurrence is illus-trated in Fig. 6, where a machined round steeltest piece was first loaded in tension to about 1%

strain, unloaded, loaded in compression to about1% strain, unloaded, and reloaded in tension.For this steel, the initial portion of tension andcompression stress-strain curves are essentiallyidentical.

Properties from Test Results

A number of tensile properties can be deter-mined from the stress-strain diagram. Two ofthese properties, the tensile strength and theyield strength, are described in the next sectionof this article, “Strength Properties.” In addition,total elongation (ASTM E 6), yield-point elon-gation (ASTM E 6), Young’s modulus (ASTME 111), and the strain-hardening exponent(ASTM E 646) are sometimes determined fromthe stress-strain diagram. Other tensile proper-ties include the following:

● Poisson’s ratio (ASTM E 132)● Plastic-strain ratio (ASTM E 517)● Elongation by manual methods (ASTM E 8)● Reduction of area

These properties require more information thanjust the data pairs generating a stress-straincurve. None of these four properties can be de-termined from a stress-strain diagram.

Strength Properties

Tensile strength and yield strength are themost common strength properties determined in


Fig. 7 Examples of stress-strain curves exhibiting pronouncedyield-point behavior. Pronounced yielding, of the type

shown, is usually called yield-point elongation (YPE). (a) Classicexample of upper-yield-strength (UYS) behavior typically ob-served in low-carbon steels with a very pronounced upper yieldstrength. (b) General example of pronounced yielding without anupper yield strength. LYS, lower yield strength

a tensile test. According to ASTM E 6, tensilestrength is calculated from the maximum forceduring a tension test that is carried to rupturedivided by the original cross-sectional area ofthe test piece. By this definition, it is a stressvalue, although some product specifications de-fine the tensile strength as the force (load) sus-taining ability of the product without consider-ation of the cross-sectional area. Fastenerspecifications, for example, often refer to tensilestrength as the applied force (load-carrying) ca-pacity of a part with specific dimensions.

The yield strength refers to the stress at whicha small, but measurable, amount of inelastic orplastic deformation occurs. There are three com-mon definitions of yield strength:

● Offset yield strength● Extension-under-load (EUL) yield strength● Upper yield strength (or upper yield point)

An upper yield strength (upper yield point) (Fig.7a) usually occurs with low-carbon steels andsome other metal systems to a limited degree.Often, the pronounced peak of the upper yieldis suppressed due to slow testing speed or non-axial loading (i.e., bending of the test piece),metallurgical factors, or a combination of these;in this case, a curve of the type shown in Fig.7(b) is obtained. The other two definitions ofyield strength, EUL and offset, were developedfor materials that do not exhibit the yield-pointbehavior shown in Fig. 7. Stress-strain curveswithout a yield point are illustrated in Fig. 4(a)for USS Con-Pac 80 and USS T-1 steels. To de-termine either the EUL or the offset yieldstrength, the stress-strain curve must be deter-mined during the test. In computer-controlledtesting systems, this curve is often stored inmemory and may not be charted or displayed.

Upper yield strength (or upper yield point)can be defined as the stress at which measurablestrain occurs without an increase in the stress;that is, there is a horizontal region of the stress-strain curve (Fig. 7) where discontinuous yield-ing occurs. Before the onset of discontinuousyielding, a peak of maximum stress for yieldingis typically observed (Fig. 7a). This pronouncedyielding, of the type shown, is usually calledyield-point elongation (YPE). This elongation isa diffusion-related phenomenon, where undercertain combinations of strain rate and tempera-ture as the material deforms, interstitial atomsare dragged along with dislocations, or disloca-tions can alternately break away and be re-pinned, with little or no increase in stress. Either

or both of these actions cause serrations or dis-continuous changes in a stress-strain curve,which are usually limited to the onset of yield-ing. This type of yield point is sometimes re-ferred to as the upper yield strength or upperyield point. This type of yield point is usuallyassociated with low-carbon steels, althoughother metal systems may exhibit yield points tosome degree. For example, the stress-straincurves for A36 and USS Tri-Ten steels shownin Fig. 4(a) exhibit this behavior.

The yield point is easy to measure because theincrease in strain that occurs without an increasein stress is visually apparent during the conductof the test by observing the force-indicating sys-tem. As shown in Fig. 7, the yield point is usu-ally quite obvious and thus can easily be deter-mined by observation during a tensile test. Itcan be determined from a stress-strain curve or


Fig. 9 Method of determining yield strength by the offsetmethod. Source: adapted from ASTM E 8

Fig. 8 Method of determining yield strength by the extension-under-load method (EUL). Source: adapted from

ASTM E 8

by the halt of the dial when the test is performedon machines that use a dial to indicate the ap-plied force. However, when watching the move-ment of the dial, sometimes a minimum value,recorded during discontinuous yielding, isnoted. This value is sometimes referred to as thelower yield point. When the value is ascertainedwithout instrumentation readouts, it is often re-ferred to as the halt-of-dial or the drop-of-beamyield point (as an average usually results fromeye readings). It is almost always the upper yieldpoint that is determined from instrument read-outs.

Extension-under-load (EUL) yield strengthis the stress at which a specified amount ofstretch has taken place in the test piece. TheEUL is determined by the use of one of the fol-lowing types of apparatus:

● Autographic devices that secure stress-straindata, followed by an analysis of this data(graphically or using automated methods) todetermine the stress at the specified value ofextension

● Devices that indicate when the specified ex-tension occurs so that the stress at that pointmay be ascertained

Graphical determination is illustrated in Fig. 8.On the stress-strain curve, the specified amountof extension, 0-m, is measured along the strainaxis from the origin of the curve and a verticalline, m-n, is raised to intersect the stress-straincurve. The point of intersection, r, is the EUL

yield strength, and the value R is read from thestress axis. Typically, for many materials, the ex-tension specified is 0.5%; however, other valuesmay be specified. Therefore, when reporting theEUL, the extension also must be reported. Forexample, yield strength (EUL � 0.5%) �52,500 psi is a correct way to report an EULyield strength. The value determined by the EULmethod may also be termed a yield point.

Offset yield strength is the stress that causesa specified amount of set to occur; that is, at thisstress, the test piece exhibits plastic deformation(set) equal to a specific amount. To determinethe offset yield strength, it is necessary to securedata (autographic or numerical) from which astress-strain diagram may be constructed graph-ically or in computer memory. Figure 9 showshow to use these data; the amount of the speci-fied offset 0-m is laid out on the strain axis. Aline, m-n, parallel to the modulus of elasticityline, 0-A, is drawn to intersect the stress-straincurve. The point of intersection, r, is the offsetyield strength, and the value, R, is read from thestress axis. Typically, for many materials, theoffset specified is 0.2%; however, other valuesmay be specified. Therefore, when reporting theoffset yield strength, the amount of the offsetalso must be reported; for example, “0.2% offsetyield strength � 52.8 ksi” or “yield strength(0.2% offset) � 52.8 ksi” are common formatsused in reporting this information.

In Fig. 8 and 9, the initial portion of the stress-strain curve is shown in ideal terms as a straightline. Unfortunately, the initial portion of thestress-strain curve sometimes does not begin as


Fig. 11 Stress-strain curves showing straight lines corresponding to (a) Young’s modulus between stress, P, below proportional limitand R, or preload; (b) tangent modulus at any stress, R; and (c) chord modulus between any two stresses, P and R. Source:

Ref 6

Fig. 10 Examples of stress-strain curves requiring foot correction. Point D is the point where the extension of the straight (elastic)part diverges from the stress-strain curve. Source: Ref 5

a straight line but rather has either a concave ora convex foot (Fig. 10) (Ref 5). The shape ofthe initial portion of a stress-strain curve may beinfluenced by numerous factors such as, but notlimited to, the following:

● Seating of the test piece in the grips● Straightening of a test piece that is initially

bent by residual stresses or bent by coil set● Initial speed of testing

Generally, the aberrations in this portion of thecurve should be ignored when fitting a modulusline, such as that used to determine the origin ofthe curve. As shown in Fig. 10, a “foot correc-tion” may be determined by fitting a line,whether by eye or by using a computer program,to the linear portion and then extending this lineback to the abscissa, which becomes point 0 inFig. 8 and 9. As a rule of thumb, point D in Fig.10 should be less than one-half the specifiedyield point or yield strength.

Tangent or Chord Moduli. For materials thatdo not have a linear relationship between stressand strain, even at very low stresses, the offset

yield is meaningless without defining how to de-termine the modulus of elasticity. Often, a chordmodulus or a tangent modulus is specified. Achord modulus is the slope of a chord betweenany two specified points on the stress-straincurve, usually below the elastic limit. A tangentmodulus is the slope of the stress-strain curve ata specified value of stress or of strain. Chord andtangent moduli are illustrated in Fig. 11. An-other technique that has been used is sketchedin Fig. 12. The test piece is stressed to approx-imately the yield strength, unloaded to about10% of this value, and reloaded. As previouslydiscussed, the unloading line will be parallel towhat would have been the initial modulus line,and the reloading line will coincide with the un-loading line (assuming no hysteresis in any ofthe system components). The slope of this lineis transferred to the initial loading line, and theoffset is determined as before. The stress orstrain at which the test piece is unloaded usuallyis not important. This technique is specified inthe ISO standard for the tensile test of metallicmaterials, ISO 6892.


Fig. 13 Sketch of fractured, round tensile test piece. Dashedlines show original shape. Strain � elongation/gage

lengthFig. 12 Alternate technique for establishing Young’s modulus

for a material without an initial linear portion

Yield-strength-property values generallydepend on the definition being used. As shownin Fig. 4(a) for the USS Con-Pac steel, the EULyield is greater than the offset yield, but for theUSS T-1 steel (Fig. 4a), the opposite is true. Theamount of the difference between the two valuesis dependent upon the slope of the stress-straincurve between the two intersections. When thestress-strain data pairs are sampled by a com-puter, and a yield spike or peak of the typeshown in Fig. 7(a) occurs, the EUL and the off-set yield strength will probably be less than theupper yield point and will probably differ be-cause the m-n lines of Fig. 8 and 9 will intersectat different points in the region of discontinuousyielding.

Ductility

Ductility is the ability of a material to deformplastically without fracturing. Figure 13 is asketch of a test piece with a circular cross sectionthat has been pulled to fracture. As indicated inthis sketch, the test piece elongates during thetensile test and correspondingly reduces incross-sectional area. The two measures of theductility of a material are the amount of elon-gation and reduction of area that occurs duringa tensile test.

Elongation, as previously noted, is defined inASTM E 6 as the increase in the gage length ofa test piece subjected to a tension force, dividedby the original gage length on the test piece.Elongation usually is expressed as a percentageof the original gage length. ASTM E 6 furtherindicates the following:

● The increase in gage length may be deter-mined either at or after fracture, as specifiedfor the material under test.

● The gage length shall be stated when report-ing values of elongation.

● Elongation is affected by test-piece geome-try (gage length, width, and thickness of thegage section and of adjacent regions) and testprocedure variables, such as alignment andspeed of pulling.

The manual measurement of elongation on atensile test piece can be done with the aid ofgage marks applied to the unstrained reducedsection. After the test, the amount of stretch be-tween gage marks is measured with an appro-priate device. The use of the term elongation inthis instance refers to the total amount of stretchor extension. Elongation, in the sense of nominalengineering strain, e, is the value of gage exten-sion divided by the original distance between thegage marks. Strain elongation is usually ex-pressed as a percentage, where the nominal en-gineering strain is multiplied by 100 to obtain apercent value; that is:

e, % �(final gage length � original gage length)� �original gage length

� 100

The final gage length at the completion of thetest may be determined in two ways. Histori-cally, it was determined manually by carefullyfitting the two ends of the fractured test piecetogether (Fig. 13) and measuring the distancebetween the gage marks. However, some mod-


Fig. 14 Effect of gage length on the percent elongation. (a)Elongation, %, as a function of gage length for a frac-

tured tensile test piece. (b) Distribution of elongation along a frac-tured tension test piece. Original spacing between gage marks,12.5 mm (0.5 in.). Source: Ref 7

ern computer-controlled testing systems obtaindata from an extensometer that is left on the testpiece through fracture. In this case, the computermay be programmed to report the elongation asthe last strain value obtained prior to some event,perhaps the point at which the applied forcedrops to 90% of the maximum value recorded.There has been no general agreement about whatevent should be the trigger, and users and ma-chine manufacturers find that different eventsmay be appropriate for different materials (al-though some consensus has been reached, seeASTM E 8). The elongation values determinedby these two methods are not the same; in gen-eral, the result obtained by the manual methodis a couple of percent larger and is more variablebecause the test-piece ends do not fit togetherperfectly. It is strongly recommended that whendisagreements arise about elongation results,agreement should be reached on which methodwill be used prior to any further testing.

Test methods often specify special conditionsthat must be followed when a product specifi-cation specifies elongation values that are small,or when the expected elongation values aresmall. For example, ASTM E 8 defines small as3% or less.

Effect of Gage Length and Necking. Figure14 (Ref 7) shows the effect of gage length onelongation values. Gage length is very impor-tant; however, as the gage length becomes quitelarge, the elongation tends to be independent ofthe gage length. The gage length must be spec-ified prior to the test, and it must be shown inthe data record for the test.

Figures 13 and 14 also illustrate considerablelocalized deformation in the vicinity of the frac-ture. This region of local deformation is oftencalled a neck, and the occurrence of this defor-mation is termed necking. Necking occurs as theforce begins to drop after the maximum forcehas been reached on the stress-strain curve. Upto the point at which the maximum force occurs,the strain is uniform along the gage length; thatis, the strain is independent of the gage length.However, once necking begins, the gage lengthbecomes very important. When the gage lengthis short, this localized deformation becomes theprincipal portion of measured elongation. Forlong gage lengths, the localized deformation isa much smaller portion of the total. For this rea-son, when elongation values are reported, thegage length must also be reported, for example,elongation � 25% (50 mm, or 2.00 in., gagelength).

Effect of Test-Piece Dimensions. Test-piecedimensions also have a significant effect onelongation measurements. Experimental workhas verified the general applicability of the fol-lowing equation:

1/2 �ae � e (L/A )0

where e0 is the specific elongation constant; L/A1/2 the slimness ratio, K, of gage length, L, andcross-sectional areas, A; and a is another mate-rial constant. This equation is known as the Ber-tella-Oliver equation, and it may be transformedinto logarithmic form and plotted as shown inFig. 15. In one study, quadruplet sets of ma-chined circular test pieces (four different diam-eters ranging from 0.125 to 0.750 in.) and rec-tangular test pieces (1⁄2 in. wide with threethicknesses and 11⁄2 in. wide with three thick-nesses) were machined from a single plate. Mul-tiple gage lengths were scribed on each testpiece to produce a total of 40 slimness ratios.The results of this study, for one of the gradesof steel tested, are shown in Fig. 16.


Fig. 16 Graphical form of the Bertella-Oliver equation show-ing actual data

In order to compare elongation values of testpieces with different slimness ratios, it is nec-essary only to determine the value of the mate-rial constant, a. This calculation can be made bytesting the same material with two different ge-ometries (or the same geometry with differentgage lengths) with different slimness ratios, K1and K2, where

�a �ae � e /K � e /K0 1 1 2 2

solving for a, then:

�a(K /K ) � e /e2 1 2 1

or:

ln(e /e )2 1�a �

ln(K /K )2 1

ln(e ) � ln(e )2 1�a �

ln(K ) � ln(K )2 1

The values of the e0 and a parameters depend onthe material composition, the strength, and thematerial condition and are determined empiri-cally with a best-fit line plot around data points.Reference 8 specifies value a � 0.4 for carbon,carbon-manganese, molybdenum, and chro-mium-molybdenum steels within the tensilestrength range of 275 to 585 MPa (40 to 85 ksi)and in the hot-rolled, in the hot-rolled and nor-malized, or in the annealed condition, with orwithout tempering. Materials that have beencold reduced require the use of a different valuefor a, and an appropriate value is not suggested.Reference 8 uses a value of a � 0.127 for an-nealed, austenitic stainless steels. However, Ref8 states that “these conversions shall not be usedwhere the width-to-thickness ratio, w/t, of thetest piece exceeds 20.” ISO 2566/1 (Ref 9) con-tains similar statements. In addition to the limit

of (w/t) � 20, Ref 9 also specifies that the slim-ness ratio shall be less than 25.

Some tensile-test specifications do not containstandard test-piece geometries but require thatthe slimness ratio be either 5.65 or 11.3. For around test piece, a slimness ratio of 5.65 pro-duces a 5-to-1 relation between the diameter andthe gage length, and a slimness ratio of 4.51 pro-duces a 4-to-1 relation between the diameter andgage length (which is that of the test piece inASTM E 8).

Reduction of area is another measure of theductility of metal. As a test piece is stretched,the cross-sectional area decreases, and as longas the stretch is uniform, the reduction of area isproportional to the amount of stretch or exten-sion. However, once necking begins to occur,proportionality is no longer valid.

According to ASTM E 6, reduction of area isdefined as “the difference between the originalcross-sectional area of a tension test piece andthe area of its smallest cross section.” Reductionof area is usually expressed as a percentage ofthe original cross-sectional area of the test piece.The smallest final cross section may be mea-sured at or after fracture as specified for the ma-terial under test. The reduction of area (RA) isalmost always expressed as a percentage:

(original area � final area)RA, % � � 100� �original area

Reduction of area is customarily measuredonly on test pieces with an initial circular cross

Fig. 15 Graphical form of the Bertella-Oliver equation


Fig. 17 Sketch of end view of rectangular test piece after frac-ture showing constraint at corners indicating the dif-

ficulty of determining reduced area

section because the shape of the reduced arearemains circular or nearly circular throughoutthe test for such test pieces. With rectangular testpieces, in contrast, the corners prevent uniformflow from occurring, and consequently, afterfracture, the shape of the reduced area is not rec-tangular (Fig. 17). Although a number of ex-pressions have been used in an attempt to de-scribe the way to determine the reduced area,none has received general agreement. Thus, if atest specification requires the measurement ofthe reduction of area of a test piece that is notcircular, the method of determining the reducedarea should be agreed to prior to performing thetest.

General Procedures

Numerous groups have developed standardmethods for conducting the tensile test. In theUnited States, standards published by ASTM arecommonly used to define tensile-test proceduresand parameters. Of the various ASTM standardsrelated to tensile tests (for example, those listedin “Selected References” at the end of this chap-ter), the most common method for tension test-ing of metallic materials is ASTM E 8 “StandardTest Methods for Tension Testing of MetallicMaterials” (or the version using metric units,ASTM E 8M). Standard methods for conductingthe tensile test are also available from other stan-dards organizations, such as the Japanese Indus-trial Standards (JIS), the Deutsche Institut furNormung (DIN), and the International Organi-zation for Standardization (ISO). Other domes-tic technical groups in the United States havedeveloped standards, but in general, these arebased on ASTM E 8.

With the increasing internationalization oftrade, methods developed by other national stan-dards organizations (such as JIS, DIN, or ISOstandards) are increasingly being used in theUnited States. Although most tensile-test stan-dards address the same concerns, they differ inthe values assigned to variables. Thus, a tensiletest performed in accordance with ASTM E 8will not necessarily have been conducted in ac-cordance with ISO 6892 or JIS Z2241, and soon, and vice versa. Therefore, it is necessary tospecify the applicable testing standard for anytest results or mechanical property data.

Unless specifically indicated otherwise, thevalues of all variables discussed hereafter arethose related to ASTM E 8 “Standard Test Meth-ods for Tension Testing of Metallic Materials.”

A flow diagram of the steps involved when atensile test is conducted in accordance withASTM E 8 is shown in Fig. 18. The test consistsof three distinct parts:

● Test-piece preparation, geometry, and mate-rial condition

● Test setup and equipment● Test

The Test Piece

The test piece, also commonly referred to asthe test specimen (see discussion below), is oneof two basic types. Either it is a full cross sectionof the product form, or it is a small portion thathas been machined to specific dimensions. Full-section test pieces consist of a part of the testunit as it is fabricated. Examples of full-sectiontest pieces include bars, wires, and hot-rolled orextruded angles cut to a suitable length and thengripped at the ends and tested. In contrast, a ma-chined test piece is a representative sample, suchas one of the following:

● Test piece machined from a rough specimentaken from a coil or plate

● Test piece machined from a bar with dimen-sions that preclude testing a full-section testpiece because a full-section test piece ex-ceeds the capacity of the grips or the forcecapacity of the available testing machine orboth

● Test piece machined from material of greatmonetary or technical value

In these cases, representative samples of the ma-terial must be obtained for testing. The descrip-tions of the tensile test in this chapter proceedfrom the point that a rough specimen (Fig. 19)has been obtained. That is, the rough specimenhas been selected based on some criteria, usuallya material specification or a test order issued fora specific reason.

In this chapter, the term test piece is usedfor what is often called a specimen. This ter-


minology is based on the convention estab-lished by ISO Technical Committee 17, Steelin ISO 377-1, “Selection and Preparation ofSamples and Test Pieces of Wrought Steel,”where terms for a test unit, a sample product,sample, rough specimen, and test piece are de-fined as follows:

● Test unit: The quantity specified in an orderthat requires testing (for example, 10 tons of3⁄4 in. bars in random lengths)

● Sample product: Item (in the previous ex-ample, a single bar) selected from a test unitfor the purpose of obtaining the test pieces

● Sample: A sufficient quantity of materialtaken from the sample product for the pur-pose of producing one or more test pieces.In some cases, the sample may be the sampleproduct itself (i.e., a 2 ft length of the sampleproduct).

● Rough specimen: Part of the sample havingundergone mechanical treatment, followed

Fig. 18 General flow chart of the tensile test per procedures in ASTM E 8. Relevant paragraph numbers from ASTM E 8 are shownin parentheses.


Fig. 20 System for identifying the axes of test-piece orienta-tion in various product forms. (a) Flat-rolled products.

(b) Cylindrical sections. (c) Tubular products

Fig. 19 Illustration of ISO terminology used to differentiatebetween sample, specimen, and test piece (see text

for definitions of test unit, sample product, sample, rough speci-men, and test piece). As an example, a test unit may be a 250-ton heat of steel that has been rolled into a single thickness ofplate. The sample product is thus one plate from which a singletest piece is obtained.

by heat treatment where appropriate, for thepurpose of producing test pieces; in the ex-ample, the sample is the rough specimen.

● Test piece: Part of the sample or rough spec-imen, with specified dimensions, machinedor unmachined, brought to the required con-dition for submission to a given test. If a test-ing machine with sufficient force capacity isavailable, the test piece may be the roughspecimen; if sufficient capacity is not avail-able, or for another reason, the test piece maybe machined from the rough specimen to di-mensions specified by a standard.

These terms are shown graphically in Fig. 19.As can be seen, the test piece, or what is com-monly called a specimen, is a very small part ofthe entire test unit.

Description of Test Material

Test-Piece Orientation. Orientation and lo-cation of a test material from a product can in-fluence measured tensile properties. Althoughmodern metal-working practices, such as crossrolling, have tended to reduce the magnitude ofthe variations in the tensile properties, it mustnot be neglected when locating the test piecewithin the specimen or the sample.

Because most materials are not isotropic, test-piece orientation is defined with respect to a setof axes as shown in Fig. 20. These terms for theorientation of the test-piece axes in Fig. 20 arebased on the convention used by ASTM. Thisscheme is identical to that used by the ISO Tech-nical Committee 164 “Mechanical Testing,” al-though the L, T, and S axes are referred to as theX, Y, and Z axes, respectively, in the ISO doc-uments.

When a test is being performed to determineconformance to a product standard, the product

standard must state the proper orientation of thetest piece with regard to the axis of prior work-ing, (e.g., the rolling direction of a flat product).Because alloy systems behave differently, nogeneral rule of thumb can be stated on how priorworking may affect the directionality of prop-erties. As can be seen in Table 1, the longitudinalstrengths of steel are generally somewhat lessthan the transverse strength. However, for alu-minum alloys, the opposite is generally true.

Many standards, such as ASTM A 370, E 8,and B 557, provide guidance in the selection oftest-piece orientation relative to the rolling di-rection of the plate or the major forming axes ofother types of products and in the selection ofspecimen and test-piece location relative to thesurface of the product. Orientation is also im-portant when characterizing the directionality ofproperties that often develops in the microstruc-ture of materials during processing. For exam-ple, some causes of directionality include the fi-bering of inclusions in steels, the formation ofcrystallographic textures in most metals and al-loys, and the alignment of molecular chains inpolymers.

The location from which a test material istaken from the initial product form is important


Fig. 21 Nomenclature for a typical tensile test piece

Table 1 Effect of test-piece orientation on tensile properties

Orientation Yield strength, ksi Tensile strength, ksi Elongation in 50 mm (2 in.), % Reduction of area, %

ASTM A 572, Grade 50 (3⁄4 in. thick plate, low sulfur level)

Longitudinal 58.8 84.0 27.0 70.2Transverse 59.8 85.2 28.0 69.0

ASTM A 656, Grade 80 (3⁄4 in. thick plate, low sulfur level � controlled rolled)


ASTM A 5414 (3⁄4 in. thick plate, low sulfur level)


Source: Courtesy of Francis J. Marsh

because the manner in which a material is pro-cessed influences the uniformity of microstruc-ture along the length of the product as well asthrough its thickness properties. For example,the properties of metal cut from castings are in-fluenced by the rate of cooling and by shrinkagestresses at changes in section. Generally, testpieces taken from near the surface of iron cast-ings are stronger. To standardize test results rela-tive to location, ASTM A 370 recommends thattensile test pieces be taken from midway be-tween the surface and the center of round,square, hexagon, or octagonal bars. ASTM E 8recommends that test pieces be taken from thethickest part of a forging from which a test cou-pon can be obtained, from a prolongation of theforging, or in some cases, from separately forgedcoupons representative of the forging.

Test-Piece Geometry

As previously noted, the item being testedmay be either the full cross section of the item,

or a portion of the item that has been machinedto specific dimensions. This chapter focuses ontensile testing with test pieces that are machinedfrom rough samples. Component testing is dis-cussed in Chapter 12, “Tensile Testing of Com-ponents.”

Test-piece geometry is often influenced byproduct form. For example, only test pieces withrectangular cross sections can be obtained fromsheet products. Test pieces taken from thickplate may have either flat (plate-type) or roundcross sections. Most tensile-test specificationsshow machined test pieces with either circularcross sections or rectangular cross sections. No-menclature for the various sections of amachined test piece are shown in Fig. 21. Mosttensile-test specifications present a set of dimen-sions, for each cross-section type, that are stan-dard, as well as additional sets of dimensions foralternative test pieces. In general, the standarddimensions published by ASTM, ISO, JIS, andDIN are similar, but they are not identical.


Gage lengths and standard dimensions formachined test pieces specified in ASTM E 8 areshown in Fig. 22(a) and (b) for rectangular andround test pieces. From this figure, it can be seenthat the gage length is proportionally four times(4 to 1) the diameter (or width) of the test piecefor the standard machined round test pieces andthe sheet-type, rectangular test pieces. Thelength of the reduced section is also a minimumof 41⁄2 times the diameter (or width) of these test-piece types. These relationships do not apply toplate-type rectangular test pieces.

Many specifications outside the United Statesrequire that the gage length of a test piece be afixed ratio of the square root of the cross-sec-tional area, that is:

1/2Gage length � constant x (cross-sectional area)

The value of this constant is often specified as5.65 or 11.3 and applies to both round and rec-tangular test pieces. For machined round testpieces, a value of 5.65 results in a 5-to-1 rela-tionship between the gage length and the diam-eter.

Many tensile-test specifications permit aslight taper toward the center of the reduced sec-tion of machined test pieces so that the minimumcross section occurs at the center of the gagelength and thereby tends to cause fracture to oc-cur at the middle of the gage length. ASTM E 8specifies that this taper cannot exceed 1% andrequires that the taper is the same on both sidesof the midlength.

When test pieces are machined, it is importantthat the longitudinal centerline of the reducedsection be coincident with the longitudinal cen-terlines of the grip ends. In addition, for the rec-tangular test pieces, it is essential that the centersof the transition radii at each end of the reducedsection are on common lines that are perpendic-ular to the longitudinal centerline. If any of theserequirements is violated, bending will occur,which may affect test results.

The transition radii between the reduced sec-tion and the grip ends can be critical for testpieces from materials with very high strength orwith very little ductility or both. This is dis-cussed more fully in the section “Effect of StrainConcentrations” in this chapter.

Measurement of Initial Test-Piece Dimen-sions. Machined test pieces are expected to meetsize specifications, but to ensure dimensional ac-curacy, each test piece should be measured priorto testing. Gage length, fillet radius, and cross-sectional dimensions are measured easily. Cylin-

drical test pieces should be measured for concen-tricity. Maintaining acceptable concentricity isextremely important in minimizing unintendedbending stresses on materials in a brittle state.

Measurement of Cross-Sectional Dimensions.The test pieces must be measured to determinewhether they meet the requirements of the testmethod. Test-piece measurements must also de-termine the initial cross-sectional area when it iscompared against the final cross section aftertesting as a measure of ductility.

The precision with which these measurementsare made is based on the requirements of the testmethod, or if none are given, on good engineer-ing judgment. Specified requirements of ASTME 8 are summarized as follows:

● For referee testing of test pieces under 3⁄16 in.in their least dimension, the dimensionsshould be measured where the least cross-sectional area is found.

● For cross sectional dimensions of 0.200 in.or more, cross-sectional dimensions shouldbe measured and recorded to the nearest0.001 in.

● For cross sectional dimensions from 0.100in. but less than 0.200 in., cross-sectional di-mensions should be measured and recordedto the nearest 0.0005 in.

● For cross sectional dimensions from 0.020in. but less than 0.100 in., cross-sectional di-mensions should be measured and recordedto the nearest 0.0001 in.

● When practical, for cross-sectional dimen-sions less than 0.020 in., cross-sectional di-mensions should be measured to the nearest1%, but in all cases, to at least the nearest0.0001 in.

ASTM E 8 goes on to state how to determinethe cross-sectional area of a test piece that has anonsymmetrical cross section using the weightand density. When measuring dimensions of thetest piece, ASTM E 8 makes no distinction be-tween the shape of the cross section for standardtest pieces.

Measurement of the Initial Gage Length.ASTM E 8 assumes that the initial gage lengthis within specified tolerance; therefore, it is nec-essary only to verify that the gage length of thetest piece is within the tolerance.

Marking Gage Length. As shown in the flowdiagram in Fig. 18, measurement of elongationrequires marking the gage length of the testpiece. The gage marks should be placed on thetest piece in a manner so that when fracture oc-curs, the fracture will be located within the cen-


Fig. 22(b) Example of a round tensile test piece per ASTM E 8.

Fig. 22(a) Example of rectangular (flat) tensile test pieces per ASTM E 8.


ter one-third of the gage length (or within thecenter one-third of one of several sets of gage-length marks). For a test piece machined with areduced-section length that is the minimumspecified by ASTM E 8 and with a gage lengthequal to the maximum allowed for that geome-try, a single set of marks is usually sufficient.However, multiple sets of gage lengths must beapplied to the test piece to ensure that one setspans the fracture under any of the followingconditions:

● Testing full-section test pieces● Testing pieces with reduced sections signifi-

cantly longer than the minimum● Test requirements specify a gage length that

is significantly shorter than the reduced sec-tion

For example, some product specifications re-quire that the elongation be measured over a 2in. gage length using the machined plate-typetest piece with a 9 in. reduced section (Fig. 22a).In this case, it is recommended that a staggeredseries of marks (either in increments of 1 in.when testing to ASTM E 8 or in increments of25.0 mm when testing to ASTM E 8M) beplaced on the test piece such that, after fracture,the elongation can be measured using the set thatbest meets the center-third criteria. Many ten-sile-test methods permit a retest when the elon-gation is less than the minimum specified by aproduct specification if the fracture occurredoutside the center third of the gage length. Whentesting full-section test pieces and determining

elongation, it is important that the distance be-tween the grips be greater than the specifiedgage length unless otherwise specified. As a ruleof thumb, the distance between grips should beequal to at least the gage length plus twice theminimum dimension of the cross section.

The gage marks may be marks made with acenter punch, or may be lines scribed using asharp, pointed tool, such as a machinist’s scribe(or any other means that will establish the gagelength within the tolerance permitted by the testmethod). If scribed lines are used, a broad lineor band may first be drawn along the length ofthe test piece using machinist’s layout ink (or asimilar substance), and the gage marks are madeon this line. This practice is especially helpfulto improve visibility of scribed gage marks afterfracture. If punched marks are used, a circlearound each mark or other indication made byink may help improve visibility after fracture.Care must be taken to ensure that the gagemarks, especially those made using a punch, arenot deep enough to become stress raisers, whichcould cause the fracture to occur through them.This precaution is especially important whentesting materials with high strength and low duc-tility.

Notched Test Pieces. Tensile test pieces aresometimes intentionally notched in the center ofthe gage length (Fig. 23). ASTM E 338 and E602 describe procedures for testing notched testpieces. Results obtained using notched testpieces are useful for evaluating the response ofa material to a localized stress concentration.

Fig. 23 Example of notched tensile-test test piece per ASTM E 338, “Standard Test Method of Sharp-Notch Tension Testing of High-Strength Sheet Materials”


Additional information on the notch tensile testand a discussion of the related material charac-teristics (notch sensitivity and notch strength)can be found in Chapter 2, “Mechanical Behav-ior of Materials under Tensile Loads.” The effectof stress (or strain) concentrations is also dis-cussed in the section “Effect of Strain Concen-trations” in this chapter.

Surface Finish and Condition. The finish ofmachined surfaces usually is not specified in ge-neric test methods (that is, a method that is notwritten for a specific item or material) becausethe effect of finish differs for different materials.For example, test pieces from materials that arenot high strength or that are ductile are usuallyinsensitive to surface finish effects. However, ifsurface finish in the gage length of a tensile testpiece is extremely poor (with machine toolmarks deep enough to act as stress-concentratingnotches, for example), test results may exhibit atendency toward decreased and variable strengthand ductility.

It is good practice to examine the test piecesurface for deep scratches, gouges, edge tears,or shear burrs. These discontinuities may some-times be minimized or removed by polishing or,if necessary, by further machining; however, di-mensional requirements often may no longer bemet after additional machining or polishing. Inall cases, the reduced sections of machined testpieces must be free of detrimental characteris-tics, such as cold work, chatter marks, grooves,gouges, burrs, and so on. Unless one or more ofthese characteristics is typical of the product be-ing tested, an unmachined test piece must alsobe free of these characteristics in the portion ofthe test piece that is between the gripping de-vices. When rectangular test pieces are preparedfrom thin-gage sheet material by shearing(punching) using a die the shape of the testpiece, ASTM E 8 states that the sides of thereduced section may need to be further ma-chined to remove the cold work and shear burrsthat occur when the test piece is sheared fromthe rough specimen. This method is impracticalfor material less than 0.38 mm (0.015 in.) thick.Burrs on test pieces can be virtually eliminatedif punch-to-die clearances are minimized.

Test Setup

The setup of a tensile test involves the instal-lation of a test piece in the load frame of a suit-able test machine. Force capacity is the most im-

portant factor of a test machine. Other testmachine factors, such as calibration and load-frame rigidity, are discussed in more detail inChapter 4, “Tensile Testing Equipment andStrain Sensors.” The other aspects of the testsetup include proper gripping and alignment ofthe test piece, and the installation of extensom-eters or strain sensors when plastic deformation(yield behavior) of the piece is being measured,as described below.

Gripping Devices. The grips must furnish anaxial connection between the test piece and thetesting machine; that is, the grips must not causebending in the test piece during loading. Thechoice of grip is primarily dependent on the ge-ometry of the test piece and, to a lesser degree,on the preference of the test laboratory. That is,rarely do tension-test methods or requirementsspecify the method of gripping the test pieces.

Figure 24 shows several of the many gripsthat are in common use, but many other designsare also used. As can be seen, the gripping de-vices can be classified into several distinct types,wedges, threaded, button, and snubbing. Wedgegrips can be used for almost any test-piece ge-ometry; however, the wedge blocks must be de-signed and installed in the machine to ensureaxial loading. Threaded grips and button gripsare used only for machined round test pieces.Snubbing grips are used for wire (as shown) orfor thin, rectangular test pieces, such as thosemade from foil.

As shown in Fig. 22, the dimensions of thegrip ends for machined round test pieces are usu-ally not specified, and only approximate dimen-sions are given for the rectangular test pieces.Thus, each test lab must prepare/machine gripends appropriate for its testing machine. For ma-chined-round test pieces, the grip end is oftenthreaded, but many laboratories prefer either aplain end, which is gripped with the wedges inthe same manner as a rectangular test piece, orwith a button end that is gripped in a matingfemale grip. Because the principal disadvantageof a threaded grip is that the pitch of the threadstend to cause a bending moment, a fine-seriesthread is often used.

Bending stresses are normally not criticalwith test pieces from ductile materials. How-ever, for test pieces from materials with limitedductility, bending stresses can be important, bet-ter alignment may be required. Button grips areoften used, but adequate alignment is usuallyachieved with threaded test pieces. ASTM E 8also recommends threaded gripping for brittle


Fig. 24 Examples of gripping methods for tensile test pieces. (a) Round specimen with threaded grips. (b) Gripping with serratedwedges with hatched region showing bad practice of wedges extending below the outer holding ring. (c) Butt-end specimen

constrained by a split collar. (d) Sheet specimen with pin constraint. (e) Sheet specimen with serrated-wedge grip with hatched regionshowing the bad practice of wedges extended below the outer holding ring. (f ) Gripping device for threaded-end specimen. (g) Grippingdevice for sheet and wire. (h) Snubbing device for testing wire

materials. The principal disadvantage of the but-ton-end grip is that the diameter of the button orthe base of the cone is usually at least twice thediameter of the reduced section, which necessi-tates a larger, rough specimen and more metalremoval during machining.

Alignment of the Test Piece. The force-application axis of the gripping device must co-incide with the longitudinal axis of symmetry ofthe test piece. If these axes do not coincide, thetest piece will be subjected to a combination ofaxial loading and bending. The stress acting onthe different locations in the cross section of thetest piece then varies, from the sum of the axialand bending stresses on one side of the testpiece, to the difference between the two stresses

on the other side. Obviously, yielding will beginon the side where the stresses are additive andat a lower apparent stress than would be the caseif only the axial stress were present. For this rea-son, the yield stress may be lowered, and theupper yield stress would appear suppressed intest pieces that normally exhibit an upper yieldpoint. For ductile materials, the effect of bendingis minimal, other than the suppression of the up-per yield stress. However, if the material has lit-tle ductility, the increased strain due to bendingmay cause fracture to occur at a lower stress thanif there were no bending.

Similarly, if the test piece is initially bent, forexample, coil set in a machined-rectangularcross section or a piece of rod being tested in a


full section, bending will occur as the test piecestraightens, and the problems exist.

Methods for verification of alignment are de-scribed in ASTM E 1012.

Extensometers. When the tensile test re-quires the measurement of strain behavior (i.e.,the amount of elastic and/or plastic deformationoccurring during loading), extensometers mustbe attached to the test piece. The amount ofstrain can be quite small (e.g., approximately0.5% or less for elastic strain in steels), and ex-tensometers and other strain-sensing systems aredesigned to magnify strain measurement into ameaningful signal for data processing.

Several types of extensometers are available,as described in more detail in Chapter 4, “Ten-sile Testing Equipment and Strain Sensors.” Ex-tensometers generally have fixed gage lengths.If an extensometer is used only to obtain a por-tion of the stress-strain curve sufficient to deter-mine the yield properties, the gage length of theextensometer may be shorter than the gagelength required for the elongation-at-fracturemeasurement. It may also be longer, but in gen-eral, the extensometer gage length should notexceed approximately 85% of the length of thereduced section or the distance between the gripsfor test pieces without reduced sections. Na-tional and international standardization groupshave prepared practices for the classification ofextensometers, as described in Chapter 4. Ex-tensometer classifications usually are based onerror limits of a device, as in ASTM E 83 “Stan-dard Practice for Verification and Classificationof Extensometers.”

Temperature Control. Tensile testing issometimes performed at temperatures other thanroom temperature. ASTM E 21 describes stan-dard procedures for elevated-temperature tensiletesting of metallic materials, which is describedfurther in Chapter 13, “Hot Tensile Testing.”ASTM E 1450 describes standard procedures fortensile testing of structural alloys in liquid he-lium (cryogenic testing), which is described fur-ther in Chapter 14, “Tensile Testing at Low Tem-peratures.”

Temperature gradients may occur in tempera-ture-controlled systems, and gradients must bekept within tolerable limits. It is not uncommonto use more than one temperature-sensing device(e.g., thermocouples) when testing at other thanroom temperature. Besides the temperature-sensing device used in the control loop, auxiliarysensing devices may be used to determinewhether temperature gradients are present alongthe gage length of the test piece.

Temperature control is also a factor duringroom-temperature tests because deformation ofthe test piece causes generation of heat withinit. Test results have shown that the heating thatoccurs during the straining of a test piece can besufficient to significantly change the propertiesthat are determined because material strengthtypically decreases with an increase in the testtemperature. When performing a test to dupli-cate the results of others, it is important to knowthe test speed and whether any special proce-dures were taken to remove the heat generatedby straining the test piece.

Test Procedures

After the test piece has been properly pre-pared and measured and the test setup estab-lished, conducting the test is fairly routine. Thetest piece is installed properly in the grips, andif required, extensometers or other strain-mea-suring devices are fastened to the test piece formeasurement and recording of extension data.Data acquisition systems also should bechecked. In addition, it is sometimes useful torepetitively apply small initial loads and vibratethe load train (a metallographic engraving toolis a suitable vibrator) to overcome friction invarious couplings, as shown in Fig. 25(a) and(b). A check can also be run to ensure that thetest will run at the proper testing speed and tem-perature. The test is then begun by initiatingforce application.

Speed of Testing

The speed of testing is extremely importantbecause mechanical properties are a function ofstrain rate, as discussed in the section “Effect ofStrain Rate” in this chapter. It is, therefore, im-perative that the speed of testing be specified ineither the tension-test method or the productspecification.

In general, a slow speed results in lowerstrength values and larger ductility values thana fast speed; this tendency is more pronouncedfor lower-strength materials than for higher-strength materials and is the reason that a tensiontest must be conducted within a narrow test-speed range.

In order to quantify the effect of deformationrate on strength and other properties, a specificdefinition of testing speed is required. A con-ventional (quasi-static) tensile test, for example,ASTM E 8, prescribes upper and lower limits on


Fig. 25 (a) Effectiveness of vibrating the load train to overcome friction in the spherical ball and seat couplings shown in Fig. 25(b).(b) Spherically seated gripping device for shouldered tensile test piece

the deformation rate, as determined by one ofthe following methods during the test:

● Strain rate● Stress rate (when loading is below the pro-

portional limit)● Cross-head separation rate (or free-running

cross-head speed) during the test● Elapsed time

These methods are listed in order of decreasingprecision, except during the occurrence of up-per-yield-strength behavior and yield point elon-gation (YPE) (where the strain rate may not nec-essarily be the most precise method). For somematerials, elapsed time may be adequate, whilefor other materials, one of the remaining meth-ods with higher precision may be necessary inorder to obtain test values within acceptable lim-its. ASTM E 8 specifies that the test speed mustbe slow enough to permit accurate determinationof forces and strains. Although the speeds spec-ified by various test methods may differ some-what, the test speeds for these methods areroughly equivalent in commercial testing.

Strain rate is expressed as the change instrain per unit time, typically expressed in unitsof min�1 or s�1 because strain is a dimension-less value expressed as a ratio of change inlength per unit length. The strain rate can usuallybe dialed, or programmed, into the control set-

tings of a computer-controlled system or pacedor timed for other systems.

Stress rate is expressed as the change instress per unit of time. When the stress rate isstipulated, ASTM E 8 requires that it not exceed100 ksi/min. This number corresponds to anelastic strain rate of about 5 � 10�5 s�1 forsteel or 15 � 10�5 s�1 for aluminum. As withstrain rate, stress rate usually can be dialed orprogrammed into the control settings of com-puter-controlled test systems. However, becausemost older systems indicate force being applied,and not stress, the operator must convert stressto force and control this quantity. Many ma-chines are equipped with pacing or indicatingdevices for the measurement and control of thestress rate, but in the absence of such a device,the average stress rate can be determined with atiming device by observing the time required toapply a known increment of stress. For example,for a test piece with a cross section of 0.500 in.by 0.250 in. and a specified stress rate of100,000 psi/min, the maximum force applicationrate would be 12,500 lbf/min (force � stressrate � area � 100,000 psi/min � (0.500 in. �0.250 in.)). A minimum rate of 1⁄10 of the max-imum rate is usually specified.

Comparison between Strain-Rate andStress-Rate Methods. Figure 26 comparesstrain-rate control with stress-rate control for de-


scribing the speed of testing. Below the elasticlimit, the two methods are identical. However,as shown in Fig. 26, once the elastic limit isexceeded, the strain rate increases when a con-stant stress rate is applied. Alternatively, thestress rate decreases when a constant strain rateis specified. For a material with discontinuousyielding and a pronounced upper yield spike(Fig. 7a), it is a physical impossibility for thestress rate to be maintained in that region be-cause, by definition, there is not a sustained in-crease in stress in this region. For these reasons,the test methods usually specify that the rate(whether stress rate or strain rate) is set prior tothe elastic limit (EL), and the crosshead speedis not adjusted thereafter. Stress rate is not ap-plicable beyond the elastic limit of the material.Test methods that specify rate of straining expectthe rate to be controlled during yield; this min-imizes effects on the test due to testing machinestiffness.

The rate of separation of the grips (or rateof separation of the cross heads or the cross-headspeed) is a commonly used method of specifyingthe speed of testing. In ASTM A 370, for ex-ample, the specification of test speed is that“through the yield, the maximum speed shall notexceed 1⁄16 in. per inch of reduced section perminute; beyond yield or when determining ten-sile strength alone, the maximum speed shall notexceed 1⁄2 in. per inch of reduced section perminute. For both cases, the minimum speed shallbe greater than 1⁄10 of this amount.” This meansthat for a machined round test piece with a 21⁄4

in. reduced section, the rate prior to yielding canrange from a maximum of 9⁄64 in./min (i.e., 21⁄4in. reduced-section length � 1⁄16 in./min) downto 9⁄640 in./min (i.e., 21⁄4 in. reduced-sectionlength � 1⁄160 in./min).

The elapsed time to reach some event,such as the onset of yielding or the tensilestrength, or the elapsed time to complete the test,is sometimes specified. In this case, multiple testpieces are usually required so that the correct testspeed can be determined by trial and error.

Many test methods permit any speed of test-ing below some percentage of the specified yieldor tensile strength to allow time to adjust theforce application mechanism, ensure that the ex-tensometer is working, and so on. Values of 50and 25%, respectively, are often used.

Post-Test Measurements

After the test has been completed, it is oftenrequired that the cross-sectional dimensionsagain be measured to obtain measures of ductil-ity. ASTM E 8 states that measurements madeafter the test shall be to the same accuracy as theinitial measurements.

Method E 8 also states that upon completionof the test, gage lengths 2 in. and under are tobe measured to the nearest 0.01 in., and gagelengths over 2 in. are to be measured to the near-est 0.5%. The document goes on to state that apercentage scale reading to 0.5% of the gagelength may be used. However, if the tensile test

Fig. 26 Illustration of the differences between constant stress increments and constant strain increments. (a) Equal stress increments(increasing strain increments). (b) Equal strain increments (decreasing stress increments)


Fig. 28 Contour maps of (a) constant yield strength (0.5% elongation under load, ksi) and (b) constant tensile strength (ksi) for aplate of alloy steel

is being performed as part of a product specifi-cation, and the elongation is specified to meet avalue of 3% or less, special techniques, whichare described, are to be used to measure the finalgage length. These measurements are discussedin a previous section, “Elongation,” in this chap-ter.

Variability of Tensile Properties

Even carefully performed tests will exhibitvariability because of the nonhomogenous na-ture of metallic materials. Figure 27 (Ref 10)shows the three-sigma distribution of the offsetyield strength and tensile strength values thatwere obtained from multiple tests on a singlealuminum alloy. Distribution curves are pre-sented for the results from multiple tests of asingle sheet and for the results from tests on anumber of sheets from a number of lots of the

same alloy. Because these data are plotted withthe minus three-sigma value as zero, it appearsthere is a difference between the mean values;however, this appearance is due only to the waythe data are presented. Figures 28(a) and (b)show lines of constant offset yield strength andconstant tensile strength, respectively, for a 1 in.thick, quenched and tempered plate of an alloysteel. In this case, rectangular test pieces 11⁄2 in.wide were taken along the transverse direction(T orientation in Fig. 20) every 3 in. along eachof the four test-piece centerlines shown. Thesedata indicate that the yield and tensile strengthsvary greatly within this relatively small sampleand that the shape and location of the yieldstrength contour lines are not the same as theshape and location of the tensile strength lines.

Effect of Strain Concentrations. Duringtesting, strain concentrations (often called stressconcentrations) occur in the test piece wherethere is a change in the geometry. In particular,

Fig. 27 Distribution of (a) yield and (b) tensile strengths for multiple tests on single sheet and on multiple lots of aluminum alloy7075-T6. Source: Ref 10


the transition radii between the reduced sectionand the grip ends are important, as previouslynoted in the section “Test-Piece Geometry.”Most test methods specify a minimum value forthese radii. However, because there is a changein geometry, there is still a strain concentrationat the point of tangency between the radii andthe reduced section. Figure 29(a) (Ref 11) showsa test piece of rubber with an abrupt change ofsection, which is a model of a tensile test piecein the transition region. Prior to applying theforce at the ends of the model, a rectangular gridwas placed on the test piece. When force is ap-plied, it can be seen that the grid is severelydistorted at the point of tangency but to a muchlesser degree at the center of the model. The dis-tortion is a visual measure of strain. The straindistribution across section n-n is plotted in Fig.29(b). From the stress-strain curve for the ma-terial (Fig. 29c), the stresses on this section can

be determined. It is apparent that the test piecewill yield at the point of tangency prior to gen-eral yielding in the reduced section. The ratiobetween the nominal strain and actual, maxi-mum strain is often referred to as the strain-con-centration factor, or the stress-concentration fac-tor if the actual stress is less than the elasticlimit. This ratio is often abbreviated as kt. Stud-ies have shown that kt is about 1.25 when theradii are 1⁄2 in., the width (or diameter) of thereduced section is 0.500 in., and the width (ordiameter) of the grip end is 3⁄4 in. That is, theactual strain or the actual elastic stress at thetransition (if less than the yield of the material)is 25% greater than would be expected withoutconsideration of the strain or stress concentra-tion. The value of kt decreases as the radii in-

Fig. 29 Effect of strain concentrations on section n-n. (a)Strain distribution caused by an abrupt change in

cross section (grid on sheet of rubber) (Ref 11). (b) Schematic ofstrain distribution on cross section (Ref 11). (c) Calculation ofstresses at abrupt change in cross section n-n by graphical means

Fig. 31 Stress-strain curves for tests conducted at “normal”and “zero” strain rates

Fig. 30 Effect of strain rate on the ratio of dynamic yield-stress and static yield-stress level of A36 structural

steel. Source: Ref 12


crease such that, for the above example, if theradii are 1.0 in., and kt decreases to about 1.15.

Various techniques have been tried to mini-mize kt, including the use of spirals instead ofradii, but there will always be strain concentra-tion in the transition region. This indicates thatthe yielding of the test piece will always initiateat this point of tangency and proceed towardmidlength. For these reasons, it is extremely im-portant that the radii be as large as feasible whentesting materials with low ductility.

Strain concentrations can be caused bynotches deliberately machined in the test piece,nicks from accidental causes, or shear burrs, ma-chining marks, or gouges that occur during thepreparation of the test piece or from many othercauses.

Effect of Strain Rate. Although the mechan-ical response of different materials varies, thestrength properties of most materials tend to in-crease at higher strain rates. For example, thevariability in yield strength of ASTM A 36

Fig. 32 Effect of temperature and strain rate on (a) tensile strength and (b) yield strength of 21⁄4 Cr-1 Mo Steel. Note: Strain-rate rangepermitted by ASTM Method E 8 when determining yield strength at room temperature is indicated. Source: Ref 13


structural steel over a limited range of strainrates is shown in Fig. 30 (Ref 12). A “zero-strain-rate” stress-strain curve (Fig. 31) is gen-erated by applying forces to a test piece to obtaina small plastic strain and then maintaining thatstrain until the force ceases to decrease (PointA). Force is reapplied to the test piece to obtainanother increment of plastic strain, which ismaintained until the force ceases to decrease(Point B). This procedure is continued for sev-eral more cycles. The smooth curve fittedthrough Points A, B, and so on is the “zero-strain-rate” stress-strain curve, and the yieldvalue is determined from this curve.

The effect of strain rate on strength dependson the material and the test temperature. Figure32 (Ref 13) shows graphs of tensile strength andyield strength for a common heat-resistant low-alloy steel (21⁄4Cr-1Mo) over a wide range oftemperatures and strain rates. In this figure, thestrain rates were generally faster than those pre-scribed in ASTM E 8.

Another example of strain effects on strengthis shown in Fig. 33 (Ref 14). This figure illus-trates true yield stress at various strains for alow-carbon steel at room temperature. Betweenstrain rates of 10�6 s�1 and 10�3 s�1 (a thou-sandfold increase), yield stress increases only by10%. Above 1 s�1, however, an equivalent rateincrease doubles the yield stress. For the data inFig. 33, at every level of strain the yield stressincreases with increasing strain rate. However, adecrease in strain-hardening rate is exhibited atthe higher deformation rates. For a low-carbonsteel tested at elevated temperatures, the effectsof strain rate on strength can become more com-plicated by various metallurgical factors such asdynamic strain aging in the “blue brittleness”region of some mild steels (Ref 14).

Structural aluminum is less strain-rate sensi-tive than steels. Figure 34 (Ref 15) shows dataobtained for 1060-O aluminum. Between strainrates of 10�3 s�1 and 103 s�1 (a millionfoldincrease), the stress at 2% plastic strain increasesby less than 20%.

ACKNOWLEDGMENT

This article was adapted from J.M. Holt, Uni-axial Tension Testing, Mechanical Testing andEvaluation, Volume 8, ASM Handbook, ASMInternational, 2000, p 124–142

REFERENCES

1. D. Lewis, Tensile Testing of Ceramics andCeramic-Matrix Composites, Tensile Test-ing, P. Han, Ed., ASM International, 1992,p 147–182

2. R.J. Del Vecchio, Tensile Testing of Elas-tomers, Tensile Testing, P. Han, Ed., ASMInternational, 1992, p 135–146

3. N.E. Dowling, Mechanical Behavior of Ma-terials—Engineering Methods for Defor-mation, Fracture, and Fatigue, 2nd ed.,Prentice Hall, 1999, p 123

4. R.L. Brockenbough and B.G. Johnson,“Steel Design Manual,” United States SteelCorporation, ADUSS 27 3400 03, 1974, p2–3

5. P.M. Mumford, Test Methodology and DataAnalysis, Tensile Testing, P. Han, Ed., ASMInternational, 1992, p 55

6. “Standard Test Method for Young’s Modu-Fig. 34 Uniaxial stress/strain/strain rate data for aluminum

1060-O. Source: Ref 15

Fig. 33 True stresses at various strains vs. strain rate for a low-carbon steel at room temperature. The top line in the

graph is tensile strength, and the other lines are yield points forthe indicated level of strain. Source: Ref 14


lus, Tangent Modulus, and Chord Modu-lus,” E 111, ASTM

7. Making, Shaping, and Treating of Steel,10th ed., U.S. Steel, 1985, Fig. 50-12 and50-13

8. “Standard Test Methods and Definitions forMechanical Testing of Steel Products,” A370, Annex 6, Annual Book of ASTM Stan-dards, ASTM, Vol 1.03

9. “Conversion of Elongation Values, Part 1:Carbon and Low-Alloy Steels,” 2566/1, In-ternational Organization for Standardiza-tion, revised 1984

10. W.P. Goepfert, Statistical Aspects of Me-chanical Property Assurance, Reproducibil-ity and Accuracy of Mechanical Tests, STP626, ASTM, 1977, p 136–144

11. F.B. Seely and J.O. Smith, Resistance ofMaterials, 4th ed., John Wiley & Sons, p 45

12. N.R.N. Rao et al., “Effect of Strain Rate onthe Yield Stress of Structural Steel,” FritzEngineering Laboratory Report 249.23,1964

13. R.L. Klueh and R.E. Oakes, Jr., High Strain-Rate Tensile Properties of 21⁄4 Cr-1 MoSteel, J. Eng. Mater. Technol., Oct 1976, p361–367

14. M.J. Manjoine, Influence of Rate of Strainand Temperature on Yield Stresses of MildSteel, J. Appl. Mech., Vol 2, 1944, p A-211to A-218

15. A.H. Jones, C.J. Maiden, S.J. Green, and H.Chin, Prediction of Elastic-Plastic WaveProfiles in Aluminum 1060-O under Uni-axial Strain Loading, Mechanical Behaviorof Materials under Dynamic Loads, U.S.

Lindholm, Ed., Springer-Verlag, 1968, p254–269

SELECTED REFERENCES

● “Standard Method of Sharp-Notch TensionTesting of High-Strength Sheet Materials,”E 338, ASTM

● “Standard Method of Sharp-Notch TensionTesting with Cylindrical Specimens,” E 602,ASTM

● “Standard Methods and Definitions for Me-chanical Testing of Steel Products,” A 370,ASTM

● “Standard Methods of Tension Testing ofMetallic Foil,” E 345, ASTM

● “Standard Test Methods for Poisson’s Ratioat Room Temperature,” E 132, ASTM

● “Standard Test Methods for Static Determi-nation of Young’s Modulus of Metals at Lowand Elevated Temperatures,” E 231, ASTM

● “Standard Test Methods for Young’s Mod-ulus, Tangent Modulus, and Chord Modu-lus,” E 111, ASTM

● “Standard Methods of Tension Testing ofMetallic Materials,” E 8, ASTM

● “Standard Methods of Tension TestingWrought and Cast Aluminum- and Magne-sium-Alloy Products,” B 557, ASTM

● “Standard Recommended Practice for Ele-vated Temperature Tension Tests of MetallicMaterials,” E 21, ASTM

● “Standard Recommended Practice for Veri-fication of Specimen Alignment Under Ten-sile Loading,” E 1012, ASTM

CHAPTER 4

Tensile TestingEquipment and Strain Sensors

Fig. 1 Screw-driven balance-beam universal testing machine(1890 model)

TENSILE-TESTING EQUIPMENT consistsof several types of devices used to apply con-trolled tensile loads to test specimens (testpieces). The equipment is capable of varying thespeed of load application and accurately mea-sures the forces, strains, and elongations appliedto the test piece.

Commercial tensile-testing equipment be-came available in the late 1800s. The earliestequipment used manual methods, such as handcranks, to apply the load. In 1890, Tinius Olsenwas granted a patent on the “Little Giant,” ahand-cranked, 180 kN (40,000 lbf ) capacitytesting machine. In 1891, Olsen produced thefirst autographic machine capable of producinga stress-strain diagram (Ref 1). An example ofan 1890 machine is shown in Fig. 1. Tensile test-ing equipment has evolved from purely mechan-ical machines to more advanced electromechan-ical and servohydraulic machines with advanceelectronics and microcomputers. Electronic cir-cuitry and microprocessors have increased thereliability of experimental data, while reducingthe time to analyze information. This transitionhas made it possible to determine rapidly andwith great precision ultimate tensile strength andelongation, yield strength, modulus of elasticity,and other mechanical properties. Current equip-ment manufacturers also offer workstation con-figurations that automate mechanical testing.

Conventional test machines for measuringmechanical properties include tension testers,compression testers, or the more versatile uni-versal testing machine (UTM) (Ref 2). UTMshave the capability to test material in tension,compression, or bending. The word universal re-fers to the variety of stress states that can bestudied. UTMs can load material with a single,continuous (monotonic) pulse or in a cyclic

manner. Other conventional test machines maybe limited to either tensile loading or compres-sive loading, but not both. These machines haveless versatility than UTM equipment, but areless expensive to purchase and maintain. The ba-sic aspects of UTM equipment and testing gen-erally apply to tension or compression testingmachines as well.

This chapter reviews the current technologyand examines force application systems, forcemeasurement, strain measurement, important in-strument considerations, gripping of test speci-mens, test diagnostics, and the use of computersfor gathering and reducing data. The influenceof the machine stiffness on the test results is alsodescribed, along with a general assessment oftest accuracy, precision, and repeatability ofmodern equipment. A discussion of tensile testspecimens can be found in Chapter 3, “UniaxialTensile Testing.”




Testing Machines

Although there are many types of test systemsin current use, the most common are UTMs,which are designed to test specimens in tension,compression, or bending. The testing machinesare designed to apply a force to a material todetermine its strength and resistance to defor-mation. Regardless of the method of force ap-plication, testing machines are designed to drivea crosshead or platen at a controlled rate, thusapplying a tensile or compressive load to a spec-imen. Such testing machines measure and indi-cate the applied force in pound-force (lbf ), kil-ogram-force (kgf ), or newtons (N). Thesecustomary force units are related by the follow-ing: 1 lbf � 4.448222 N; 1 kgf � 9.80665 N.All current testing machines are capable of in-dicating the applied force in either lbf or N (theuse of kgf is not recommended).

The load-applying mechanism may be a hy-draulic piston and cylinder with an associatedhydraulic power supply, or the load may be ad-ministered via precision-cut machine screwsdriven by the necessary gears, reducers, and mo-tor to provide a suitable travel speed. In somelight-capacity machines (only a few hundredpounds maximum), the force is applied by an airpiston and cylinder. Gear-driven systems obtainload capacities up to approximately 600 kN(1.35 � 105 lbf ), while hydraulic systems canobtain forces up to approximately 4500 kN (1� 106 lbf ).

Whether the machine is a gear-driven systemor hydraulic system, at some point the test ma-chine reaches a maximum speed for loading thespecimen. Gear driven test machines have amaximum crosshead speed limited by the speedof the electric motor in combination with thedesign of the gear box transmission. Crossheadspeed of hydraulic machines is limited to thecapacity of the hydraulic pump to deliver asteady pressure on the piston of the actuator orcrosshead. Servohydraulic test machines offer awider range of crosshead speeds; however, thereare continuing advances in the speed control ofscrew-driven machines, which can be just asversatile as, or perhaps more versatile than, ser-vohydraulic machines.

Conventional gear-driven systems are gener-ally designed for speeds of about 0.001 to 500mm/min (4 � 10�6 to 20 in./min), which is suit-able for quasi-static testing. Servohydraulic sys-tems are generally designed over a wider rangeof test speeds, such as:

● 1 lm/h test speeds for creep-fatigue, stress-corrosion, and stress-rupture testing

● 1 lm/min test speeds for fracture testing ofbrittle materials

● 10 m/s (400 in./s) test speeds for dynamictesting of components like bumpers or seatbelts

Servohydraulic UTM systems may also be de-signed for cycle rates from 1 cycle/day to over200 cycles/s. Gear-driven systems typically allowcycle rates between 1 cycle/h and 1 cycle/s.

Gear-driven (or screw-driven) machinesare electromechanical devices that use a largeactuator screw threaded through a moving cross-head (Fig. 2). The screw is turned in either di-rection by an electric motor through a gear re-duction system. The screws are rotated by avariable-control motor and drive the moveablecrosshead up or down. This motion can load thespecimen in either tension or compression, de-pending on how the specimen is to be held andtested.

Screw-driven testing machines currently usedare of either a one-, two-, or four-screw design.To eliminate twist in the specimen from the ro-tation of the screws in multiple-screw systems,one screw has a right-hand thread, and the otherhas a left-hand thread. For alignment and lateralstability, the screws are supported in bearings oneach end. In some machines, loading crossheadsare guided by columns or guideways to achievealignment.

A range of crosshead speeds can be achievedby varying the speed of the electric motor andby changing the gear ratio. A closed-loop ser-vodrive system ensures that the crossheadmoves at a constant speed. The desired or user-selected speed and direction information is com-pared with a known reference signal, and theservomechanism provides positional control ofthe moving crosshead to reduce any error or dif-ference. State-of-the-art systems use precisionoptical encoders mounted directly on preloadedtwin ball screws. These types of systems are ca-pable of measuring crosshead displacement toan accuracy of 0.125% or better with a resolu-tion of 0.6 lm.

As noted previously, typical screw-driven ma-chines are designed for speeds of 1 to 20 mm/min (0.0394–0.788 in./min) for quasi-static testapplications; however, machines can be de-signed to obtain higher speeds, although the use-ful force available for application to the speci-men decreases as the speed of the crosshead

Tensile Testing Equipment and Strain Sensors / 67

Fig. 2 Components of an electromechanical (screw-driven) testing machine. For the configuration shown, moving the lower (inter-mediate) head upward produces tension in the lower space between the crosshead and the base

motion increases. Modern high-speed systemsgenerally are useful in ranges up to 500 mm/min(20 in./min) (Ref 3). Nonetheless, top crossheadspeeds of 1250 mm/min (50 in./min) can be at-tained in screw-driven machines, and servohy-draulic machines can be driven up to 2.5 � 105

mm/min (104 in./min) or higher.Due to the high forces involved, bearings and

gears require particular attention to reduce fric-tion and wear. Backlash, which is the free move-ment between the mechanical drive components,is particularly undesirable. Many instruments in-corporate antibacklash preloading so that forces

are translated evenly through the lead screw andcrosshead. However, when the crosshead direc-tion is constantly in one direction, antibacklashdevices may be unnecessary.

Servohydraulic machines use a hydraulicpump and servohydraulic valves that move anactuator piston (Fig. 3). The actuator piston isattached to one end of the specimen. The motionof the actuator piston can be controlled in bothdirections to conduct tension, compression, orcyclic loading tests.

Servohydraulic test systems have the capabil-ity of testing at rates from as low as 45 � 10�11


Fig. 4 Servohydraulic testing machine and load frame with adedicated microprocessor-based controller

Fig. 3 Schematic of a basic servohydraulic, closed-loop testing machine

m/s (1.8 � 10�9 in./s) to 30 m/s (1200 in./s) ormore. The actual useful rate for any particularsystem depends on the size of the actuator, theflow rating of the servovalve, and the noise levelpresent in the system electronics. A typical ser-vohydraulic UTM system is shown in Fig. 4.

Hydraulic actuators are available in a widevariety of force ranges. They are unique in theirability to economically provide forces of 4450kN (1,000,000 lbf ) or more. Screw-driven ma-chines are limited in their ability to provide highforces due to problems associated with low ma-chine stiffness and large and expensive loadingscrews, which are increasingly more difficult toproduce as the force rating goes up.

Microprocessors for Testing and Data Re-duction. Contemporary UTMs are controlled bymicroprocessor-based electronics. One class ofcontroller is based on dedicated microprocessorsfor test machines (Fig. 4). Dedicated microproc-essors are designed to perform specific tasks andhave displays and input functions that are lim-ited to those tasks. The dedicated microproces-sor sends signals to the experimental apparatusand receives information from various sensors.The data received from sensors can be passed tooscilloscopes or computers for display and stor-age. The experimental results consist of time andvoltage information that must be further reducedto analyze material behavior. Analysis of thedata requires the conversion of test results, suchas voltage, to specific quantities, such as dis-placement and load, based on known conversionfactors.

The second class of controller is the personalcomputer (PC) designed with an electronic in-terface to the experimental apparatus, and theappropriate application software. The softwaretakes the description of the test to be performed,including specimen geometry data, and estab-lishes the requisite electronic signals. Once the

test is underway, the computer controls the testsand collects, reduces, displays, and stores thedata. The obvious advantage of the PC-basedcontroller is reduced time to generate graphicresults, or reports. The other advantage is theelimination of some procedural errors, or the re-duction of the interfacing details between the op-erator and the experimental apparatus. Somesystems are designed with both types of con-trollers. Having both types of controllers pro-vides maximum flexibility in data gathering witha minimal amount of time required for reducingdata when conducting standard experiments.

Principles of Operation

The operation of a universal testing machinecan be understood in terms of the main elementsfor any stress analysis, which include materialresponse, specimen geometry, and load orboundary condition.

Material response, or material characteriza-tion, is studied by adopting standards for the


Table 1 Strain rate ranges for different tests

Type of testStrain rate range,

s�1

Creep tests 10�8 to 10�5

Pseudostatic tensile or compression tests 10�5 to 10�1

Dynamic tensile or compression tests 10�1 to 102

Impact bar tests involving wave propagationeffects

102 to 104

Source: Ref 4

other two elements. Specimen geometries aredescribed in the section “Tensile Testing Re-quirements and Standards” at the end of thischapter. This section briefly describes load con-dition factors, such as strain rate, machine rigid-ity, and various testing modes by load control,speed control, strain control, and strain-rate con-trol.

Strain Rate

Strain rate, or the rate at which a specimen isdeformed, is a key test variable that is controlledwithin prescribed limits, depending on the typeof test being performed. Table 1 summarizes thegeneral strain-rate ranges that are required forvarious types of property tests. Conventional(quasi-static) tensile tests require strain rates be-tween 10�5 and 10�1 s�1.

A typical mechanical test on metallic materi-als is performed at a strain rate of approximately10�3 s�1, which yields a strain of 0.5 in 500 s.Conventional equipment and techniques gener-ally can be extended to strain rates as high as0.1 s�1 without difficulty. Tests at higher strainrates necessitate additional considerations ofmachine stiffness and strain measurement tech-niques. In terms of machine capability, servo-hydraulic load frames equipped with high-ca-pacity valves can be used to generate strain ratesas high as 200 s�1. These tests are complicatedby load and strain measurement and data acqui-sition.

If the crosshead speed is too high, inertia ef-fects can become important in the analysis of thespecimen stress state. Under conditions of highcrosshead speed, errors in the load cell outputand crosshead position data may become unac-ceptably large. A potential exists to damage loadcells and extensometers under rapid loading.The damage occurs when the specimen fracturesand the load is instantaneously removed fromthe specimen and the load frame.

At strain rates greater than 200 s�1, the re-quired crosshead speeds exceed the speeds eas-ily obtained with screw-driven or hydraulic ma-chines. Specialized high strain rate methods arediscussed in more detail in Chapter 15, “HighStrain Rate Testing.”

Determination of StrainRates for Quasi-Static Tensile Tests

Strength properties for most materials tend toincrease at higher rates of deformation. In order

to quantify the effect of deformation rate onstrength and other properties, a specific defini-tion of strain rate is required. During a conven-tional (quasi-static) tension test, for example,ASTM E 8 “Tension Testing of Metallic Mate-rials” prescribes an upper limit of deformationrate as determined quantitatively during the testby one of the following methods (listed in de-creasing order of precision):

● Rate of straining● Rate of stressing (when loading is below the

proportional limit)● Rate of crosshead separation during the tests● Elapsed time● Free-running crosshead speed

For some materials, the free-running crossheadspeed, which is the least accurate, may be ade-quate, while for other materials, one of the re-maining methods with higher precision may benecessary in order to obtain test values withinacceptable limits. When loading is below theproportional limit, the deformation rate can bespecified by the “loading rate” units of stress perunit of time such that:

r � Ee

where, according to Hooke’s law, is stress. Eris the modulus of elasticity, is strain, and theesuperposed dots denote time derivatives.

ASTM E 8 specifies that the test speed mustbe low enough to permit accurate determinationof loads and strains. When the rate of stressingis stipulated, ASTM E 8 requires that it not ex-ceed 690 MPa/min (100 ksi/min). This corre-sponds to an elastic strain rate of about 5 �10�5 s�1 for steel or 15 � 10�5 s�1 for alu-minum. When the rate of straining is stipulated,ASTM E 8 prescribes that after the yield pointhas been passed, the rate can be increased toabout 1000 � 10�5 s�1; presumably, the stressrate limitation must be applied until the yieldpoint is passed. Lower limits are also given inASTM E 8.


Fig. 6 Oscilloscope record of load cell force versus time dur-ing a dynamic tensile test depicting the phenomenon

of ringing. The uncontrolled oscillations result when the loadingrate is near the resonant frequency of the load cell. The scalesare arbitrary. Source: Ref 5

Fig. 5 The deformation of an elemental length, dx0, of a ten-sile test specimen of initial cross-sectional area, A0, by

a stress wave. The displacement of the element is u; the differ-ential length of the element as a function of time is dx; the forcesacting on the faces of the element are given by F and F � dF.

In ASTM standard E 345, “Tension Testingof Metallic Foil,” the same upper limit on therate of stressing is recommended. In addition, alower limit of 7 MPa/min (1 ksi/min) is given.ASTM E 345 further specifies that when theyield strength is to be determined, the strain ratemust be in the range from approximately 3 �10�5 to 15 � 10�5 s�1.

Inertia Effects

A fundamental difference between a highstrain rate tensile test and a quasi-static tensiletest is that inertia and wave propagation effectsare present at high rates. An analysis of resultsfrom a high strain rate test thus requires consid-eration of the effect of stress wave propagationalong the length of the test specimen in order todetermine how fast a uniaxial test can be run toobtain valid stress-strain data.

For high loading rates, the strain in the spec-imen may not be uniform. Figure 5 illustrates anelemental length dx0 of a tensile test specimenwhose initial cross-sectional area is A0 andwhose initial location is prescribed by the co-ordinate x. Neglecting gravity, no forces act onthis element in its initial configuration. After thetest has begun, the element is shown displacedby a distance u, deformed to new dimensions dxand A, and subjected to forces F and F � dF.The difference, dF, between these end-faceforces causes the motion of the element that ismanifested by the displacement, u. This motionis governed by Newton’s second law, forceequals mass times acceleration:

2d udF � q A dx (Eq 1)0 0 0� 2�dt

where q0A0dx0 is the mass of the element, A0dx0is the volume, q is the density of the material,and (d2u/dt2) is its acceleration. Tests that areconducted very slowly involve extremely smallaccelerations. Thus, Eq 1 shows that the varia-tion of force dF along the specimen length isnegligible.

However, for tests of increasingly shorter du-rations, the acceleration term on the right side ofEq 1 becomes increasingly significant. This pro-duces an increasing variation of axial forcealong the length of the specimen. As the forcebecomes more nonuniform, so must the stress.Consequently, the strain and strain rate will alsovary with axial position in the specimen. Whenthese effects become pronounced, the concept ofaverage values of stress, strain, and strain ratebecome meaningless, and the test results mustbe analyzed in terms of the propagation of wavesthrough the specimen. This is shown in Table 1as beginning near strain rates of 102 s�1.

In an intermediate range of strain rates (de-noted as dynamic tests in Table 1), an effectknown as “ringing” of the load-measuring de-vice obscures the interpretation of test data. Anexample of this condition is shown in Fig. 6,which is a tracing of load cell force versus timeduring a dynamic tensile test of a 2024-T4 alu-minum specimen. Calculation showed that theoscillations apparent in the figure are consistentwith vibrations at the approximate natural fre-quency of the load cell used for this test (Ref5, 6).

In many machines currently available for dy-namic testing, electronic signal processing isused to filter out such vibrations, thus makingthe instrumentation records appear muchsmoother than the actual load cell signal. How-ever, there is still a great deal of uncertainty inthe interpretation of dynamic test data. Conse-


Fig. 7 Schematic illustrating crosshead displacement and elastic deflection in a tensile testing machine. D is the displacement of thecrosshead relative to the zero load displacement; L0 is the initial gage length of the specimen; K is the composite stiffness of

the grips, loading frame, load cell, specimen ends, etc.; F is the force acting on the specimen. The development of Eq 2 through 12describes the effects of testing machine stiffness on tensile properties. Source: Ref 7

quently, the average value of the high-frequencyvibrations associated with the load cell can beexpected to differ from the force in the speci-men. This difference is caused by vibrations nearthe natural frequency of the testing machine,which are so low that the entire test can occurin less than 1⁄10 of a cycle. Hence, these low-frequency vibrations usually are impossible todetect in a test record, but can produce signifi-cant errors in the analysis of test results. Theringing frequency for typical load cells rangesfrom 2400 to 3600 Hz.

Machine Stiffness

The most common misconception relating tostrain rate effects is that the testing machine ismuch stiffer than the specimen. Such an as-sumption leads to the concept of deformation ofthe specimen by an essentially rigid machine.However, for most tests the opposite is true: theconventional tensile specimen is much stifferthan most testing machines. As shown in Fig. 7,for example, if crosshead displacement is de-fined as the relative displacement, D, that wouldoccur under conditions of zero load, then with aspecimen gripped in a testing machine and thedriving mechanism engaged, the crosshead dis-placement equals the deformation in the gagelength of the specimen plus elastic deflections incomponents such as the machine frame, loadcell, grips, and specimen ends. Before yielding,the gage length deformation is a small fractionof the crosshead displacement.

After the onset of gross plastic yielding of thespecimen, conditions change. During this phaseof deformation, the load varies slowly as the ma-terial strain hardens. Thus, the elastic deflectionsin the machine change slowly, and most of the

relative crosshead displacement produces plasticdeformation in the specimen. Qualitatively, in atest at approximately constant crosshead speed,the initial elastic strain rate in the specimen willbe small, but the specimen strain rate will in-crease when plastic flow occurs.

Quantitatively, this effect can be estimated asfollows. Consider a specimen having an initialcross-sectional area A0 and modulus of elasticityE gripped in a testing machine so that its axiallystressed gage length initially is L0. (This discus-sion is limited to the range of testing speedswhere wave propagation effects are negligible.This restriction implies that the load is uniformthroughout the gage length of the specimen.)Denote the stiffness of the machine, grips, andso on, by K and the crosshead displacement rate(nominal crosshead speed) by S. The ratio S/L0is sometimes called the nominal rate of strain,but because it is often substantially differentfrom the rate of strain in the specimen, the termspecific crosshead rate is preferred (Ref 8).

Let loading begin at time t equal to zero. Atany moment thereafter, the displacement of thecrosshead must equal the elastic deflection of themachine plus the elastic and plastic deflectionsof the specimen. Letting s denote the engineer-ing stress in the specimen, the machine deflec-tion is then sA0/K. It is reasonable to assume thatHooke’s law adequately describes the elastic de-formation of the specimen at ordinary stress lev-els. Thus, the elastic strain ee is s/E.

Denoting the average plastic strain in thespecimen by ep, the above displacement balancecan be expressed as:

t A L0 0Sdt � s � � e L (Eq 2)p 0� � �0 K E


Differentiating Eq 2 with respect to time anddividing by L0 gives:

S s A E0� � 1 � e (Eq 3)p� �� L E KL0 0

The strain rate in the specimen is the sum of theelastic and plastic strain rates:

se � e � e � � e (Eq 4)e p p� �E

Using Eq 3 to eliminate the stress rate from Eq4 yields:

SK� ep� �A E0

e � (Eq 5)KL0

� 1� �A E0

Thus, it is seen that the specimen strain rate usu-ally will differ from the specific crosshead rateby an amount dependent on the rate of plasticdeformation and the relative stiffnesses of thespecimen (A0E/L0) and the machine, K.

Determination of Testing Machine Stiffness

Machine stiffness is the amount of deflectionin the load frame and the grips for each unit ofload applied to the specimen. This deflection notonly encompasses elastic deflection of the loadframe, but includes any motion in the grip mech-anism, or at any interface (threads, etc.) in thesystem. These deflections are substantial duringthe initial loading of the specimen, that is,through the elastic regime. This means that theinitial crosshead speed (specified by the opera-tor) is not an accurate measure of specimen dis-placement (strain). If the strain in the elastic re-gime is not accurately known, then extremelylarge errors may result in the calculation ofYoung’s modulus (E, the ratio of stress versusstrain in the elastic regime). In the analysis byHockett and Gillis (Ref 9), the machine stiffnessK is accounted for in the following equation:

�1S L0K � � (Eq 6)� �P A E0 0

where L0 is initial specimen gage length, S iscrosshead speed of the testing machine, A0is initial cross-sectional area of the specimen, P0is specimen load rate (dF/dt � A0s), and E isYoung’s modulus of the specimen material.

Research in this area showed that a significantamount of scatter was found in the measurementof machine stiffness. This variability can be at-tributed to relatively small differences in testconditions. For characterization of the elastic re-sponse of a material and for a precise measureof yield point, the influence of machine stiffnessrequires that an extensometer, or a bonded straingage, be used. After yielding of the specimenmaterial, the change of machine deflection isvery small because the load changes slowly. Ifthe purpose of the experiment is to study largestrain behavior, then the error associated withthe use of the crosshead displacement is smallrelative to other forms of experimental uncer-tainties.

Control Modes

During a test, control circuits and servomech-anisms monitor and control the key experimen-tal conditions, such as force, specimen defor-mation, and the position of the moveablecrosshead. These are the key boundary condi-tions, which are analyzed to provide mechanicalproperty data. These boundary conditions on thespecimen can also be controlled in differentways, such as constant load control, constantstrain control, and constant crosshead speed con-trol. Constant crosshead speed is the most com-mon method for tensile tests.

Constant Load Rate Testing. With appropri-ate modules on a UTM system, a constant loadrate test can be accomplished easily. In this con-figuration, a load-control module allows the ma-chine with the constant rate of extension to func-tion as a constant load rate device. This isaccomplished by a feedback signal from a loadcell, which generates a signal that automaticallyadjusts to the motion controller of the crosshead.Usually, the servomechanism system response isparticularly critical when materials are loadedthrough the yield point.

Constant Strain Rate Testing. Commercialsystems have been developed to control the ex-periment based on a constant rate of straining inthe specimen. These systems rely on extensom-eters measuring the change in gage length toprovide data on strain as a function of time. Theresulting signal is processed to determine thecurrent strain rate and is used to adjust the cross-head displacement rate throughout the test.Again, servomechanism response time is par-ticularly critical when materials are takenthrough yield.


Table 2 Experimental values of testing machinestiffness

Machine stiffness

kg/mm lb/ln. Source

740 41,500 Ref 10460 26,000 Ref 11

1800 100,000 Ref 121390–2970 77,900–166,500 Ref 13

To maintain a constant average strain rate dur-ing a test, the crosshead speed must be adjustedas plastic flow occurs so that the sum (SK/A0E� ep) remains constant. For most metallic ma-terials at the beginning of a test, the plastic strainrate is ostensibly zero, and from Eq 5 the initialstrain rate is:

S0� �L0e � (Eq 7)0 A E01 � � �KL0

where S0 is the crosshead speed at the beginningof the test. For materials that have a definiteyield, s � 0 at the yield point. Therefore, fromEq 3 and 4, the yield point strain rate is:

S1e � (Eq 8)1 � �L0

where S1 is the crosshead speed at the yieldpoint. Equating these two values of strain rateshows that the crosshead speed must be reducedfrom its initial value to its yield-point value bya factor of:

S A E0 0� 1 � (Eq 9)� �S KL1 0

For particular measured values of machine stiff-ness given in Table 2, this factor for a standard12.8 mm (0.505 in.) diameter steel specimen istypically greater than 20 and can be as high as100. Only for specially designed machines willthe relative stiffness of the machine exceed thatof the specimen. Even for wire-like specimens,the correspondingly delicate gripping arrange-ment will ensure that the machine stiffness isless than that of the specimen. Thus, largechanges in crosshead speed usually are requiredto maintain a constant strain rate from the be-ginning of the test through the yield point.

Furthermore, for many materials, the onset ofyielding is quite rapid, so that this large changein speed must be accomplished quickly. Makingthe necessary changes in speed generally re-quires not only special strain-sensing equip-ment, but also a driving unit that is capable ofextremely fast response. The need for fast re-sponse in the driving system eliminates the useof screw-driven machines for constant strain-rate testing. Servohydraulic machines may be

capable of conducting tests at constant strain ratethrough the yield point of a material.

Equation 9 indicates the magnitude of speedchanges required only for tests in which there isno yield drop. For materials having upper andlower yield points, the direction of crossheadmotion may have to be reversed after initialyielding to maintain a constant strain rate. Thisreversal may be necessary, because plasticstrains beyond the upper yield point can be im-posed at a strain rate greater than the desired rateby recovery of elastic deflections of the machineas the load decreases.

Another important test feature related to thespeed change capability of the testing machineis the rate at which the crosshead can acceleratefrom zero to the prescribed test speed at the be-ginning of the test. For a slow test this may notbe critical, but for a high-speed test, the yieldpoint could be passed before the crossheadachieves full testing speed. Thus, the crossheadmay still be accelerating when it should be de-celerating, and accurate information concerningthe strain rate will not be obtained. With the ad-vent of closed-loop servohydraulic machinesand electromagnetic shakers, the speed at whichthe ram (crosshead) responds is two orders ofmagnitude greater than for screw-driven ma-chines.

Tests at Constant Crosshead Speeds. Ma-chines with a constant rate of extension are themost common type of screw-driven testers andare characterized by a constant rate of crossheadtravel regardless of applied loads. They permittesting without speed variations that might altertest results; this is particularly important whentesting rate-sensitive materials such as polymers,which exhibit different ultimate strengths andelongations when tested at different speeds.

For a gear-driven system, applying the bound-ary condition is as simple as engaging the elec-tric motor with a gear box transmission. At thispoint, the crosshead displacement will be what-ever speed and direction was selected. More so-phisticated systems use a command signal that


is compared with a feedback signal from a trans-ducer monitoring the position of the crosshead.Using this feedback circuit, the desired bound-ary condition can be achieved.

Tensile tests usually can be carried out at aconstant crosshead speed on a conventional test-ing machine, provided the machine has an ade-quate speed controller and the driving mecha-nism is sufficiently powerful to be insensitive tochanges in the loading rate. Because special ac-cessory equipment is not required, such tests arerelatively simple to perform. Also, constantcrosshead speed tests typically provide as gooda comparison among materials and as adequatea measure of strain-rate sensitivity as constantstrain-rate tests.

Two of the most significant test quantities—yield strength and ultimate tensile strength—frequently can be correlated with initial strainrate and specific crosshead rate, respectively.The strain rate up to the proportional limit equalsthe initial strain rate. Thus, for materials thatyield sharply, the time-average strain rate fromthe beginning of the test to yield is only slightlygreater than the initial strain rate:

S

L0e � (Eq 10)0 A E0� �1 �KL0

even though the instantaneous strain rate at yieldis the specific crosshead rate:

Se � (Eq 11)1 � �L0

However, beyond the yield point, the stress rateis small so that the strain rate remains close tothe specific crosshead rate (Eq 11). Thus, ductilematerials, for which a rather long time willelapse before reaching ultimate strength, have atime-average strain rate from the beginning ofthe test to ultimate that is only slightly less thanthe specific crosshead rate. Also, because theload rate is zero at ultimate as well as at yield,the instantaneous strain rate at ultimate equalsthe specific crosshead rate.

During a test at constant crosshead speed, thevariation of strain rate from initial to yield-pointvalues is precisely the inverse of the crossheadspeed change required to maintain a constantstrain rate (Eq 9):

e A E1 0� 1 � (Eq 12)� �e KL0 0

Consequently, in an ordinary tensile test, theyield strength and ultimate tensile strength maybe determined at two different strain rates, whichcan vary by a factor of 20 to 100, depending onmachine stiffness. If a yield drop occurs, elasticrecovery of machine deflections will impose astrain rate even greater than the specific cross-head rate given by Eq 12.

A point of interest from the analysis involvestesting of different sized specimens at about thesame initial strain rate. Assuming that these testsare to be made on one machine under conditionsfor which K remains substantially constant, thecrosshead speed must be adjusted to ensure thatspecimens of different lengths, diameters, or ma-terials will experience the same initial strain rate.In the typical case where the specimen is muchstiffer than the machine, (1 � A0E/KL0) in Eq10 can be approximated simply by (A0E/KL0),so that the initial strain rate is approximately e0� SK/A0E. Thus, specimens of various lengths,tested at the same crosshead speed, will gener-ally experience nearly the same initial strain rate.However, changing either the specimen crosssection or material necessitates a correspondingchange in crosshead speed to obtain the sameinitial rate.

A change in specimen length has substantiallythe same effect on both the specific crossheadrate (S/L0) and the stiffness ratio of specimen tomachine (A0E/KL0) and, therefore, has no neteffect. For example, an increase in specimenlength tends to decrease the strain rate by dis-tributing the crosshead displacement over thelonger length; however, at the same time, theincrease in length reduces the stiffness of thespecimen so that more of the crosshead displace-ment goes into deformation of the specimen andless into deflection of the machine. These twoeffects are almost exactly equal in magnitude.Thus, no change in initial strain rate is expectedfor specimens of different lengths tested at thesame crosshead speed.

Load-Measurement Systems

Prior to the development of load cells, testingmachine manufacturers used several types of de-vices for the measurement of force. Early sys-tems, some of which are still in use, employ a


graduated balanced beam similar to platform-scale weighing systems. Subsequent systemshave used Bourdon tube hydraulic test gages,Bourdon tubes with various support and assistdevices, and load cells of several types. One ofthe most common load-measuring systems, priorto the development of load cells, was the dis-placement pendulum, which measured load bythe movement of the balance displacement pen-dulum. The pendulum measuring system wasused widely, because it is applicable to both hy-draulic and screw-driven machines and has ahigh degree of reliability and stability. Manymachines of this design are still in use, and theyare still manufactured in Europe, India, SouthAmerica, and Asia. Another widely used testingsystem was the Emery-Tate oil-pneumatic sys-tem, which accurately senses the hydraulic pres-sure in a closed, flat capsule.

Load Cells. Current testing machines usestrain-gage load cells and pressure transducers.In a load cell, strain gages are mounted on pre-cision-machined alloy-steel elements, hermeti-cally sealed in a case with the necessary electri-cal outlets, and arranged for tensile and/orcompressive loading. The load cell can bemounted so that the specimen is in direct con-tact, or the cell can be indirectly loaded throughthe machine crosshead, table, or columns of theload frame. The load cell and the load cell circuitare calibrated to provide a specific voltage as anoutput signal when a certain force is detected. Inpressure transducers, which are variations ofstrain-gage load cells, the strain-gaged memberis activated by the hydraulic pressure of the sys-tem.

Strain gages, strain-gage load cells, and pres-sure transducers are manufactured to several de-grees of accuracy; however, when used as theload-measuring mechanism of a testing ma-chine, the mechanisms must conform to ASTME 4, as well as to the manufacturer’s qualitystandards. Load cells are rated by the maximumforce in their operating range, and the deflectionof the load cell must be maintained within theelastic regime of the material from which theload cell was constructed. Because the load celloperates within its elastic range, both tensile andcompressive forces can be monitored.

Electronics provide a wide range of signalprocessing capability to optimize the resolutionof the output signal from the load cell. Tem-perature-compensating gages reduce measure-ment errors from changes in ambient tempera-ture. A prior knowledge of the mechanical

properties of the material being studied is alsouseful to obtain full optimization of these sig-nals.

Within individual load cells, mechanical stopscan be incorporated to minimize possible dam-age that could be caused by accidental over-loads. Also, guidance and supports can be in-cluded to prevent the deleterious effects of sideloading and to give desired rigidity and rugged-ness. This is important in tensile testing of met-als because of the elastic recoil that can occurwhen a stiff specimen fails.

Calibration of load-measuring devices re-fers to the procedure of determining themagnitude of error in the indicated loads. Onlyload-indicating mechanisms that comply withstandard calibration methods (e.g., ASTM E 74)should be used for the load calibration and ver-ification of universal testing machines (see thesection “Force Verification of Universal TestingMachines” later in this chapter).

Calibration of load-measuring devices for me-chanical test machines is covered in specifica-tions of several standards organizations such as:

Specificationnumber Specification title

ASTM E 74 Standard Practice for Calibration of Force-Measuring Instruments for Verifying theForce Indication of Testing Machines

EN 10002-3 Part 3: Calibration of Force-Proving InstrumentsUsed for the Verification of Testing Machines

ISO 376 Metallic Materials—Calibration of Force-Proving Instruments Used for the Verificationof Testing Machines

BS EN 10002-3 Calibration of Force-Proving Instruments Usedfor the Verification of Uniaxial TestingMachines

To ensure valid load verification, calibrationprocedures should be performed by skilled per-sonnel who are knowledgeable about testing ma-chines and related instruments and the properuse of calibration standards.

Load verification of load-weighing systemscan be accomplished using methods based onthe use of standard weights, standard weightsand lever balances, and elastic calibration de-vices. Of these calibration methods, elastic cal-ibration devices have the fewest inherent prob-lems and are widely used. The two main typesof elastic load-calibration devices are elasticproving rings and strain-gage load cells, asbriefly described below.

The elastic proving ring (Fig. 8a, b) is aforged steel ring that is precisely machined to afine finish and closely maintained tolerances.


Fig. 8 Proving rings. (a) Elastic proving ring with precision micrometer for deflection/load readout. (b) Load calibration of 120,000lbf screw-driven testing machine with a proving ring

This device has a uniform and repeatable de-flection throughout its loaded range. Elasticproving rings usually are designed to be usedonly in compression, but special rings are de-signed to be used in tension or compression.

As the term “elastic device” implies, the ringis used well within its elastic range, and the de-flection is read by a precise micrometer. Provingrings are available with capacities ranging from4.5 to over 5000 kN (1000 to 1.2 � 106 lbf ).Their usable range is from 10 to 100% of loadcapacity, based on compliance with the ASTME 74 verification procedure.

Proving rings vary in weight from about 2 kg(5 lb) to hundreds of kilograms (or several hun-dred pounds). They are portable and easy to use.After initial certification, they should be recali-brated and recertified at intervals not exceeding2 years.

Proving rings are not load rings. Although thetwo devices are of similar design and construc-tion, only proving rings that use a precise mi-crometer for measuring deflection can be usedfor calibration. Load rings employ a dial indi-cator to measure deflection and usually do notcomply with the requirements of ASTM E 74.

Calibration strain-gage load cells are pre-cisely machined high-alloy steel elements de-signed to have a positive and predetermined uni-

form deflection under load. The steel load cellelement contains one or more reduced sections,onto which wire or foil strain gages are attachedto form a balanced circuit containing a tempera-ture-compensating element.

Strain-gage load cells used for calibrationpurposes are either compression or tension-com-pression types and have built-in capacities rang-ing from about 0.4 to 4000 kN (100 to 1,000,000lbf ). Their usable range is typically from 5 to100% of capacity load, and their accuracy is�0.05%, based on compliance with applicablecalibration procedures, such as ASTM E 74.Figure 9 illustrates a load cell system used tocalibrate a UTM. This particular system incor-porates a digital load indicator unit.

Comparison of Elastic Calibration De-vices. The deflection of a proving ring is mea-sured in divisions that are assigned a value inlbf, kgf, or N. The force is then calculated in thedesired units. Although the deflection of a loadcell is given numerically and a force value canbe assigned with a load cell reading, electric cir-cuits can provide direct readout in lbf, kgf, or N.Thus, certified load cells are more practical andconvenient to use and minimize errors in cal-culation.

In small capacities (5 to 20 kN, or 1000 to5000 lbf ), proving rings and load cells are of


Fig. 9 Load cell and digital load indicator used to calibrate a200,000 lbf hydraulic testing machine

similar size and weight (2 to 5 kg, or 4 to 10 lb).In large capacities (2000 to 2700 kN, or 400,000to 600,000 lbf ), load cells are about one half thesize and weight of proving rings. Proving ringsare a single-piece, self-contained unit. A loadcell calibration kit consists of two parts: the loadcell and the display indicator (Fig. 9). Althoughthe display indicator is designed to be used witha load cell of any capacity, it can only be usedwith load cells that have been verified with it asa system.

Although both proving rings and load cellsare portable, the lighter weight and smaller sizeof high-capacity load cells enhance their suit-ability for general use. Load cells and their dis-play indicators require a longer setup time: how-ever, their direct readout feature reduces theoverall calibration and reporting time. After ini-tial certification, the load cell should be recali-brated after one year and thereafter at intervalsnot exceeding two years.

Both types of calibration devices are certifiedin accordance with the provisions of calibrationstandards. In the United States, devices are cer-tified in accordance with ASTM E 74 and theverification values determined by the NationalInstitute of Standards and Technology (NIST).NIST maintains a 1,000,000 lbf deadweight cal-ibrator that is kept in a temperature- and humid-ity-controlled environment. This force-calibrat-ing machine incorporates twenty 50,000 lbstainless steel weights, each accurate to within�0.25 lb. This machine, and six others ofsmaller capacities, are used to calibrate elasticcalibrating devices, which in turn are employedto accurately calibrate other testing equipment.

Elastic calibrating devices for verification oftesting machines are calibrated to primary stan-dards, which are weights. The masses of theweights used are determined to 0.005% of theirvalues.

Strain-Measurement Systems

Deformation of the specimen can be mea-sured in several ways, depending on the size ofspecimen, environmental conditions, and mea-surement requirements for accuracy and preci-sion of anticipated strain levels. A simplemethod is to use the velocity of the crossheadwhile tracking the load as a function of time. Forthe load and time data pair, the stress in the spec-imen and the amount of deformation, or strain,can be calculated. When the displacement of the

platen is assumed to be equal to the specimendisplacement, an error is introduced by the factthat the entire load frame has been deflected un-der the stress state. This effect is related to theconcept of machine stiffness, as previously dis-cussed.

Extensometry

The elongation of a specimen during load ap-plication can be measured directly with varioustypes of devices, such as clip-on extensometers(Fig. 10), directly-mounted strain gages (Fig.11), and various optical devices. These devicesare used extensively and can provide a high de-gree of deformation- (strain-) measurement ac-curacy. Other more advanced instrumentations,such as laser interferometry and video exten-someters, are also available.

Various types of extensometers and straingages are described below. Selection of a devicefor strain measurement depends on various fac-tors:

● The useable range and accuracy of the gage● Techniques for mounting the gage● Specimen size● Environmental test conditions● Electronic circuit configuration and analysis

for signal processing

The last item should include the calibration ofthe extensometer device over its full operating


Fig. 10 Test specimen with an extensometer attached to measure specimen deformation. Courtesy of Epsilon Technology Corpo-ration

range. In addition, one challenge of workingwith clip-on extensometers is to ensure properattachment to the specimen. If the extensometerslips as the specimen deforms, the resulting sig-nal will give a false reading.

Clip-on extensometers can be attached to atest specimen to measure elongation or strain asthe load is applied. This is particularly importantfor metals and similar materials that exhibit highstiffness. As shown in Fig. 12, typical extensom-eters have fixed gage lengths such as 25 or 50mm (1 or 2 in.). They are also classified by max-imum percent elongation so that a typical 25 mm(1 in.) gage length unit would have differentmodels for 10, 50, or 100% maximum strain.Extensometers are used to measure axial strainin specimens. There also are transverse strain-measuring devices that indicate the reduction inwidth or diameter as the specimen is tested.

The two basic types of clip-on extensometersare linear variable differential transformer(LVDT) devices and strain-gage devices. Thesetwo types are described along with a descriptionof earlier dial-type extensometers.

Early extensometers were held to the speci-men with center points matching the specimengage-length punch marks, and elongation wasindicated between the points by a dial indicator.Because of mechanical problems associated

with these early devices, most dial extensome-ters use knife edges and leaf-spring pressure forspecimen attachment. An extensometer using adial indicator to measure elongation is shown inFig. 13. The dial indicator usually is marked offin 0.0025 mm (0.0001 in.) increments and mea-sures the total extension between the gagepoints. This value divided by the gage lengthgives strain in mm/mm, or in./in.

LVDT extensometers employ an LVDT with acore, which moves from specimen deformationand produces an electrical signal proportional toamount of core movement (Fig. 14). LVDT ex-tensometers are small, lightweight, and easy touse. Knife edges provide an exact point of con-tact and are mechanically set to the exact gagelength. Unless the test report specifies total elon-gation, center punch marks or scribed lines arenot required to define the gage length. They areavailable with gage lengths ranging from 10 to2500 mm (0.4 to 100 in.) and can be fitted withbreakaway features (Fig. 15), sheet metalclamps, low-pressure clamping arrangements(film clamps, as shown in Fig. 16), and otherdevices. Thus, they can be used on small spec-imens—such as thread, yarn, and foil—and onlarge test specimens—such as reinforcing bars,heavy steel plate, and tubing up to 75 mm (3 in.)in diameter.


Fig. 12 Typical clip-on extensometers. (a) Extensometer with 25 mm (1 in.) gage length and �3.75 mm (�0.150 in.) travel suitablefor static and dynamic applications with a variety of specimen geometries, dimensions, and materials. (b) Extensometer with

50 mm (2 in.) gage length and 25 mm (1 in.) travel suitable for large specimens and materials with long elongation patterns

Modifications of the LVDT extensometer alsopermit linear measurements at temperaturesranging from �75 to 1205 �C (�100 to 2200

�F). Accurate measurements can also be madein a vacuum. For standard instruments, theworking temperature range is approximately�75 to 120 �C (�100 to 250 �F). However, bysubstituting an elevated-temperature trans-former coil, the usable range of the instrumentcan be extended to �130 to 260 �C (�200 to500 �F).

Strain-gage extensometers, which use straingages rather than LVDTs, are also common andare lighter in weight and smaller in size, butstrain gages are somewhat more fragile thanLVDTs. The strain gage usually is mounted ona pivoting beam, which is an integral part of theextensometer. The beam is deflected by themovement of the extensometer knife edge whenthe specimen is stressed. The strain gage at-tached to the beam is an electrically conductivesmall-sized grid that changes its resistance whendeformed in tension, compression, bending, ortorsion. Thus, strain gages can be used to supplythe information necessary to calculate strain,stress, angular torsion, and pressure.

Strain gages have been improved and refined,and their use has become widespread. Basictypes include wire gages, foil gages, and capac-itive gages. Wire and foil bonded resistancestrain gages are used for measuring stress andstrain and for calibration of load cells, pressuretransducers, and extensometers. These gagestypically measure 9.5 to 13 mm (3⁄8 to 1⁄2 in.) inwidth and 13 to 19 mm (1⁄2 to 3⁄4 in.) in lengthFig. 11 Strain gages mounted directly to a specimen


Fig. 13 Dial-type extensometer, 50 mm (2 in.) gage lengthFig. 14 Averaging LVDT extensometer (50 mm, or 2 in. gage

length) mounted on a threaded tension specimen

and are adhesively bonded to a metal element(Fig. 17).

Operation of strain-gage extensometers isbased on gages that are bonded to a metallic ele-ment and connected to a bridge circuit. Deflec-tion of the element, due to specimen strain,changes the gage’s resistance that produces anoutput signal from a bridge circuit. This signalis amplified and processed by signal condition-ers before being displayed on a digital readout,chart recorder, or computer. The circuitry in thestrain-measuring system allows multiple rangesof sensitivity, so one transducer can be used overbroad ranges. The magnification ratio, which isthe ratio of output to extensometer deflection,can be as high as 10,000 to 1.

Strain Gages Mounted Directly to the TestSpecimen. For some strain measurements,strain gages are mounted on the part being tested(Fig. 11). When used in this manner, they differfrom extensometers in that they measure average

unit elongation over nominal gage length ratherthan total elongation between definite gagepoints. For some testing applications, straingages are used in conjunction with extensome-ters (Fig. 17).

In conventional use, wire or foil strain gages,when mounted on structures and parts for stressanalysis, are discarded with the tested item.Thus, strain gages are seldom used in productiontesting of standard tension specimens. Foil straingages currently are the most widely used, due tothe ease of their attachment.

Averaging Extensometers. Typically exten-someters are either nonaveraging or averagingtypes. A nonaveraging extensometer has onefixed nonmovable knife edge or center point andone movable knife edge or center point on thesame side of the specimen. This arrangement re-sults in extension measurements that are takenon one side of the specimen only; such mea-surements do not take into account that elonga-tion may be slightly different on the other side.

For most specimens, notably those with ma-chined rounds or reduced gage length flats, thereis no significant difference in elongation be-tween the two sides. However, for as-cast spec-imens, high-modulus materials, some forgedparts, and specimens made from tubing, a dif-


Fig. 15 Breakaway-type LVDT extensometer (50 mm, or 2 in.gage length) that can remain on the specimen

through rupture

Fig. 16 Averaging LVDT extensometer (50 mm, or 2 in. gagelength) mounted on a 0.127 mm (0.005 in.) wire

specimen. The extensometer is fitted with a low-pressure clamp-ing arrangement (film clamps) and is supported by a counterbal-ance device.

ference in elongation sometimes exists on op-posite sides of the specimen when subjected toa tensile load. This is due to part configurationand/or internal stress. Misalignment of grips alsocontributes to elongation measurement varia-tions in the specimen. For these situations, av-eraging extensometers are used. Averaging ex-tensometers use dual-measuring elements thatmeasure elongation on both sides of a sample(Fig. 18); the measurements are then averagedto obtain a mean strain.

Optical Systems. Lasers and other systemscan also be used to obtain linear strain measure-ments. Optical extensometers are particularlyuseful with materials such as rubber, thin films,plastics, and other materials where the weight ofa conventional extensometer would distort theworkpiece and affect the readings obtained. In

the past, such strain-measuring systems were ex-pensive, and their principal use has been pri-marily in research and development work. How-ever, these optical techniques are becomingmore accessible for commercial testing ma-chines. For example, bench-top UTM systemswith a laser extensometer are available (Fig. 19).This laser extensometer allows accurate mea-surement of strain in thin films, which would nototherwise be practical by mechanical attachmentof extensometer devices. Optical systems alsoallow noncontact measurement from environ-mental test chambers.

Calibration, Classification, and Verifica-tion of Extensometers. All types of extensom-eters for materials testing must be verified, clas-sified, and calibrated in accordance withapplicable standards. Calibration of extensome-ters refers to the procedure of determining themagnitude of error in strain measurements. Ver-ification is a calibration to ascertain whether theerrors are within a predetermined range. Verifi-cation also implies certification that an exten-someter meets stated accuracy requirements,which are defined by classifications such asthose in ASTM E 83 (Table 3).

Several calibration devices can be used, in-cluding an interferometer, calibrated standardgage blocks and an indicator, and a micrometer


Fig. 17 Test specimen with bonded resistance strain gagesand a 25 mm (1 in.) gage length extensometer

mounted on the reduced sectionFig. 18 Averaging extensometer with dual measuring ele-

ments mounted on a specimen. Source: Ref 3

standard also establishes a verification proce-dure to ascertain compliance of an instrument toa particular classification. In addition, it stipu-lates that a certified calibration apparatus mustbe used for all applied displacements and thatthe accuracy of the apparatus must be five timesmore precise than allowable classification errors.Ten displacement readings are required for ver-ification of a classification.

Class A extensometers, if available, would beused for determining precise values of the mod-ulus of elasticity and for precise measurementsof permanent set or very slight deviations fromHooke’s law. Currently, however, there are nocommercially available extensometers manufac-tured that are certified to comply with class Arequirements.

Class B-1 extensometers are frequently usedto determine values of the modulus of elasticityand to measure permanent set or deviations fromHooke’s law. They are also used for determiningvalues such as the yield strength of metallic ma-terials.

Class B-2 extensometers are used for deter-mining the yield strength of metallic materials.

All LVDT and strain-gage extensometers cancomply with class B-1 or class B-2 requirementsif their measuring ranges do not exceed 0.5 mm(0.02 in.). Instruments with measuring ranges ofover 0.5 mm (0.02 in.) can be class C instru-ments.

Most electrical differential transformer exten-someters of 500-strain magnification and highercan conform to class B-1 requirements through-out their measuring range. Extensometers of less

screw. Applicable standards for extensometercalibration or verification include:


DIN EN 10002-4 Part 4: Verification of Extensometers Used inUniaxial Testing, Tensile

ISO 9513 Metallic Materials—Verification ofExtensometers Used in Uniaxial Testing

BS EN 10002-4 Verification of Extensometers Used in UniaxialTesting

ASTM E 83 Standard Practice for Verification andClassification of Extensometers

BS 3846 Methods for Calibration and Grading ofExtensometers for Testing of Materials

Verification and classification of extensometersare applicable to instruments of both the aver-aging and nonaveraging type.

Procedures for the verification and classifi-cation of extensometers can be found in ASTME 83. It establishes six classes of extensometers(Table 3), which are based on allowable errordeviations, as discussed later in this article. This


Table 3 Classification of extensometer systems

Error of strain not to exceed the greater of(a): Error of gage length not to exceed the greater of:

Classification Fixed error, in./in. Variable error, % of strain Fixed error, in. Variable error, % of gage length

Class A 0.00002 �0.1 �0.001 �0.1Class B-1 0.0001 �0.5 �0.0025 �0.25Class B-2 0.0002 �0.5 �0.005 �0.5Class C 0.001 �1 �0.01 �1Class D 0.01 �1 �0.01 �1Class E 0.1 �1 �0.01 �1

(a) Strain of extensometer system—ratio of applied extension to the gage length. Source: ASTM E 83

Fig. 19 Bench-top UTM with laser extensometer. Courtesy of Tinius Olsen Testing Machine Company, Inc.

than 500-strain magnification can comply onlywith class B-1 requirements in their lower (40%)measuring range and are basically class B-2 in-struments.

Dial Extensometers. Although all dial instru-ments usually are considered class C instru-ments, the majority (up to a gage length of 200mm, or 8 in.) are class B-1 and class B-2 in theirinitial 40% measuring range, and class Cthroughout the remainder of the range. Dial in-struments are used universally for determiningyield strength by the extension-under-loadmethod and yield strength of 0.1% offset andgreater.

Class C and D Extensometers. Extensometerswith a gage length of 610 mm (24 in.) begin inclass C, although their overall measuring rangemust be considered as class D.

Gripping Techniques

The use of proper grips and faces for testingmaterials in tension is critical in obtainingmeaningful results. Trial and error often willsolve a particular gripping problem. Tensiletesting of most flat or round specimens can be


Fig. 20 Test setup using wedge grips on (a) a flat specimen with axial extensometer and (b) a round specimen with diametralextensometer

accommodated with wedge-type grips (Fig. 20).Wire and other forms may require differentgrips, such as capstan or snubber types. Theload capacities of grips range from under 4.5kgf (10 lbf ) to 45,000 kgf (100,000 lbf ) ormore. ASTM E 8 describes the various typesof gripping devices used to transmit the mea-sured load applied by the test machine to thetensile test specimen. Additional information ongripping devices can also be found in Chapter3, “Uniaxial Tensile Testing.”

Screw-action grips, or mechanical grips, arelow in cost and are available with load capac-ities of up to 450 kgf (1000 lbf ). This type ofgrip, which is normally used for testing flatspecimens, can be equipped with interchange-able grip faces that have a variety of surfaces.Faces are adjustable to compensate for differentspecimen thicknesses.

Wedge-type grips (Fig. 20) are self-tight-ening and are built with capacities of up to45,000 kgf (100,000 lbf ) or more. Some unitscan be tightened without altering the verticalposition of the faces, making it possible to pre-select the exact point at which the specimenwill be held. The wedge-action design workswell on hard-to-hold specimens and preventsthe introduction of large compressive forcesthat cause specimen buckling.

Pneumatic-action grips are available invarious designs with capacities of up to 90 kgf(200 lbf ). This type of grip clamps the speci-men by lever arms that are actuated by com-

pressed air cylinders built into the grip bodies.A constant force maintained on the specimencompensates for decrease of force due to creepof the specimen in the grip. Another advantageof this design is the ability to optimize grippingforce by adjusting the air pressure, whichmakes it possible to minimize specimen breaksat the grip faces.

Buttonhead grips enable the rapid insertionof threaded-end or mechanical-end specimens.They can be manually or pneumatically oper-ated, as required by the type of material or testconditions.

Alignment. Whether the specimen isthreaded into the crossheads, held by grips, oris in direct contact with platens, the specimenmust be well aligned with the load cell. Anymisalignment will cause a deviation from uni-axial stress in the material studied.

Environmental Chambers

Elevated- and low-temperature tensile testsare conducted with basically the same speci-mens and procedures as those used for room-temperature tensile tests. However, the speci-mens must be heated or cooled in anappropriate environmental chamber (Fig. 21).Also, the test fixtures must be sufficientlystrong and corrosion resistant, and the strain-measuring system must be usable at the testtemperature.


Fig. 21 Tensile-testing apparatus with environmental chamber for testing at up to 540 �C (1000 �F). Source: Ref 3

Strain gages are generally adequate betweencryogenic temperatures and about 600 �C (1100�F), but at higher temperatures, other devicesmust be used. Rod and tube extensometers,which are manufactured from a variety of ma-terials, are most commonly used. When testingis done below room temperature, Teflon is suit-able. Nickel-base superalloys are adequate fortesting in air at up to 1100 �C (2010 �F). Above1100 �C, ceramics are used in reactive atmo-spheres, whereas refractory metals are adequatefor inert environments.

Environmental chambers contain automatedsystems for temperature control and can alsosimulate vacuum and high-humidity environ-ments. More detailed information on environ-mental chambers can be found in Chapter 13,“Hot Tensile Testing,” and Chapter 14, “TensileTesting at Low Temperatures.”

Force Verification ofUniversal Testing Machines

The calibration and verification of UTM sys-tems refer to two different methods that are notsynonymous. Calibration of testing machines re-fers to the procedure of determining the mag-nitude of error in the indicated loads. Verifica-tion is a calibration to ascertain whether theerrors are within a predetermined range. Verifi-cation also implies certification that a machinemeets stated accuracy requirements. Valid veri-fication requires device calibration by skilledpersonnel who are knowledgeable about testingmachines, related instruments, and the properuse of device calibration standards (such asASTM E 74 for load indicators and ASTM E 83for extensometer devices). After verification is


performed, the calibrator or agency must issuereports and certificates attesting to complianceof the equipment with the verification require-ments, including the loading range(s) for whichthe system may be used.

Force Verification. For the load verificationto be valid, the weighing system(s) and associ-ated instrumentation and data systems must beverified annually. In no case should the time in-terval between verifications exceed 18 months.Testing systems and their loading ranges shouldbe verified immediately after relocation ofequipment, after repairs or parts replacement(mechanical or electric/electronic) that could af-fect the accuracy of the load-measuring sys-tem(s), or whenever the accuracy of indicatedloads is suspect, regardless of when the last ver-ification was made.

Force verification standards for mechanicaltesting machines include specifications fromvarious standards organizations such as:


EN 10002-2 Metallic Materials—Tensile Testing—Part 2:Verification of the Force Measurements

DIN EN 10002-2 Part 2: Verification of the Force-MeasuringSystem of Tensile Testing Machines

BS 1610 Materials Testing Machines and ForceVerification Equipment

BS EN 10002-2 Verification of the Force Measuring System ofthe Tensile Testing Machine

ASTM E 4 Standard Practices for Force Verification ofTesting Machines

To comply with ASTM E 4, one or a combi-nation of the three allowable verification meth-ods must be used in the determination of theloading range or multiple loading ranges of thetesting system. These methods are based on theuse of:

● Standard weights● Standard weights and lever balances● Elastic calibration devices

For each loading range, at least five (preferablymore) verification load levels must be selected.The difference between any two successive testloads must not be larger than one third of thedifference between the maximum and minimumtest loads. The maximum can be the full capacityof an individual range. For example, acceptabletest load levels could be 10, 25, 50, 75, and100%, or 10, 20, 40, 70, and 100%, of the statedmachine range.

Regardless of the load verification methodused at each of the test levels, the values indi-

cated by the load-measuring system(s) of thetesting machine must be accurate to within�1% of the loads indicated by the calibrationstandard. If all five or more of the successivetest load deviations are within the �1% requiredin ASTM E 4, the loading ranges may be estab-lished and reported to include all of the values.If any deviations are larger than �1%, the sys-tem should be corrected or repaired immedi-ately. For determining accuracy of values atvarious test loads (or the deviation from the in-dicated load of the standard), ASTM E 74 spec-ifies the required calibration accuracy tolerancesof the three allowable types of verification meth-ods.

For determining material properties, the test-ing machine loads should be as accurate as pos-sible. In addition, deformations resulting fromload applications should be measured as pre-cisely as possible. This is particularly importantbecause the relationship of load to deformation,which may be, for example, extension or com-pression, is the main factor in determining ma-terial properties.

As described previously, load accuracy maybe ensured by following the ASTM E 4 proce-dure. In a similar manner, the methods containedin ASTM E 83, if followed precisely, will ensurethat the devices or instruments used for defor-mation (strain) measurements will operate sat-isfactorily.

Manufacturers of testing machines calibratebefore shipping and certify conformation to themanufacturer’s guarantee of accuracy and anyapplicable standards, such as ASTM E 4. Sub-sequent calibrations can be made by the manu-facturer or another organization with recognizedequipment that is properly maintained and re-certified periodically.

Example: Calibrating a 60,000 lbf Capac-ity Testing Machine. A 60,000 lbf capacitydial-type UTM of either hydraulic or screw-driven design will have the following typicalscale ranges:

● 0 to 60,000 lbf reading by 50 lbf divisions● 0 to 30,000 lbf reading by 25 lbf divisions● 0 to 12,000 lbf reading by 10 lbf divisions● 0 to 1200 lbf reading by 1 lbf divisions

As discussed previously, the ASTM required ac-curacy is �1% of the indicated load above 10%of each scale range. Most manufacturers pro-duce equipment to an accuracy of �0.5% of theindicated load or � one division, whichever isgreater.


According to ASTM specifications, the60,000 lbf scale range must be within 1% at60,000 lbf (�600 lbf ) and at 6000 lbf (�60lbf ). In both cases, the increment division is 50lbf. Although the initial calibration by the man-ufacturer is to closer tolerance than ASTM E 4,subsequent recalibrations are usually to the�1% requirement. In the low range, the ma-chine must be accurate (�1%) from 120 to 1200lbf. Thus, the machine must be verified from 120to 60,000 lbf.

If proving rings are used in calibration, a60,000 lbf capacity proving ring is usable downto a 6000 lbf load level. A 6000 lbf capacityproving ring is usable down to a 600 lbf loadlevel, and a 1000 lbf capacity proving ring isusable down to a 100 lbf load level.

If calibrating load cells are used, a 60,000 lbfcapacity load cell is usable down to a 3000 lbfload level, a 6000 lbf capacity load cell is usableto a 3000 lbf load level, and a 600 lbf capacityload cell is usable down to a 120 lbf load level.

Before use, proving rings and load cells mustbe removed from their cases and allowed to sta-bilize to ambient (surrounding) temperature.Upon stabilization, either type of unit is placedon the table of the testing machine. At this stage,proving rings are ready to operate, but load cellsmust be connected to an appropriate powersource and again be allowed to stabilize, gen-erally for 5 to 15 min.

Each system is set to zero, loaded to the fullcapacity of the machine or elastic device, thenunloaded to zero for checking. Loading to fullcapacity and unloading must be repeated until astable zero is obtained, after which the load ver-ification readings are made at the selected testload levels.

For the highest load range of 60,000 lbf, loadsare applied to the calibrating device from itsminimum lower limit (6000 lbf for proving ringsand 3000 lbf for load cells) to its maximum60,000 lbf in a minimum of five steps, or testload levels, as discussed previously in the sec-tion “Force Verification of Universal TestingMachines” in this chapter. In the verificationloading procedure for proving rings, a “set-the-load” method usually is used. The test load isdetermined, and the nominal load is preset onthe proving ring. The machine load readout isread when the nominal load on the proving ringis achieved. For load cells, a “follow-the-load”method can be used, wherein the load on thedisplay indicator is followed until the loadreaches the nominal load, which is the pre-

selected load level on the readout of the testingmachine.

In both methods, the load of the testing ma-chine and the load of the calibration device arerecorded. The error, E, and the percent error, Ep,can be calculated as:

E � A � B(A � B)

E � � 100 (Eq 13)p B

where A is the load indicated by the machinebeing verified in lbf, kgf, or N, and B is the cor-rect value of the applied load (lbf, kgf, or N), asdetermined by the calibration device.

This procedure is repeated until each scalerange of the testing machine has been calibratedfrom minimum to maximum capacity. The nec-essary reports and certificates are then prepared,with the loading range(s) indicated clearly as re-quired by ASTM E 4. Figures 8(b) and 9 illus-trate UTMs being calibrated with elastic provingrings and calibration load cells.

Tensile TestingRequirements and Standards

Tensile testing requirements are specified invarious standards for a wide variety of differentmaterials and products. Table 4 lists various ten-sile testing specifications from several standardsorganizations. These specifications define re-quirements for the test apparatus, test specimens,and test procedures.

Standard tensile tests are conducted using athreaded tensile specimen geometry, like thestandard ASTM geometry (Fig. 22) of ASTM E8. To load the specimen in tension, the threadedspecimen is screwed into grips attached to eachcrosshead. The boundary condition, or load, isapplied by moving the crossheads away fromone another.

For a variety of reasons, it is not always pos-sible to fabricate a specimen as shown in Fig.22. For thin plate or sheet materials, a flat, ordog-bone, specimen geometry is used. The dog-bone specimen is held in place by wedge shapedgrips. The holding capacity of the grips providesa practical limit to the strength of material thata machine can test. Other specimen geometriescan be tested, with certain cautions, and for-mulas for critical dimensions are given in ASTME 8 and in Chapter 3, “Uniaxial Tensile Testing.”


Table 4 Tensile testing standards for various materials and product forms


ASTM A 770 Standard Specification for Through-Thickness Tension Testing of Steel Plates for Special ApplicationsASTM A 931 Standard Test Method for Tension Testing of Wire Ropes and StrandASTM B 557 Standard Test Methods of Tension Testing Wrought and Cast Aluminum- and Magnesium-Alloy ProductsASTM B 557M Standard Test Methods of Tension Testing Wrought and Cast Aluminum- and Magnesium-Alloy Products [Metric]ASTM C 565 Standard Test Methods for Tension Testing of Carbon and Graphite Mechanical MaterialsASTM C 1275 Standard Test Method for Monotonic Tensile Strength Testing of Continuous Fiber-Reinforced Advanced Ceramics with

Solid Rectangular Cross-Section Specimens at Ambient TemperatureASTM C 1359 Standard Test Method for Monotonic Tensile Strength Testing of Continuous Fiber-Reinforced Advanced Ceramics with

Solid Rectangular Cross-Section Specimens at Elevated TemperaturesASTM D 76 Standard Specification for Tensile Testing Machines for TextilesASTM E 8 Standard Test Methods for Tension Testing of Metallic MaterialsASTM E 8M Standard Test Methods for Tension Testing of Metallic Materials [Metric]ASTM E 338 Standard Test Method of Sharp-Notch Tension Testing of High-Strength Sheet MaterialsASTM E 345 Standard Test Methods of Tension Testing of Metallic FoilASTM E 602 Standard Method for Sharp-Notch Tension Testing with Cylindrical SpecimensASTM E 740 Standard Practice for Fracture Testing with Surface-Crack Tension SpecimensASTM E 1450 Standard Test Method for Tension Testing of Structural Alloys in Liquid HeliumASTM F 1501 Standard Test Method for Tension Testing of Calcium Phosphate CoatingsASTM F 152 Standard Test Methods for Tension Testing of Nonmetallic Gasket MaterialsASTM F 19 Standard Test Method for Tension and Vacuum Testing Metallized Ceramic SealsASTM F 1147 Standard Test Method for Tension Testing of Porous Metal CoatingsBS EN 10002 Tensile Testing of Metallic MaterialsBS 18 Method for Tensile Testing of Metals (Including Aerospace Materials)BS 4759 Method for Determination of K-Values of a Tensile Testing SystemBS 3688-1 Tensile TestingBS 3500-6 Tensile Stress Relaxation TestingBS 3500-3 Tensile Creep TestingBS 3500-1 Tensile Rupture TestingBS 1687 Medium-Sensitivity Tensile Creep TestingBS 1686 Long-Period, High-Sensitivity, Tensile Creep TestingDIN 53455 Tensile Testing: Testing of PlasticsDIN 53328 Testing of Leather, Tensile TestDIN 50149 Tensile Test, Testing of Malleable Cast IronEN 10002-1 Metallic Materials—Tensile Testing—Part 1: Method of Test at Ambient TemperatureISO 204 Metallic Materials—Uninterrupted Uniaxial Creep Testing Intension—Method of TestISO 783 Metallic Materials—Tensile Testing at Elevated TemperatureISO 6892 Metallic Materials—Tensile Testing at Ambient TemperatureJIS B 7721 Tensile Testing MachinesJIS K 7113 Testing Methods for Tensile Properties of Plastics (English Version)

Accuracy, Repeatability, and Precision ofTensile Tests. Accuracy and precision of test re-sults can only be quantified when known quan-tities are measured. One difficulty of assessingdata is that no agreed-upon “material standard”exists as reference material with known prop-erties for strength and elongation. Tests of the“standard material” would reveal the system ac-curacy, and repeated experiments would quan-tify its precision and repeatability.

A variety of factors influence accuracy, pre-cision, and repeatability of test results. Sourcesfor errors in tensile testing are mentioned in theappendix of ASTM E 8. Errors can be groupedinto three broad categories:

● Instrumental errors: These can involve ma-chine stiffness, accuracy and resolution ofthe load cell output, alignment of the speci-men, gripping of the specimen, and accuracyof the extensometer.

● Testing errors: These can involve initialmeasurement of specimen geometry, elec-tronic zeroing, and establishing a preloadstress level in the specimen.

● Material factors: These describe the rela-tionship between the material intended to bestudied and that being tested. For example,does the material in the specimen representthe parent material, and is it homogenous?Other material factors would include speci-men preparation, specimen geometry, andmaterial strain-rate sensitivity.

The ASTM committee for tensile testing re-ported on a round robin set of experiments toassess repeatability and to judge precision ofstandard quantities. In this series (see appen-dix of ASTM E 8) six specimens of six ma-terials were tested at six different laboratories.The comparison of measurements within alaboratory and between laboratories is given


Table 5 Results of round-robin tensile testing

Coefficient of variation, %

Property Within laboratory Between laboratory

Tensile strength 0.91 1.300.02% yield strength 2.67 4.460.2% yield strength 1.35 2.32Elongation in 5D 2.97 6.36Reduction in area 2.80 4.59

Source: ASTM E 8

in Table 5. The data show the highest levelof reproducibility in the strength measure-ments; the lowest reproducibility is found inelongation and reduction of area. Within-lab-oratory results were always more reproduciblethan those between laboratories.

ACKNOWLEDGMENTS


● J.W. House and P.P. Gillis, Testing Machinesand Strain Sensors, Mechanical Testing andEvaluation, Vol 8, ASM Handbook, ASM In-ternational, 2000, p 79–92

● M.A. Bishop, J.J. Martin, and K. Hendry,Chapter 2, Tensile-Testing Equipment, Ten-sile Testing, P. Han, Ed., ASM International,1992, p 25–48

● P.P. Gillis and T.S. Gross, Effect of StrainRate on Flow Properties, Mechanical Test-

ing, Vol 8, Metals Handbook, 9th ed., Amer-ican Society for Metals, 1985, p 38–46

REFERENCES

1. R.C. Anderson, Inspection of Metals: De-structive Testing, ASM International, 1988,p 83–119

2. H.E. Davis, G.E. Troxell, and G.F.W.Hauck, The Testing of Engineering Materi-als, 4th ed., McGraw-Hill, 1982, p 80–124

3. P. Han, Ed., Tensile Testing, ASM Interna-tional, 1992, p 28

4. G.E. Dieter, Mechanical Metallurgy, Mc-Graw-Hill, 2nd ed., 1976, p 349

5. D.J. Shippy, P.P. Gillis, and K.G. Hoge,Computer Simulation of a High Speed Ten-sion Test, J. Appl. Polym. Sci., AppliedPolymer Symposia (No. 5), 1967, p 311–325

6. P.P. Gillis and D.J. Shippy, Vibration Anal-ysis of a High Speed Tension Test, J. Appl.Polym. Sci., Applied Polymer Symposia(No. 12), 1969, p 165–179

7. M.A. Hamstad and P.P. Gillis, EffectiveStrain Rates in Low-Speed Uniaxial Ten-sion Tests, Mater. Res. Stand., Vol 6 (No.11), 1966, p 569–573

8. P. Gillis and J.J. Gilman, Dynamical Dis-location Theories of Crystal Plasticity, J.Appl. Phys., Vol 36, 1965, p 3375–3386

9. J.E. Hockett and P.P. Gillis, MechanicalTesting Machine Stiffness, Parts I and II,Int. J. Mech. Sci., Vol 13, 1971, p 251–275

10. W.G. Johnston, Yield Points and DelayTimes in Single Crystals, J. Appl. Phys., Vol33, 1962, p 2716

11. H.G. Baron, Stress-Strain Curves of SomeMetals and Alloys at Low Temperatures andHigh Rates of Strain, J. Iron Steel Inst.(Brit.), Vol 182, 1956, p 354

12. J. Miklowitz, The Initiation and Propaga-tion of the Plastic Zone in a Tension Bar ofMild Steel as Influenced by the Speed ofStretching and Rigidity of the Testing Ma-chine, J. Appl. Mech. (Trans. ASME), Vol14, 1947, p A-31

13. M.A. Hamstead, “The Effect of Strain Rateand Specimen Dimensions on the YieldPoint of Mild Steel,” Lawrence RadiationLaboratory Report UCRL-14619, April1966

Fig. 22 Standard ASTM geometry for threaded tensile speci-mens. Dimensions for the specimen are taken from

ASTM E 8M (metric units), or ASTM E 8 (English units).

CHAPTER 5

Tensile Testing for Design

DESIGN is the ultimate function of engineer-ing in the development of products and pro-cesses, and an integral aspect of design is theuse of mechanical properties derived from me-chanical testing. The basic objective of productdesign is to specify the materials and geometricdetails of a part, component, and assembly sothat a system meets its performance require-ments. For example, minimum performance ofa mechanical system involves transmission ofthe required loads without failure for the pre-scribed product lifetime under anticipated envi-ronmental (thermal, chemical, electromagnetic,radiation, etc.) conditions. Optimum perfor-mance requirements may also include additionalcriteria such as minimum weight, minimum lifecycle cost, environmental responsibility, humanfactors, and product safety and reliability.

This chapter introduces the basic concepts ofmechanical design and its general relation withthe properties derived from tensile testing. Prod-uct design and the selection of materials are keyapplications of mechanical property data derivedfrom testing. Although existing and feasibleproduct shapes are of infinite variety and theseshapes may be subjected to an endless array ofcomplex load configurations, a few basic stressconditions describe the essential mechanical be-havior features of each segment or componentof the product. These stress conditions includethe following:

● Axial tension or compression● Bending, shear, and torsion● Internal or external pressure● Stress concentrations and localized contact

loads

Mechanical testing under these basic stress con-ditions using the expected product load/timeprofile (static, impact, cyclic) and within the ex-pected product environment (thermal, chemical,

electromagnetic, radiation, etc.) provides the de-sign data required for most applications.

In conducting mechanical tests, it is also veryimportant to recognize that the material maycontain flaws and that its microstructure (andproperties) may be directional (as in composites)and heterogeneous or dependent on location (asin carburized steel). To provide accurate mate-rial characteristics for design, one must take careto ensure that the geometric relationships be-tween the microstructure and the stresses in thetest specimens are the same as those in the prod-uct to be designed.

It is also important to consider the complexityof materials selection for a combination of prop-erties such as strength, toughness, weight, cost,and so on. This chapter briefly describes designcriteria for some basic property combinationssuch as strength, weight, and costs. More de-tailed information on various performance in-dices in design, based on the methodology ofAshby, can be found in the article “MaterialProperty Charts” in Materials Selection and De-sign, Volume 20 of ASM Handbook. The mate-rials selection method developed by Ashby isalso available as an interactive electronic prod-uct (Ref 1).

Product Design

Design involves the application of physicalprinciples and experience-based knowledge todevelop a predictive model of the product. Themodel may be a prototype, a simplified mathe-matical model, or a complex finite elementmodel. Regardless of the level of sophisticationof the model, reaching the product design ob-jectives of material and geometry specificationsfor successful product performance requires ac-curate material parameters (Ref 2).




Fig. 1 Bar under axial tension

Modern design methods help manage thecomplex interactions between product geometry,material microstructure, loading, and environ-ment. In particular, engineering mechanics(from simple equilibrium equations to complexfinite element methods) extrapolates the resultsof basic mechanical testing of simple shapes un-der representative environments to predict thebehavior of actual product geometries under realservice environments.

In the following sections, a simple tie bar isused to illustrate the application of mechanicalproperty data to material selection and designand to highlight the general implications for me-chanical testing. Material subjected to the basicstress conditions is considered in order to estab-lish design approaches and mechanical testmethods, first in static loading and then in dy-namic loading and aggressive environments.More detailed reference books on mechanicaldesign and engineering methods are also listedin the “Selected References” at the end of thischapter.

Design for Strength in Tension

Figure 1 shows an axial tensile load appliedto a tie bar representing, for example, a boomcrane support, cable, or bolt. For this elementarycase, the stress in the bar is uniformly distributedover the cross section of the tie bar and is givenby:

r � F/A (Eq 1)

where F is the applied force and A is the cross-sectional area of the bar. To avoid failure of thebar, this stress must be less than the failurestress, or strength, of the material:

r � F/A � r (Eq 2)f

where rf is the stress at failure. The failurestress, rf, can be the yield strength, ro, if per-manent deformation is the criterion for failure,or the ultimate tensile strength, ru, if fracture isthe criterion for failure. In a ductile metal orpolymer, the ultimate tensile strength is definedas the stress at which necking begins, leading tofracture. In a brittle material, the ultimatestrength is simply the stress at fracture. Typicalvalues of yield and ultimate tensile strength forvarious materials are summarized in Tables 1, 2,and 3. These typical values are intended only for

general comparisons; design values should bebased on statistically based minimum values oron minimum values published in the purchasespecifications of materials (such as ASTM stan-dards).

Equation 2 combines the performance of thepart (load F) with the part geometry (cross-sec-tional area A) and the material characteristics(strength rf). The equation can be used severalways for design and material selection. If thematerial and its strength are specified, then, fora given load, the minimum cross-sectional areacan be calculated; or, for a given cross-sectionalarea, the maximum load can be calculated. Con-versely, if the force and area are specified, thenmaterials with strengths satisfying Eq 2 can beselected.

Factor of Safety. Normally, designs involvethe use of some type of a factor of safety. Thisfactor, which is always greater than unity, is usedin the design of components to ensure that thecomponent can satisfactorily perform its in-tended purpose. The factor of safety is used toaccount for the uncertainties that exist in thereal-world use of any component. Two mainclassifications of factors affect the factor ofsafety in a design, and they are these:

● Uncertainties associated with the materialproperties of the component itself, includingthe expected properties of the materials usedto fabricate the component, as well as anyuncertainties introduced by manufacturingand fabrication processing

● Uncertainties associated with the level andtype of loading the component will see, aswell as the actual service conditions and anyenvironmental condition the component mayexperience

Tensile Testing for Design / 93

The factor of safety is used to establish a targetstress level for the design. This is sometimes re-ferred to as the allowable stress, the maximumallowable stress, or simply, the design stress. Inorder to determine this allowable stress condi-tion, the failure stress is simply divided by thesafety factor. Safety factors ranging from 1.5 to10 are typical. The lower the uncertainty is, thelower the safety factor.

Design for Strength, Weight, and Cost

If minimum weight or minimum cost criteriamust also be satisfied, Eq 2 can be modified byintroducing other material parameters. To illus-trate, the area A in Eq 2 is related to density andmass by A � M/qL, where M is the mass of thebar, L is the length of the bar, and q is the ma-

terial density. Solving Eq 2 for F and substitut-ing for A:

F � r A � (r /q)(M/L) (Eq 3)f f

From Eq 3 it is clear that, to transmit a givenload, F, the material mass will be minimized ifthe property ratio (rf /q) is maximized. Thestrength-to-weight ratio of a material is an im-portant design and performance index; Fig. 2 isa plot developed by Ashby for comparison ofmaterials by this design criterion. Similarly, ma-terial selection for minimum material cost canbe obtained by maximizing the parameter (rf /qc), or strength-to-cost ratio, where c representsthe material cost per unit weight. These types ofperformance indexes for design and the use ofmaterials property charts like Fig. 2 are de-scribed in more detail in Ref 7 and in the articles“Material Property Charts” and “Performance

Table 1 Typical room-temperature tensile properties of ferrous alloys and superalloysStrength in tension, MPa (ksi) Modulus of elasticity,

GPa (106 psi)

Material0.2% offset

yield strength Ultimate Tension ShearElongation in

50 mm (2 in.), %

Cast irons

Gray cast iron . . . 140 (20) 105 (15) 40 (6) 1White cast iron . . . 415 (60) 140 (20) 55 (8) . . .Nickel cast iron, 1.5% nickel . . . 310 (45) 140 (20) 55 (8) 1Malleable iron 230 (33) 345 (50) 170 (25) 70 (10) 14Ingot iron, annealed 0.02% carbon 165 (24) 290 (42) 205 (30) 85 (12) 45

Steels

Wrought iron, 0.10% carbon 205 (30) 345 (50) 185 (27) 70 (10) 30Steel, 0.20% carbon

Hot-rolled 275 (40) 415 (60) 200 (29) 85 (12) 35Cold-rolled 415 (60) 550 (80) 200 (29) 85 (12) 15Annealed castings 240 (35) 415 (60) 200 (29) 85 (12) 25

Steel, 0.40% carbonHot-rolled 290 (42) 485 (70) 200 (29) 85 (12) 25Heat-treated for fine grain 415 (60) 620 (90) 200 (29) 85 (12) 25Annealed castings 240 (35) 450 (65) 200 (29) 85 (12) 15

Steel, 0.60% carbonHot-rolled 435 (63) 690 (100) 200 (29) 85 (12) 15Heat-treated for fine grain 540 (78) 825 (120) 200 (29) 85 (12) 15

Steel, 0.80% carbonHot-rolled 505 (73) 825 (120) 200 (29) 85 (12) 10Oil-quenched, not drawn 860 (125) 1240 (180) 200 (29) 85 (12) 2

Steel, 1.00% carbonHot-rolled 570 (83) 930 (135) 200 (29) 85 (12) 10Oil-quenched, not drawn 965 (140) 1515 (220) 200 (29) 85 (12) 1

Nickel steel, 3.5% nickel, 0.40% carbon, max.hardness for machinability

1035 (150) 1170 (170) 200 (29) 85 (12) 12

Silicomanganese steel, 1.95% Si, 0.70% Mn,spring tempered

895 (130) 1200 (174) 200 (29) 85 (12) 1

Superalloys (wrought)

A286 (bar) 760 (110) 1080 (157) 180 (26) . . . 28Inconel 600 (bar) 250 (36) 620 (90) . . . . . . 47IN-100 (60 Ni-10Cr-15Co, 3Mo, 5.5Al, 4.7Ti) 850 (123) 1010 (147) 215 (31) . . . 9IN-738 915 (133) 1100 (159) 200 (29) . . . 5

Source: Ref 3–5


Table 2 Typical room-temperature tensile properties of nonferrous alloys

Metal or alloy

Approximatecomposition,

% Condition

0.2% offset tensileyield strength,

MPa (ksi)

Tensilestrength,MPa (ksi)

Tensile modulusof elasticity,

GPa (106 psi)

Elongation in50 mm (2 in.),

%

Heavy nonferrous alloys (�8–9 g/cm3)

Copper Cu Annealed 33 (4.8) 209 (30) 125 (18) 60Cold drawn 333 (48) 344 (50) 112 (16) 14

Free-cutting brass 61.5 Cu, 35.5 Zn, 3 Annealed 125 (18) 340 (49) 85 (12) 53Pb Quarter hard, 15%

reduction310 (45) 385 (56) 85 (12) 20

Half hard, 25%reduction

360 (52) 470 (68) 95 (14) 18

High-leaded brass (1mm thick)

65 Cu, 33 Zn, 2 Pb Annealed, 0.050 mmgrain

105 (15) 325 (47) 85 (12) 55

Extra hard 425 (62) 585 (85) 105 (15) 5Red brass (1 mm

thick)85 Cu, 15 Zn Annealed, 0.070 mm

grain70 (10) 270 (39) 85 (12) 48

Extra hard 420 (61) 540 (78) 105 (15) 4Aluminum bronze 89 Cu, 8 Al, 3 Fe Sand cast 195 (28) 515 (75) . . . 40

Extruded 260 (38) 565 (82) 125 (18) 25Beryllium copper 97.9 Cu, 1.9 Be, 0.2

NiA (solution

annealed). . . 500 (73) 125 (18) 35

HT (hardened) 1035 (150) 1380 (200) 125 (18) 2Manganese bronze 58.5 Cu, 39 Zn, 1.4 Soft annealed 205 (30) 450 (65) 90 (13) 35

(A) Fe, 1 Sn, 0.1 Mn Hard, 15% reduction 415 (60) 565 (82) 105 (15) 25Phosphor bronze,

5% (A)95 Cu, 5 Sn Annealed, 0.035 mm

grain150 (22) 340 (49) 90 (13) 57

Extra hard, 0.015mm grain

635 (92) 650 (94) 115 (17) 5

Cupronickel, 30% 70 Cu, 30 Ni Annealed at 760 �C 140 (20) 380 (55) 150 (22) 45Cold drawn, 50%

reduction540 (78) 585 (85) 150 (22) 15

Light nonferrous alloys (�2.7 g/cm3 for Al alloys; �1.8 g/cm3 for Mg alloys)

Aluminum Al Sand cast, 1100-F 40 (5.8 or 6) 75 (11) 60 (9) 22Annealed sheet,

1100-O35 (5.075) 90 (13) 70 (10) 35

Hard sheet, 1100-H18

145 (21) 165 (24) 70 (10) 5

Aluminum alloy 93 Al, 4.5 Cu, 1.5 Temper O 75 (11) 185 (27) 73 (11) 202024 Mg, 0.6 Mn Temper T36 395 (57) 495 (72) 73 (11) 13

Aluminum alloy 93 Al, 4.4 Cu, 0.8 Temper O 95 (14) 185 (27) 73 (11) 182014 Si, 0.8 Mn, 0.4

MgTemper T6 415 (60) 485 (70) 73 (11) 13

Aluminum alloy 97 Al, 2.5 Mg, 0.25 Temper O 90 (13) 195 (28) 69 (10) 305052 Cr Temper H38 255 (37) 290 (42) 69 (10) 8

Aluminum alloy 94 Al, 5.0 Mg, 0.7 Temper O 160 (23) 310 (45) . . . 245456 Mn, 0.15 Cu, 0.15

CrTemper H321 255 (37) 350 (51) . . . 16

Aluminum alloy 90 Al, 5.5 Zn, 1.5 Temper O 105 (15) 230 (33) . . . 177075 Cu, 2.5 Mg, 0.3

CrTemper T6 505 (73) 570 (83) . . . 11

Magnesium Mg Cast 21 (3) 90 (13) 40 (6) 2–6Extruded 69–105 (10–15) 195 (28) 40 (6) 5–8Rolled 115–140 (17–20) 200 (29) 40 (6) 2–10

Magnesium alloy 90 Mg, 10 Al, 0.1 Cast, condition F 85 (12) 150 (22) 45 (7) 2AM100A Mn Cast, condition T61 150 (22) 275 (40) 45 (7) 1

Magnesium alloy 91 Mg, 6 Al, 3 Zn, Cast, condition F 95 (14) 200 (29) 45 (7) 6AZ63A 0.2 Mn Cast, condition T6 130 (19) 275 (40) 45 (7) 5

(continued)


Indices” in Materials Selection and Design, Vol-ume 20 of ASM Handbook.

Design for Stiffness in Tension

In addition to designing for strength, anotherimportant design criterion is often the stiffnessor rigidity of a material. The elastic deflectionof a component under load is governed by thestiffness of the material. For example, if a bridgeor building is designed to avoid failure, it maystill undergo motion under applied loads if it isnot sufficiently rigid. As another example, if thetie bar in Fig. 1 were a bolt clamping a cap to apressure vessel, excessive elastic change inlength of the bolt under load might allow leak-age through a gasket between the cap and vessel.

Elastic change in length occurs when an axialload is applied to the bar and is given by:

DL � eL (Eq 4)

where DL is the change in length and e is thestrain in the bar. In the elastic range of defor-mation, axial stress is proportional to the strain:

r � Ee (Eq 5)

where the proportionality factor is E, the elasticmodulus of the bar material.

The elastic modulus can be considered aphysical property, because it is fundamentallyrelated to the bond strength between the atomsor molecules in the material; that is, the strongerthe bond, the higher the elastic modulus. Thus,

Table 3 Typical room-temperature tensile properties of plastics

Material Tensile strength, MPa (ksi) Elongation, % Modulus of elasticity, GPa (106 psi)

Thermosets

EP, reinforced with glass cloth 350 (51) . . . 175 (25)MF, alpha-cellulose filler 50–90 (7–13) 0.6–0.9 9 (1)PF, no filler 50–55 (7–9) 1.0–1.5 5–7 (0.7–1)PF, wood flour filler 45–60 (7–9) 0.4–0.8 6–8 (0.87–1.16)PF, macerated fabric filler 25–65 (4–9) 0.4–0.6 6–9 (0.87–1)PF, cast, no filler 40–65 (6–9) 1.5–2.0 3 (0.43)Polyester, glass-fiber filler 35–65 (5–9) . . . 11–14 (1.6–2.0)UF, alpha-cellulose filler 55–90 (8–13) 0.5–1.0 10 (1.5)

Thermoplastics

ABS 35–45 (5–7) 15–60 1.7–2.2 (0.25–0.32)CA 15–60 (2–9) 6–50 0.6–3.0 (0.1–0.4)CN 50–55 (7–9) 40–45 1.3–15.0 (0.18–2)PA 80 (12) 90 3.0 (0.43)PMMA 50–70 (7–10) 2–10 . . .PS 35–60 (5–9) 1–4 3.0–4.0 (0.4–0.6)PVC, rigid 40–60 (6–9) 5 2.4–2.7 (0.3–0.4)PVCAc, rigid 50–60 (7–9) . . . 2.0–3.0 (0.3–0.4)

ABS, acrylonitrile-butadiene-styrene; CA, cellulose acetate; CN, cellulose nitrate; EP, epoxy; MF, melamine formaldehyde; PA, polyamide (nylon); PF, phenol for-maldehyde; PMMA, polymethyl methacrylate; PS, polystyrene; PVC, polyvinyl chloride; PVCAc, polyvinyl chloride acetate; UF, urea formaldehyde. Source: Ref 6

Table 2 (continued)

Metal or alloy

Approximatecomposition,

% Condition

0.2% offset tensileyield strength,

MPa (ksi)

Tensilestrength,MPa (ksi)

Tensile modulusof elasticity,

GPa (106 psi)

Elongation in50 mm (2 in.),

%

Titanium alloys (�4.5 g/cm3)

Commercial ASTMgrade 2 Ti

98 Ti . . . 275 (40) 345 (50) 103 (15) 20

Ti-5Al-2.5Sn 92 Ti, 5 Al, 2.5 Sn . . . 825 (120) 860 (125) 110 (16) 8–10Ti-3Al-2.5V 94 Ti, 3 Al, 2.5 V Annealed 560 (81) 655 (95) 103 (15) 29

Cold worked andstress relieved

760 (110) 895 (130) 103 (15) 19

Ti-6A1-4V 90 Ti, 6 Al, 4 V Solution treated andaged bar (1–2 in.)

965 (140) 1035 (150) 110 (16) 8

Annealed bar 825 (120) 895 (130) 110 (16) 10Mill annealed . . . 925 (134) . . . . . .


the elastic modulus does not vary much in ma-terial with a given type of crystal structure ormicrostructure. For example, the elastic modu-lus of most steels is typically about 200 GPa (29� 106 psi) for steels of various composition andstrength levels (Fig. 3). However, the moduluscan vary with direction if the material has ananisotropic structure. For example, Fig. 4 is aplot of the tensile and compressive modulus fortype 301 austenitic stainless steel. Transverseand longitudinal values vary, as do values fortensile and compressive loads. At low stresses,the tension and compressive moduli are, by the-ory and experiment, identical. At higher stresses,however, differences in the compressive and ten-

sile moduli can be observed due to the effects ofdeformation (e.g., elongation in tension). Typi-cal values of elastic moduli are given in Table 4for various alloys and metals.

Equations 1 and 5 can be combined with Eq4 to give the design equation:

DL � FL/AE � d (Eq 6)

where d is the design limit on change in lengthof the bar. Just as the strength, or load-carryingcapacity, of the tie bar is related to geometry andmaterial strength (Eq 2), the stiffness of the baris related to geometry and the elastic modulusof the material. Again, part performance (force,

Fig. 2 Strength, rf, plotted against density, q, for various engineered materials. Strength is yield strength for metals and polymers,compressive strength for ceramics, tear strength for elastomers, and tensile strength for composites. Superimposing a line of

constant rf /q enables identification of the optimum class of materials for strength at minimum weight.


F, and deflection, d) is combined with part ge-ometry (length, L, and cross-sectional area, A)and material characteristics (elastic modulus, E)in this design equation. To assure that the changein length is less than the allowable limit for agiven force and material, the geometry param-eters L and A can be calculated; or, for givendimensions, the maximum load can be calcu-lated. Alternatively, for a given force and geo-metric parameters, materials can be selectedwhose elastic modulus, E, meets the design cri-terion given in Eq 6.

Similar to design for strength, additional cri-teria involving minimum weight or cost can beincorporated into design for stiffness. These cri-teria lead to the material selection parametersmodulus-to-weight ratio (E/q) and modulus-to-cost ratio (E/qc), values that can be found in Ref7 and ASM Handbook, Volume 20.

Mechanical Testing forStress at Failure and Elastic Modulus

In Eq 2 and 6, the material properties rf andE play critical roles in design of the tie bar.These properties are determined from a simpletensile test described in detail in Chapter 3,“Uniaxial Tensile Testing.” The elastic modulusE is determined from the slope of the elastic partof the tensile stress strain curve, and the failurestress, rf , is determined from the tensile yieldstrength, ro, or the ultimate tensile strength, ru.

Tensile-test specimens are cut from represen-tative samples, as described in more detail inChapter 3. In the example of the tie bar, testpieces would be cut from bar stock that has beenprocessed similarly to the tie bar to be used inthe product. In addition, the test piece should be

Fig. 3 Stress-strain diagram for various steels. Source: Ref 8


machined such that its gage length is parallel tothe axis of the bar. This ensures that any aniso-tropy of the microstructural features will affectperformance of the tie bar in the same way thatthey influence the measurements in the tensiletest. For example, test pieces cut longitudinallyand transverse to the rolling direction of hotrolled steel plates will exhibit the same elasticmodulus and yield strength, but the tensilestrength and ductility will be lower in the trans-verse direction because the stresses will be per-

pendicular to the alignment of inclusions causedby hot rolling (Ref 10).

During tension testing of a material to mea-sure E and rf , in addition to the change in lengthdue to the applied axial tensile loads, the mate-rial will undergo a decrease in diameter. Thisreflects another elastic property of materials, thePoisson ratio, given by:

m � �e /e (Eq 7)t l

where et is the transverse strain and el is thelongitudinal strain measured during the elasticpart of the tension test. Typical values of � rangefrom 0.25 to 0.40 for most structural materials,but � approaches zero for structural foams andapproaches 0.5 for materials undergoing plasticdeformation. While the Poisson effect is of noconsequence in the overall behavior of the tiebar (since the decrease in diameter has a negli-gible effect on the stress in the bar), the Poissonratio is a very important material parameter inparts subjected to multiple stresses. The stressin one direction affects the stress in another di-rection via �. Therefore, accurate measurementsof the Poisson ratio are essential for reliable de-sign analyses of the complex stresses in actualpart geometries, as described later. Typical val-ues of Poisson’s ratio are given in Table 4.

Table 4 Elastic constants for polycrystalline metals at 20 �C (68 �F)

Elastic modulus (E) Bulk modulus (K) Shear modulus (G)

Metal GPa 106 psi GPa 106 psi GPa 106 psi Poisson’s ratio, m

Aluminum 70 10.2 75 10.9 26 3.80 0.345Brass, 30 Zn 101 14.6 112 16.2 37 5.41 0.350Chromium 279 40.5 160 23.2 115 16.7 0.210Copper 130 18.8 138 20.0 48 7.01 0.343Iron, soft 211 30.7 170 24.6 81 11.8 0.293Iron, cast 152 22.1 110 15.9 60 8.7 0.27Lead 16 2.34 46 6.64 6 0.811 0.44Magnesium 45 6.48 36 5.16 17 2.51 0.291Molybdenum 324 47.1 261 37.9 125 18.2 0.293Nickel, soft 199 28.9 177 25.7 76 11.0 0.312Nickel, hard 219 31.8 188 27.2 84 12.2 0.306Nickel-silver, 55Cu-18Ni-27Zn 132 19.2 132 19.1 34 4.97 0.333Niobium 104 15.2 170 24.7 38 5.44 0.397Silver 83 12.0 103 15.0 30 4.39 0.367Steel, mild 211 30.7 169 24.5 82 11.9 0.291Steel, 0.75 C 210 30.5 169 24.5 81 11.8 0.293Steel, 0.75 C, hardened 201 29.2 165 23.9 78 11.3 0.296Steel, tool steel 211 30.7 165 24.0 82 11.9 0.287Steel, tool steel, hardened 203 29.5 165 24.0 79 11.4 0.295Steel, stainless, 2Ni-18Cr 215 31.2 166 24.1 84 12.2 0.283Tantalum 185 26.9 197 28.5 69 10.0 0.342Tin 50 7.24 58 8.44 18 2.67 0.357Titanium 120 17.4 108 15.7 46 6.61 0.361Tungsten 411 59.6 311 45.1 161 23.3 0.280Vanadium 128 18.5 158 22.9 46.7 6.77 0.365Zinc 105 15.2 70 10.1 42 6.08 0.249

Source: Ref 9

Fig. 4 Tensile and compressive modulus at half-hard and full-hard type 301 stainless steel in the transverse and lon-

gitudinal directions. Source: Ref 5


Sonic methods also offer an alternative andmore accurate measurement of elastic proper-ties, because the velocity of an extensionalsound wave (i.e., longitudinal wave speed, VL)is directly related to the square root of the ratioof elastic modulus and density as follows:

1/2V � (E/q) (Eq 8)L

By striking a sample of material on one endand measuring the time for the pulse to travel tothe other end, the velocity can be calculated.Combining this with independent measurementof the density, Eq 8 can be used to calculate theelastic modulus (Ref 8).

Hardness-Strength Correlation

Correlation of hardness and strength has beenexamined for several materials as summarizedin Ref 11. In hardness testing, a simple flat,spherical, or diamond-shaped indenter is forcedunder load into the surface of the material to betested, causing plastic flow of material beneaththe indenter as illustrated in Fig. 5. It would be

expected, then, that the resistance to indentationor hardness is proportional to the yield strengthof the material. Plasticity analysis (Ref 12) andempirical evidence (summarized in Ref 11)show that the pressure on the indenter is ap-proximately three times the tensile yield strengthof the material. However, correlation of hard-ness and yield strength is only straightforwardwhen the strain-hardening coefficient varies di-rectly with hardness. For carbon steels, the fol-lowing relation has been developed to relateyield strength (YS) to Vickers hardness (HV)data (Ref 11):

2 m�21YS (in kgf/mm ) � ⁄3 HV (0.1)

where m is Meyer’s strain-hardening coefficient(Ref 13). To convert kgf/mm2 values to units oflbf/in.2, multiply the former by 1422. This re-lation applies only to carbon steels. Correlationof yield strength and hardness depends on thestrengthening mechanism of the material. Withaluminum alloys, for example, aged alloys ex-hibit higher strain-hardening coefficients andlower yield strengths than cold worked alloys(Ref 11).

For many metals and alloys, there has beenfound to be a reasonably accurate correlation be-tween hardness and tensile strength, ru (Ref 11).Several studies are cited and described in Ref 11and 14, and Tables 5 and 6 summarize hardness-tensile strength multiplying factors for variousmaterials. It must be emphasized, however, thatthese are empirically based relationships, and sotesting may still be warranted to confirm a cor-relation of tensile strength and hardness for aparticular material (and/or material condition).

Fig. 5 Deformation beneath a hardness indenter. (a) Modeling clay. (b) Low-carbon steel

Table 5 Hardness-tensile strength conversionsfor steel

MaterialMultiplying

factor(a)

Heat-treated alloy steel (250–400 HB) 470 HBHeat-treated carbon and alloy steel (�250 HB) 482 HBMedium carbon steel (as-rolled, normalized, or

annealed)493 HB

(a) Tensile strength (in psi) � multiplying factor � HB. Source: Ref 11


A correlation with hardness may not be evident.For example, magnesium alloy castings did notexhibit a hardness-strength correlation in a studyby Taylor (Ref 15).

More detailed information on hardness testsand the estimation of mechanical properties canbe found in Ref 11, 13, and 14. The varioustypes of hardness tests and their selection andapplication are described in Mechanical Testingand Evaluation, Volume 8, of the ASM Hand-book series.

ACKNOWLEDGMENT

This chapter was adapted from H.A. Kuhn,Overview of Mechanical Properties and Testingfor Design, Mechanical Testing and Evaluation,Vol 8, ASM Handbook, ASM International,2000, p 49–69.

REFERENCES

1. Cambridge Engineering Selector, GrantaDesign Ltd., Cambridge, UK, 1998

2. G.E. Dieter, Engineering Design: A Mate-rials and Processing Approach, McGrawHill, 1991, p 1–51, 231–271

3. Metals Handbook, American Society forMetals, 1948

4. F.B. Seely, Resistance of Materials, JohnWiley & Sons, 1947

5. Properties and Selection of Metals, Vol 1,

Metals Handbook, 8th ed., American Soci-ety for Metals, 1961, p 503

6. Modern Plastics Encyclopedia, McGrawHill, 2000

7. M.F. Ashby, Materials Selection for Me-chanical Design, 2nd ed., Butterworth-Hei-nemann, 1999

8. H. Davis, G. Troxell, and G. Hauck, TheTesting of Engineering Materials, 4th ed.,McGraw Hill, 1982, p 314

9. G. Carter, Principles of Physical and Chem-ical Metallurgy, American Society for Met-als, 1979, p 87

10. M.A. Meyers and K.K. Chawla, MechanicalMetallurgy, Prentice-Hall, EdgewoodCliffs, NJ, 1984, p 626–627

11. George Vander Voort, Metallography: Prin-ciples and Practices, ASM International,1999, p 383–385, 391–393

12. R.T. Shield, On the Plastic Flow of Metalsunder Conditions of Axial Symmetry, Proc.R. Soc., Vol A233, 1955, p 267

13. A. Fee, Selection and Industrial Applica-tions of Hardness Tests, Mechanical Testingand Evaluation, Vol 8, ASM Handbook,ASM International, 2000, p 260–277

14. J. Datsko, L. Hartwig, and B. McClory, Onthe Tensile Strength and Hardness Relationfor Metals, Journal of Materials Engineer-ing and Performance, Vol 10 (6), Dec 2001,p 718–722

15. W.J. Taylor, The Hardness Test as a Meansof Estimating the Tensile Strength of Met-als, J.R. Aeronaut. Soc., Vol 46 (No. 380),1942, p 198–202

SELECTED REFERENCES

● M. Ashby, Materials Selection for Mechan-ical Design, 2nd ed., Butterworth-Heine-mann, 1999

● N. Dowling, Mechanical Behavior of Mate-rials: Engineering Methods for Deforma-tion, Fracture, and Fatigue, Prentice Hall,1999

● R.C. Juvinall and K.M. Marshek, Funda-mentals of Machine Component Design, 2nded., John Wiley & Sons, 1991

● J.E. Shigley and L.D. Mitchell, MechanicalEngineering Design, 4th ed., McGraw-Hill,1983

Table 6 Multiplying factors for obtainingtensile strength from hardness

MaterialMultiplying

factor range(a)

Heat treated carbon and alloy steel 470–515 HBAnnealed carbon steel 515–560 HBAll steels 448–515 HVNi-Cr austenitic steels 448–482 HVSteel; sheet, strip, and tube 414–538 HVAluminum alloys; bar and extrusions 426–650 HBAluminum alloys; bar and extrusions 414–605 HVAluminum alloys; sheet, strip, and tube 470–582 HVAl-Cu castings 246–426 HBAl-Si-Ni castings 336–426 HBAl-Si castings 381–538 HBPhosphor bronze castings 336–470 HBBrass castings 470–672 HB

(a) Tensile strength (in psi) � multiplying factor � hardness. Source: Ref 11, 15

CHAPTER 6

Tensile Testing forDetermining Sheet Formability

THE TERM FORMABILITY refers to the easewith which a metal can be shaped through plas-tic deformation. Evaluation of the formability ofa metal involves measurement of strength, duc-tility, and the amount of deformation required tocause fracture. The term “workability” is usedinterchangeably with formability; however,formability refers to the shaping of sheet metal,while workability refers to shaping materials bybulk forming processes such as forging and ex-trusion.

Sheet metal forming operations consist of alarge family of processes, ranging from simplebending to stamping and deep drawing of com-plex shapes. Because sheet forming operationsare so diverse in type, extent, and rate, no singletest provides an accurate indication of the form-ability of a material in all situations. However,as will be discussed in this chapter, the uniaxialtensile test is one of the most widely used testsfor determining sheet metal formability. Itshould also be noted that tensile testing at ele-vated temperatures is also widely used to deter-mine the workability of materials. See Chapter13, “Hot Tensile Testing,” for details.

Effect of MaterialProperties on Formability

The properties of sheet metals vary consid-erably, depending on the base metal (steel, alu-minum, copper, and so on), alloying elementspresent, processing, heat treatment, gage, andlevel of cold work. In selecting material for aparticular application, a compromise usuallymust be made between the functional propertiesrequired in the part and the forming propertiesof the available materials. For optimal forma-

bility in a wide range of applications, the workmaterial should:

● Distribute strain uniformly● Reach high strain levels without necking or

fracturing● Withstand in-plane compressive stresses

without wrinkling● Withstand in-plane shear stresses without

fracturing● Retain part shape upon removal from the die● Retain a smooth surface and resist surface

damage

Some production processes can be success-fully operated only when the forming propertiesof the work material are within a narrow range.More frequently, the process can be adjusted toaccommodate shifts in work material propertiesfrom one range to another, although sometimesat the cost of lower production and higher ma-terial waste. Some processes can be successfullyoperated using work material that has a widerange of properties. In general, consistency inthe forming properties of the work material isan important factor in producing a high outputof dimensionally accurate parts.

Strain Distribution

Three material properties determine the straindistribution in a forming operation:

● The strain-hardening coefficient (also knownas the work-hardening coefficient or expo-nent) or n value

● The strain rate sensitivity or m value● The plastic strain ratio (anisotropy factor) or

r value

The ability to distribute strain evenly dependson the n value and the m value. The ability to




reach high overall strain levels depends on manyfactors, such as the base material, alloying ele-ments, temper, n value, m value, r value, thick-ness, uniformity, and freedom from defects andinclusions.

The n value, or strain-hardening coefficient,is determined by the dependence of the flow(yield) stress on the level of strain. In materialswith a high n value, the flow stress increasesrapidly with strain. This tends to distribute fur-ther strain to regions of lower strain and flowstress. A high n value is also an indication ofgood formability in a stretching operation.

In the region of uniform elongation, the nvalue is defined as:

d ln rTn � (Eq 1)d ln e

where rT is the true stress (load/instantaneousarea). This relationship implies that the truestress-strain curve of the material can be ap-proximated by a power law constitutive equationproposed in Ref 1:

nr � ke (Eq 2)T

where k is a constant known as the strength co-efficient.

Equation 2 provides a good approximation formost steels, but is not very accurate for dual-phase steels and some aluminum alloys. Forthese materials, two or three n values may needto be calculated for the low, intermediate, andhigh strain regions.

When Eq 2 is an accurate representation ofmaterial behavior, n � ln (1 � eu), where eu isthe uniform elongation, or elongation at maxi-mum load in a tensile test. By definition, ln (1� eu) is identical to eu, which is the true strainat uniform elongation.

Most steels with yield strengths below 345MPa (50 ksi) and many aluminum alloys have nvalues ranging from 0.2 to 0.3. For many higheryield strength steels, n is given by the relation-ship (Ref 2):

70n � (Eq 3)

(yield strength in MPa)

A high n value leads to a large difference be-tween yield strength and ultimate tensilestrength (engineering stress at maximum load in

a tensile test). The ratio of these properties there-fore provides another measure of formability.

The m value, or strain rate sensitivity, is de-fined by:

d ln rTm � (Eq 4)d ln e

where is the strain rate, de/dt. This implies aerelationship of the form:

mr � f(e) • eT

or

n mr � ke • e (Eq 5)T

where Eq 5 incorporates Eq 2 between stress andstrain.

A positive strain rate sensitivity indicates thatthe flow stress increases with the rate of defor-mation. This has two consequences. First, higherstresses are required to form parts at higher rates.Second, at a given forming rate, the material re-sists further deformation in regions that are be-ing strained more rapidly than adjacent regionsby increasing the flow stress in these regions.This helps to distribute the strain more uni-formly.

The need for higher stresses in a formingoperation is usually not a major consideration,but the ability to distribute strains can be crucial.This becomes particularly important in the post-uniform elongation region, where necking andhigh strain concentrations occur. An approxi-mately linear relationship has been reported be-tween the m value and the post-uniform elon-gation for a variety of steels and nonferrousalloys (Ref 3). As m increases from �0.01 to�0.06, the post-uniform elongation increasesfrom 2 to 40%.

Metals in the superplastic range have high mvalues of 0.2 to 0.7, which are one to two ordersof magnitude higher than typical values for steel.At ambient temperatures, some metals, such asaluminum alloys and brass, have low or slightlynegative m values, which explains their lowpost-uniform elongation.

High n and m values lead to good formabilityin stretching operations, but have little effect ondrawability. In a drawing operation, metal in theflange must be drawn in without causing fracturein the wall. In this case, high n and m valuesstrengthen the wall, which is beneficial, but they

Tensile Testing for Determining Sheet Formability / 103

Fig. 2 Typical forming limit diagram for steelFig. 1 Drawn cup with ears in the directions of high r value

also strengthen the flange and make it harder todraw in, which is detrimental.

The r value, or plastic strain ratio, relates todrawability and is known as the anisotropy fac-tor. This is defined as the ratio of the true widthstrain to the true thickness strain in the uniformelongation region of a tensile test:

wln� �we owr � � (Eq 6)

e tt ln� �to

The r value is a measure of the ability of amaterial to resist thinning. In drawing, materialin the flange is stretched in one direction (radi-ally) and compressed in the perpendicular direc-tion (circumferentially). A high r value indicatesa material with good drawing properties.

The r value frequently changes with directionin the sheet. In a cylindrical cup drawing opera-tion, this variation leads to a cup with a wall thatvaries in height, a phenomenon known as earing(Fig. 1). It is therefore common to measure theaverage r value, or average normal anisotropy,rm, and the planar anisotropy, Dr.

The property rm is defined as (r0 � 2r45 �r90)/4, where the subscripts refer to the anglebetween the tensile specimen axis and the rollingdirection. The value Dr is defined as (r0 � 2r45� r90)/2. It is a measure of the variation of rwith direction in the plane of a sheet. The valuerm determines the average depth (that is, the wallheight) of the deepest draw possible. The valueDr determines the extent of earing. A combi-nation of a high rm value and a low Dr valueprovides optimal drawability.

Hot-rolled low-carbon steels have rm valuesranging from 0.8 to 1.0, cold-rolled rimmedsteels range from 1.0 to 1.4, and cold-rolled alu-minum-killed (deoxidized) steels range from 1.4to 2.0. Interstitial-free steels have values ranging

from 1.8 to 2.5, and aluminum alloys range from0.6 to 0.8. The theoretical maximum rm valuefor a ferritic steel is 3.0; a measured value of 2.8has been reported (Ref 4).

Maximum Strain Levels:The Forming Limit Diagram

Each type of steel, aluminum, brass, or othersheet metal can be deformed only to a certainlevel before local thinning (necking) and frac-ture occur. This level depends principally on thecombination of strains imposed, that is, the ratioof major and minor strains. The lowest level oc-curs at or near plane strain, that is, when theminor strain is zero.

This information was first represented graph-ically as the forming limit diagram, which is agraph of the major strain at the onset of neckingfor all values of the minor strain that can be re-alized (Ref 5, 6). Figure 2 shows a typical form-ing limit diagram for steel. The diagram is usedin combination with strain measurements, usu-ally obtained from circle grids, to determine howclose to failure (necking) a forming operation isor whether a particular failure is due to inferiorwork material or to a poor die condition (Ref 7).

For most low-carbon steels, the forming limitdiagram has the same shape as the one shown inFig. 2, but the vertical position of the curve de-pends on the sheet thickness and the n value.The intercept of the curve with the vertical axis,which represents plane strain and is also theminimum point on the curve, has a value equalto n in the (extrapolated) zero thickness limit.


Fig. 3 Effect of thickness and n value on the plane-strain in-tercept of a forming limit diagram. Source: Ref 8

The intercept increases linearly with thicknessto a thickness of about 3 mm (0.12 in.).

The rate of increase is proportional to the nvalue up to n � 0.2, as shown in Fig. 3. Beyondthese limits, further increases in thickness and nvalue have little effect on the position of thecurve. The level of the forming limits also in-creases with the m value (Ref 3).

The shape of the curve for aluminum alloys,brass, and other materials differs from that inFig. 2 and varies from alloy to alloy within asystem. The position of the curve also varies andrises with an increase in the thickness, n value,or m value, but at rates that are generally not thesame as those for low-carbon steel.

The forming limit diagram is also dependenton the strain path. The standard diagram is basedon an approximately uniform strain path. Dia-grams generated by uniaxial straining followedby biaxial straining, or the reverse, differ con-siderably from the standard diagram. Therefore,the effect of the strain path must be taken intoaccount when using the diagram to analyze aforming problem.

Material Properties and Wrinkling

The effect of material properties on the for-mation of buckles or wrinkles is the subject ofextensive research. In drawing operations, thereis general agreement, based primarily on exper-iments with conical and cylindrical cups, that ahigh rm value and a low Dr value reduce buck-ling in both flanges and walls (Ref 9–11). Inaddition to the above correlations, a low flow-stress-to-elastic-modulus ratio (rF /E) decreaseswall wrinkling (Ref 12). The n value has an in-direct effect. When the binder force is kept con-stant, the n value has no effect. However, highn values enable higher binder forces to be used,which reduces buckling.

In stretching operations, the situation appearsto be different. A close correlation between theformation of buckles at low strain levels and theyield-strength-to-tensile-strength ratio (YS/TS)has been reported, as well as an inverse corre-lation with the low strain n value and an absenceof correlation with the rm value and uniformelongation (Ref 13). Some of the differences be-tween these results may be attributed to the factthat the experiments with cups involved highstrains and high compressive stresses, while thestretching experiments were conducted at lowstrain and low compressive stress levels. In bothsituations, the problem becomes significantlymore severe as the sheet thickness decreases.

Material Properties and Shear Fracture

Shear fractures due to in-plane shear stressesare more prevalent in high-strength cold-workedmaterials, particularly when internal defectssuch as inclusions are present. Typical straincombinations that cause shear fracture areshown on the forming limit diagram in Fig. 4.For this material, Fig. 4 shows that, at high strainlevels in the regions close to e2 � �e1, failureoccurs by shearing before the initiation of neck-ing.

The position and shape of the shear fracturecurve depends on the material, its temper, andthe type and degree of prestrain or cold work(Ref 14–16). Limited data are available on shearfracture.

Material Properties and Springback

Material properties that control the amount ofspringback that occurs after a forming operationare:

● Elastic modulus, E● Yield stress, ry● Slope of the true stress/strain curve, or tan-

gent modulus, drT /de

Springback is best described by means of threeexamples involving a rectangular beam: elasticbending below the yield stress, simple bendingwith the yield stress exceeded in the outer layersof the beam, and combined stretching and bend-ing. In an actual part, springback is determinedby the complex interaction of the residual inter-nal elastic stresses, subject to the constraints ofthe part geometry.


Fig. 5 Springback of a beam in simple bending. (a) Elastic bending. (b) Elastic and plastic bending. (c) Bending and stretching

Fig. 4 Forming limit diagram including shear fracture. Source: Ref 14

Elastic Bending Below the Yield Stress.Tensile elastic stresses are generated on the out-side of the bend. These stresses decrease linearlyfrom a maximum at the surface to zero at thecenter (neutral axis). They then become com-pressive and increase linearly to a maximum atthe inner surface. Upon removal of the exter-nally applied bending forces, the internal elasticforces cause the beam to unbend as they de-crease to zero throughout the cross section(Fig. 5a).

The maximum amount of elastic deflectionthat can be produced without entering the plastic

range is proportional to the yield stress dividedby the elastic modulus. The strain at the yieldpoint is equal to ry /E (E � r/e). The springbackmoment for a given deflection is therefore pro-portional to the elastic modulus (r � Ee).

Simple Bending. In this example, the yieldstress is exceeded in the outer layers of thebeam. The outer layers deform plastically, andtheir stored elastic stresses continue to increase,but at a much lower rate that is proportional tothe slope of the true stress-strain curve, or tan-gent modulus, drT /de, instead of the elasticmodulus. Figure 5(b) illustrates this condition


for a beam bent so that 50% of its volume is inthe plastic range.

Upon removal of the externally applied bend-ing forces, the stored elastic stresses cause thebeam to unbend until their combined bendingmoment is zero. This produces compressivestresses at the outer surface and tensile stressesat the inner surface.

The springback in this case is less than for amaterial whose yield strength is not exceeded atthe same strain level. This can result from eithera higher yield stress or a lower elastic modulus.It is also apparent that higher values of the tan-gent modulus cause greater springback when theyield strength is exceeded.

In actual conditions, the neutral axis movesinward upon bending because the outer part ofthe beam is stretched and becomes thinner andbecause the inner part is compressed and be-comes thicker. This effect is analyzed in detailin Ref 17.

Combined Stretching and Bending. In thiscase, the entire beam can be plastically deformedin tension by as little as 0.5% stretching. How-ever, a stress gradient still exists from the outerto the inner surface (Fig. 5c). Upon removingthe external forces, the internal elastic stressesrecover.

This causes unbending, but to a lesser extentthan in the previous cases. As the level ofstretching is increased, the amount of springbackdecreases because the tangent modulus andtherefore the stress gradient through the beamdecrease at higher strains. The yield strengthceases to be a factor in springback once all re-gions are plastically deformed in tension.

In the bending of wide sheets, the metal isdeformed in plane strain, and the plane-strainproperties (elastic modulus, yield stress, and tan-gent modulus) should be used. The effects of alow elastic modulus and a high yield stress andtangent modulus in increasing springback havebeen experienced in forming operations. Spring-back is more severe with aluminum alloys thanwith low-carbon steel (1 to 3 modulus ratio).High-strength steels exhibit more springbackthan low-carbon steels (�2 to 1 yield strengthratio), and dual-phase steels spring back morethan high-strength steels of the same yieldstrength (higher tangent modulus).

The effect of stretching in reducing spring-back to very low levels has also been reported(Ref 18). Springback is also greatly influencedby geometrical factors, and it increases as thebend angle and ratio of bend radius to sheetthickness increase.

Surface Quality

The previously mentioned conditions thatlead to undesirable surface textures can be min-imized or prevented. The formation of orangepeel in heavily deformed regions can be mini-mized by using a fine-grain material. The de-velopment of Luders lines in rimmed steels canbe prevented by temper rolling to 0.25 to 1.25%extension or by flex rolling, which produces mo-bile dislocations for a limited period of time, un-til they are trapped by nitrogen atoms. This alsoreduces elongation slightly. This problem is be-coming less common with the increased use ofcontinuous casting, which requires killed steels.These steels have less free nitrogen to interactwith the dislocations and do not develop Luderslines. Similar treatments can be applied to alu-minum-magnesium alloys to prevent this defect.

Effect of Temperature on Formability

A change in the overall temperature alters theproperties of the material, which thus affectsformability. In addition, local temperature dif-ferences within a deforming blank lead to localdifferences in properties that affect formability.

At high temperatures, above one-half of themelting point on the absolute temperature scale,extremely fine-grain aluminum, copper, mag-nesium, nickel, stainless steel, steel, titanium,zinc, and other alloys become superplastic. Su-perplasticity is characterized by extremely highelongation, ranging from several hundred tomore than 1000%, but only at low strain rates(usually below about 10�2/s�1) at high tem-peratures.

The requirements of high temperatures andlow forming rates have limited superplasticforming to low-volume production. In the aero-space industry, titanium is formed in this man-ner. The process is particularly attractive for zincalloys because they require comparatively lowtemperatures (�270 �C, or �520 �F).

At intermediate elevated temperatures, steelsand many other alloys have less ductility than atroom temperature (Ref 19, 20). Aluminum andmagnesium alloys are exceptions and have min-imum ductility near room temperature. Alloysof these metals have been formed commerciallyat slightly elevated temperatures (�250 �C, or�480 �F). The strain rate sensitivity (m value)and post-uniform elongation for aluminum-


Fig. 6 Sheet tensile test specimen

magnesium alloys have been found to increasesignificantly in this temperature range (Ref 21).

Low-temperature forming has potential ad-vantages for some materials, based on their ten-sile properties, but practical problems have lim-ited application. Local increases in temperatureoccur during forming because of the surface fric-tion and internal heating produced by the defor-mation. Generally, this is detrimental because itlowers the flow stress in the area of greateststrain and tends to localize deformation.

A method of improving drawability by cre-ating local temperature differences has been de-veloped and is being used commercially (Ref22). It involves water cooling the punch in adeep-drawing operation. This lowers the tem-perature of the blank where it contacts thepunch, which is the principal failure zone, andincreases the local flow stress. Heating the diein order to lower the flow stress in the defor-mation zone at the top of the draw wall has alsobeen found to be beneficial. The combination ofthese procedures has produced an increase ofover 20% in the drawability of an austeniticstainless steel.

Types of Formability Tests

Formability tests are of two basic types: in-trinsic and simulative (Ref 23). Intrinsic testsmeasure the basic characteristic properties ofmaterials that can be related to their formability.Examples include the uniaxial tensile test andthe plane-strain tensile test which will be sub-sequently described in this chapter. Other intrin-sic tests reviewed in Ref 23 are the Marciniakstretching and sheet torsion tests, the hydraulicbulge test, the Miyauchi shear test, and hardnesstests. Simulative tests subject the material to de-formation that closely resembles the deforma-tion that occurs in a particular forming opera-tion. Many simulative tests, such as the Olsenand Swift cup tests, have been used extensivelyfor many years with good correlation to produc-tion in specific cases. A number of simulativetests are described in Ref 23.

Uniaxial Tensile Testing

The most widely used intrinsic test of sheetmetal formability is the uniaxial tensile test. Aspecimen such as that illustrated in Fig. 6 is

used; its sides are accurately parallel over thegage length, which is usually 50.8 mm (2.00 in.)long and 12.7 mm (0.50 in.) wide. The specimenis gripped at each end and stretched at a constantrate in a tensile machine until it fractures, as de-scribed in ASTM E 8, “Standard Test Methodsfor Tension Testing of Metallic Materials.” Theapplied load and extension are measured bymeans of a load cell and strain gage extensom-eter.

The load extension data can be plotted di-rectly. However, data are usually converted intoengineering (conventional) stress, rE (load/original cross section), and engineering strain, e(elongation/original length), or to true stress, rT

(load/instantaneous cross section), and truestrain, e (natural logarithm of strained length/original length).

In addition, for formability testing, it is com-mon practice to measure the width of the spec-imen during the test. This is done either inter-mittently by interrupting the test at preselectedelongations to make measurements manually orcontinuously by means of width extensometers.From these measurements, the plastic strain ratio(anisotropy factor), or r value, can be deter-mined.

During the rolling process used to producemetals in sheet form and the subsequent anneal-ing, the grains and any inclusions present be-come elongated in the rolling direction, and apreferred crystallographic orientation develops.This causes a variation of properties with direc-tion. Therefore, it is common practice to testspecimens cut parallel to the rolling directionand at 45 and 90� to this direction. These areknown as longitudinal, diagonal, and transversespecimens, respectively. This also enables thevalues of rm and Dr to be calculated. Becausethe mechanical properties and elongation tend tobe lower in the transverse direction, tests in thisdirection are often used as the basis for specifi-cations.


Fig. 7 Typical engineering and true stress-strain curves

Fig. 8 Engineering stress-strain curve for rimmed steel

The rate at which the test is performed canhave a significant effect on the end results. Twomethods are commonly used to determine thiseffect. In the first method, replicate samples aretested at different rates, and the results are influ-enced by variations between the samples. In thesecond method, the test rate is alternated be-tween two levels. This approach avoids theproblem of variation between samples, but itcannot be used at very high rates and is compli-cated by transients, which occur each time therate is changed. The strain rate sensitivity, or mvalue, can be calculated from these tests.

Figure 7 shows a typical engineering stress-strain curve and the corresponding true stress-strain curve for a material that has a smooth tran-sition between the very low strain (elastic) andthe higher strain (plastic) regions of the curve.When the load is removed in the elastic region,the sample returns to its original dimensions.When this is done in the plastic region, the sam-ple retains permanent deformation.

In the tensile test, the load increases to a max-imum value and then decreases prior to fracture.The decrease is due to the localization of thedeformation, which causes a reduction in crosssection. This reduction has a greater effect thanthe opposing increase in flow stress due to strainhardening.

Some materials such as aged rimmed steelsdo not have a smooth transition between theelastic and plastic regions of the stress-straincurve. The load they can support decreases atthe beginning of the plastic region and remainsapproximately constant for up to about 7% elon-gation. Subsequently, the load increases to amaximum and then decreases again at high elon-gations. This type of stress-strain curve is shown

in Fig. 8. With the increasing use of continuouscasting, which requires killed steels (steels de-oxidized by small additions of aluminum, forexample), rimmed steels are becoming less com-mon.

Test Procedure

For accurate and reproducible results, uniax-ial tensile testing must be performed in a care-fully controlled manner. The main steps in theprocedure are discussed in detail in Chapter 3,“Uniaxial Tensile Testing.” These proceduresare summarized below.

Specimen Preparation. The surfaces of thespecimen should be free from scratches or otherdamage that can act as stress raisers and causeearly failure. The edges should be smooth andfree from irregularities. Care should be taken notto cold work the edges, or to ensure that any coldwork introduced is removed in a subsequentoperation, because this changes mechanicalproperties and lowers ductility.

It is common practice to mill and grind theedges, but other procedures such as fine milling,nibbling, and laser cutting are also used. Whena new method is used, initial tests should be per-


formed to compare the results with those ob-tained by conventional methods.

The width of a nominally 12.7 mm (0.50 in.)wide specimen should be measured to the near-est 0.025 mm (0.001 in.), and the thickness forspecimens in the range of 0.5 to 2.5 mm (0.02to 0.1 in.) should be measured to the nearest0.0025 mm (0.0001 in.). If this is impracticalbecause of surface roughness, the thicknessshould be measured to the nearest 0.025 mm(0.001 in.).

The tensile test is sensitive to variations in thewidth of the specimen, which should be accu-rately controlled. For a specimen 12.7 mm (0.50in.) wide, the width of the reduced sectionshould not deviate by more than �0.25 mm(�0.01 in.) from the nominal value and shouldnot differ by more than �0.05 mm (�0.002 in.)from end to end.

Some investigators intentionally taper the re-duced section slightly toward the center to in-crease the probability that fracture will occurwithin the gage length. In this case, the centershould not be narrower than the ends by morethan 0.10 mm (0.004 in.).

Alignment of Specimens. The specimenshould be accurately aligned with the centerlineof the grips. The effect of small displacements(10% of the specimen width) of one or both endsfrom the centerline has been calculated (Ref 24).It has been determined that the latter case is themore serious, but both strongly affect the strainin the outermost fibers. It has also been con-cluded that the calculated stress-strain curve isnot significantly affected at strains above 0.3%.

Measurement of Load and Elongation. Theapplied load is measured by means of a load cellin the test machine, for which the usual calibra-tion procedures must be followed (ASTM E 4,“Standard Practices for Force Verification ofTesting Machines”). Elongation is usually deter-mined by using a clip-on strain gage extensom-eter (ASTM E 83, “Standard Practice for Veri-fication and Classification of ExtensometerSystem”). In addition, small scratches are oftenscribed across the specimen at the ends of thegage length so that the total elongation can bedetermined from the broken specimen.

Circle grids are sometimes etched or printedon the specimen. These can be used to measurethe strain distribution and width strain as well asthe overall strain. This can be done continuouslyby means of a video camera and data processingsystem if required. Optical extensometers areused for some applications, particularly high-

speed testing. These units require well-illumi-nated boundaries that are clearly delineated bymeans of high-contrast coatings, such as black-and-white paint.

An approximate measure of elongation can beobtained from the crosshead travel. This in-volves errors due to elongation of the specimenoutside the gage length and elastic strain in thegrips, which can be compensated for to someextent. This method is used when the specimenis inaccessible, such as in nonambient testing.

The signals from the load cell and extensom-eter can be plotted on a chart recorder or pro-cessed by a data processing system to the re-quired form, such as plots of stress versus strainor tables of mechanical and forming properties.

Measurement of Width and Thickness. Inaddition to the initial measurements of specimenwidth and thickness, which are required to cal-culate the stress, measurements can be made atintervals during the test to determine the r value(ASTM E 517, “Standard Test Method for Plas-tic Strain Ratio r for Sheet Metal”) and to de-termine the reduction in area and true strain. Ther value is measured at a specified strain levelbetween the yield point and the uniform elon-gation (for example, at 15% elongation). It canbe measured by stopping the test at this strainlevel and then measuring the width accurately(�0.013 mm, or �0.0005 in.) at a minimum ofthree equally spaced points in the gage length(for a 50.8 mm, or 2.0 in., gage length). In prac-tice, the thickness is calculated from the speci-men width and length, assuming no change involume.

Alternatively, width measurements can bemade during the test using width extensometers,although this is a more complicated procedure.Attempts are underway to develop combinedwidth and length extensometers to simplify thismethod.

Reduction in area is the ratio (Ao � A)/Ao,where A is the instantaneous cross-sectional areaand Ao is the original cross-sectional area. It isused to calculate the true strain in the region ofpost-uniform elongation. A large reduction inarea at fracture correlates with a small minimumbend radius, a high m value, and high energyabsorption. To calculate the reduction in area,the width and thickness must be measured in thenarrowest part of the necked region.

Effect of Gage Length on Elongation. Inpost-uniform elongation, part of the specimen iselongated uniformly, and the remainder is nar-rowed into a necked region of higher strain


Table 1 Typical tensile properties of selected sheet metals

Young’smodulus, E

Yieldstrength

Tensilestrength

Uniformelongation,

Totalelongation,

Strain-hardeningexponent,

Averagenormal

anisotropy,Planar

anisotropy,

Strainrate

sensitivity,Material GPa 106 psi MPa ksi MPa ksi % % n rm Dr m

Aluminum-killed drawingquality steel

207 30 193 28 296 43 24 43 0.22 1.8 0.7 0.013

Interstitial-freesteel

207 30 165 24 317 46 25 45 0.23 1.9 0.5 0.015

Rimmed steel 207 30 214 31 303 44 22 42 0.20 1.1 0.4 0.012High-strength

low-alloysteel

207 30 345 50 448 65 20 31 0.18 1.2 0.2 0.007

Dual-phase steel 207 30 414 60 621 90 14 20 0.16 1.0 0.1 0.008301 stainless

steel193 28 276 40 690 100 58 60 0.48 1.0 0.0 0.012

409 stainlesssteel

207 30 262 38 469 68 23 30 0.20 1.2 0.1 0.012

3003-Oaluminum

69 10 48 7 110 16 23 33 0.24 0.6 0.2 0.005

6009-T4aluminum

69 10 131 19 234 34 21 26 0.23 0.6 0.1 �0.002

70-30 brass 110 16 110 16 331 48 54 61 0.56 0.9 0.2 0.001

level. A change in the gage length alters the ratioof these two regions and has a significant effecton the total elongation measurement. This phe-nomenon is discussed in detail in Ref 25.

To obtain results that are comparable for dif-ferent gage lengths, the ratio of the square rootof the cross-sectional area to the length, A/L,�should be the same. When comparing samplesof different thickness, this implies that the gagelength or the width should be adjusted to main-tain this ratio.

Rate of Testing. Most tensile tests are per-formed on screw-driven or hydraulic testing ma-chines at strain rates of 10�5 to 10�2 s�1. Thestrain rate is defined as the increase in length perunit length per second. These tests are known aslow strain rate or static tests.

Most high-volume production forming opera-tions are performed at considerably higher strainrates—in the range of 1 to 102 s�1. To determinethe tensile properties in this range, dynamic testmachines, which operate at rates of 10�1 to 102

s�1, are used (Ref 25). As mentioned previously,steels have higher tensile properties and lowerelongations at high strain rates. The propertiesof aluminum alloys have little sensitivity to thestrain rate.

Determination of Material Properties

The stress-strain curve determined by uniaxialtensile testing provides values of many forma-bility-related material properties. These proper-ties include the modulus of elasticity (Young’s

modulus), yield strength, tensile strength, uni-form elongation, total elongation, and reductionin area. Determination of these properties is de-scribed in Chapter 3, “Uniaxial Tensile Testing.”As discussed earlier in this chapter, other keyproperties are the strain-hardening exponent, theplastic strain ratio, and the strain rate sensitivity.Table 1 lists typical values of properties mea-sured in tensile tests on thin (0.5 to 1.0 mm, or0.02 to 0.04 in.) sheet materials.

Strain-Hardening Exponent. The n value, dln rT /d lne, is given by the slope of a graph ofthe logarithm of the true stress versus the loga-rithm of the true strain in the region of uniformelongation. For materials that closely follow theHolloman constitutive equation (Eq 2), an ap-proximate n value can be obtained from twopoints on the stress-strain curve by the Nelson-Winlock procedure (Ref 26). The two pointscommonly used are at 10% strain and at themaximum load. The ratio of the loads or stressesat these two points is calculated, and the n valueand uniform elongation can then be determinedfrom a table or graph. The accuracy of the nvalue determined in this way is �0.02.

The n value can be determined more accu-rately by linear regression analysis, as in ASTME 646, “Standard Test Method for Tensile Strain-Hardening Exponents (n-Values) of MetallicSheet Materials.” For some materials, n is notconstant, and initial (low strain), terminal (highstrain), and sometimes intermediate n values aredetermined. The initial n value relates to the lowdeformation region, in which springback is often


Fig. 9 Methods for determining strain-rate sensitivity (m value). (a) Duplicate test method. (b) Changing rate method

a problem. The terminal n value relates to thehigh deformation region, in which fracture mayoccur.

Plastic Strain Ratio. The r value, or aniso-tropy factor, is defined as the ratio of the truewidth strain to the true thickness strain in a ten-sile test. Generally, its value depends on theelongation at which it is measured. It is usuallymeasured at 10, 15, or 20% elongation.

The r value is calculated from the measuredwidth and length as:

we � lnw � �wo

t L wo oe � ln � ln (Eq 7)t � � � �t Lwo

where constancy of volume (Lwt � Lowoto) hasbeen used and:

wln� �we owr � � (Eq 8)

e L wt o oln� �Lw

The average r value, or normal anisotropy (rm),and the planar anisotropy, or Dr value, can becalculated from the values of r in different di-rections using Eq 6 and 7.

Strain Rate Sensitivity. The m value, d ln rT /d is determined either from duplicate tensilelne,tests performed at different strain rates or froma single test in which the rate is alternated be-tween two levels during the test. These methodsare shown schematically in Fig. 9. The m value

can be determined at various strain levels in theregion of uniform elongation:

r1ln� �r2m � (Eq 9)

e1ln� �e2

In some materials, m is insensitive to strain(Ref 3, 27). In other materials, however, m issensitive to strain and strain rate (Ref 28). Inmany materials, m increases and n decreaseswith an increase in temperature (Ref 29), some-times to the extent that superplastic propertiesdevelop.

Plane-Strain Tensile Testing

In conventional uniaxial tensile testing, thesample is strained in the region of drawing; thatis, the minor or width strain is negative. The testdoes not provide information on the response ofsheet materials in the plane-strain state, in whichthe minor strain is zero. However, it can be mod-ified to produce this strain state in part of thesample. This modification involves the use of avery wide, short sample or the use of knife-edgesto prevent transverse (width) strain in part of thesample.

Wide Sample Methods. Increasing the widthof the sample and decreasing the gage lengthchanges the strain state from one with a largenegative minor strain component toward theplane-strain state, in which the minor straincomponent is zero. In the rectangular sheet ten-


Fig. 10 Plane-strain tensile test specimen. Source: Ref 33

sion test, samples with length-to-width ratios of1 to 1, 1 to 2, and 1 to 4 are used to approachthe plane-strain conditions (Ref 30). Gagelengths are constrained further by reinforce-ments welded onto each side of the sample atboth ends, thus making the samples three layersthick except in the gage length.

The minimum minor strain obtained with the1 to 4 length-to-width ratio is �0.05 times themajor strain, which is close to the plane-straincondition of zero minor strain. The in-planestrains are measured by means of grid markingson the samples, and through-thickness defor-mations can be observed by holographic inter-ferometry.

A similar approach was used in testing manywide specimen designs to determine the effectof edge profile and length-to-width ratio onstrain state (Ref 31–33). The specimen geometrythat yielded the highest center strain at failurewith a large region of plane strain is shown inFig. 10. The plane-strain region, which is arbi-trarily taken as the region where |e2/e1| is lessthan 0.2, occupies about 80% of the specimenwidth. The outer part of the specimen deformsin a similar manner to a standard tensile testspecimen.

Special grips were developed that exert a highclamping force at the inner contact lines. Thisminimizes distortion and slippage in these re-gions, giving the test well-defined boundaryconditions. The results of both types of widespecimen tensile tests described above corre-lated well with stress-strain predictions obtainedby finite-element modeling using material prop-erties obtained in the standard tensile test (Ref31, 34).

Width Constraint Method. In the width con-straint method, a rectangular sample is used that

has a central gage section reduced in width bycircular notches (Ref 35). The gage section isclamped between two pairs of opposing parallelknife-edges (stingers) aligned with the sampleaxis. The knife-edges prevent transverse (width)strain in this region. The sample is pulled to frac-ture in a tension-testing machine, and the plane-strain limit (necking) and fracture strains are de-termined from thickness measurements made onthe fractured sample. This procedure is de-scribed in detail in Ref 35. The use of a spring-loaded clamp around the knife-edges makesadjustment of the clamp during testing unnec-essary.

ACKNOWLEDGMENT

This chapter was adapted from B. Taylor,Formability Testing of Sheet Metals, Formingand Forging, Vol 14, Metals Handbook, 9th ed.,ASM International, 1988, p 877–899.

REFERENCES

1. J.H. Holloman, Tensile Deformation, Trans.AIME, Vol 162, 1945, p 268–290

2. W.A. Backofen, Massachusetts Institute ofTechnology Industrial Liaison Symposium,Chicago, March 1974

3. A.K. Ghosh, The Influence of Strain Hard-ening and Strain-Rate Sensitivity on SheetMetal Forming, Trans. ASME, Vol 99, July1977, p 264–274

4. I.S. Brammar and D.A. Harris, Productionand Properties of Sheet Steel and Alumi-num Alloys for Forming Applications, J.Austral. Inst. Met., Vol 20 (No. 2), 1975, p85–100

5. S.P. Keeler and W.A. Backofen, Plastic In-stability and Fracture in Sheets StretchedOver Rigid Punches, Trans. ASM, Vol 56(No. 1), 1963, p 25–48

6. G.M. Goodwin, “Application of StrainAnalysis to Sheet Metal Forming Problemsin the Press Shop,” Paper 680093, Societyof Automotive Engineers, 1968

7. S.P. Keeler, Determination of Forming Lim-its in Automotive Stampings, Sheet Met.Ind., Vol 42, Sept 1965, p 683–691

8. S.P. Keeler and W.G. Brazier, RelationshipBetween Laboratory Material Characteriza-tion and Press-Shop Formability, in Mi-croalloying 75 Proceedings, Union CarbideCorporation, 1977, p 517–530


9. H. Naziri and R. Pearce, The Effect of Plas-tic Anisotropy on Flange-Wrinkling Behav-ior During Sheet Metal Forming, Int. J.Mech. Sci., Vol 10, 1968, p 681–694

10. K. Yoshida and K. Miyauchi, ExperimentalStudies of Material Behavior as Related toSheet Metal Forming, in Mechanics of SheetMetal Forming, Plenum Press, 1978, p 19–49

11. W.F. Hosford and R.M. Caddell, in MetalForming, Mechanics and Metallurgy, Pren-tice-Hall, 1983, p 273, 309

12. J. Havranek, The Effect of MechanicalProperties of Sheet Steels on the WrinklingBehavior During Deep Drawing of ConicalShells, in Sheet Metal Forming and EnergyConservation, Proceedings of the 9th Bi-ennial Congress of the International DeepDrawing Research Group, Ann Arbor, MI,American Society for Metals, 1976, p 245–263

13. J.S.H. Lake, The Yoshida Test—A CriticalEvaluation and Correlation with Low-StrainTensile Parameters, in Efficiency in SheetMetal Forming, Proceedings of the 13th Bi-ennial Congress, Melbourne, Australia, In-ternational Deep Drawing Research Group,Feb 1984, p 555–564

14. J.L. Duncan, R. Sowerby, and M.P. Sklad,“Failure Modes in Aluminum Sheet in DeepDrawing Square Cups,” Paper presented atthe Conference on Sheet Forming, Univer-sity of Aston, Birmingham, England, Sept1981

15. G. Glover, J.L. Duncan, and J.D. Embury,Failure Maps for Sheet Metal, Met. Tech-nol., March 1977, p 153–159

16. J.D. Embury and J.L. Duncan, FormabilityMaps, Ann. Rev. Mat. Sci., Vol 11, 1981, p505–521

17. J. Datsko, Materials in Design and Manu-facturing, J. Datsko Consultants, 1977, p 7–16

18. N. Kuhn, On the Springback Behavior ofLow-Carbon Steel Sheet After StretchBending, J. Austral. Inst. Met., Vol 12 (No.1), Feb 1967, p 71–76

19. G.V. Smith, Elevated Temperature StaticProperties of Wrought Carbon Steel, in Spe-cial Technical Publication on TemperatureEffects, STP 503, American Society forTesting and Materials, 1972

20. F.N. Rhines and P.J. Wray, Investigation ofthe Intermediate Temperature DuctilityMinimum in Metals, Trans. ASM, Vol 54,1961, p 117–128

21. B. Taylor, R.A. Heimbuch, and S.G. Bab-cock, Warm Forming of Aluminum, in Pro-ceedings of the Second International Con-ference on Mechanical Behavior ofMaterials, American Society for Metals,1976, p 2004–2008

22. W.G. Granzow, The Influence of ToolingTemperature on the Formability of StainlessSheet Steel, in Formability of Metallic Ma-terials—2000 A.D., STP 753, J.R. Newbyand B.A. Niemeier, Ed., American Societyfor Testing and Materials, 1981, p 137–146

23. B. Taylor, Formability Testing of SheetMetals, Forming and Forging, Vol 14, Met-als Handbook, 9th ed., ASM International,1988, p 877–899

24. H.C. Wu and D.R. Rummler, Analysis ofMisalignment in the Tension Test, Trans.ASME, Vol 101, Jan 1979, p 68–74

25. G.E. Dieter, Mechanical Metallurgy, 2nded., McGraw-Hill, 1976, p 347, 349, 681

26. R.L. Whitely, Correlation of Deep DrawingPress Performance With Tensile Properties,STP 390, American Society for Testing andMaterials, 1965

27. S.J. Green, J.J. Langan, J.D. Leasia, andW.H. Yang, Material Properties, IncludingStrain-Rate Effects, as Related to SheetMetal Forming, Met. Trans. A, Vol 2A,1971, p 1813–1820

28. G. Rai and N.J. Grant, On the Measure-ments of Superplasticity in an Al-Cu Alloy,Met. Trans A., Vol 6A, 1975, p 385–390

29. W.J. McGregor Tegart, in Elements of Me-chanical Metallurgy, Macmillan, 1966, p29–38

30. M.L. Devenpeck and O. Richmond, Limit-ing Strain Tests for In-Plane Sheet Stretch-ing, in Novel Techniques in Metal Defor-mation Testing, The Metallurgical Society,1983, p 79–88

31. R.H. Wagoner and N.M. Wang, An Exper-imental and Analytical Investigation of In-Plane Deformation of 2036-T4 Aluminum,Int. J. Mech. Sci., Vol 21, 1979, p 255–264

32. R.H. Wagoner, Measurement and Analysisof Plane-Strain Work Hardening, Met.Trans. A, Vol 11A, Jan 1980, p 165–175

33. R.H. Wagoner, Plane-Strain and TensileHardening Behavior of Three AutomotiveSheet Alloys, in Experimental Verificationof Process Models, Symposium proceed-ings, Cincinnati, OH, Sept 1981, AmericanSociety for Metals, 1983, p 236

34. E.J. Appleby, M.L. Devenpeck, L.M.


O’Hara, and O. Richmond, Finite ElementAnalysis and Experimental Examination ofthe Rectangular-Sheet Tension Test, in Ap-plications of Numerical Methods to Form-ing Processes, Vol 28, Proceedings of theASME Winter Annual Meeting, San Fran-

cisco, Applied Mechanics Division, Amer-ican Society of Mechanical Engineers, Dec1978, p 95–105

35. H. Sang and Y. Nishikawa, A Plane StrainTensile Apparatus, J. Met., Feb 1983, p 30–33

CHAPTER 7

Tensile Testing of Metals and Alloys

THE TENSILE TEST provides a relativelyeasy, inexpensive technique for developing me-chanical property data for the selection, qualifi-cation, and utilization of metals and alloys inengineering service. This data may be used toestablish the suitability of the alloy for a partic-ular application, and/or to provide a basis forcomparison with other candidate materials. De-sign guidelines generally require that the tensileproperties of metals and alloys meet specific,well-defined criteria. ASME has establishedcode requirements for the strengths and ductili-ties of many classes of metals and alloys. Step-by-step procedures for conducting the tensiletest are defined in various ASTM standards (see,for example, ASTM E 8, “Standard Test Meth-ods for Tension Testing of Metallic Materials”).Descriptions of the test methodology and dis-cussions on the importance of both material andtest variables on the measured tensile propertiescan be found in Chapter 3, “Uniaxial TensileTesting.” Because such variables have signifi-cant influences on the measured tensile proper-ties, an understanding of the influences is nec-essary for accurate interpretation and use ofmost tensile data.

The elastic moduli of cast iron, carbon steel,and many other engineering materials are de-pendent on the rate at which the test specimenis stretched (strain rate). The yield strength orstress at which a specified amount of plasticstrain takes place is also dependent on the teststrain rate. Alloy composition, grain size, priordeformation, test temperature and heat treatmentmay also influence the measured yield strength.Generally, factors that increase the yield strengthdecrease the tensile ductility because these fac-tors also inhibit plastic deformation. However, anotable exception to this trend is the increase inductility that accompanies an increase in yieldstrength when the grain size is reduced.

Most structural metals and alloys, whenstrained to failure in a tensile test, fracture byductile processes. The fracture surface is formedby the coalescence or combination of micro-voids. These microvoids generally nucleate dur-ing plastic deformation processes, and coales-cence begins after the plastic deformationprocesses become highly localized. Strain rate,test temperature, and microstructure influencethe coalescence process and, under selected con-ditions (decreasing temperature, for example),the fracture may undergo a transition from duc-tile to brittle processes. Such transitions maylimit the utility of the alloy and may not be ap-parent from strength measurements. The tensiletest, therefore, may require interpretation, andinterpretation requires a knowledge of the fac-tors that influence the test results. This chapterprovides a metallurgical perspective for such in-terpretation. Additional information can also befound in Chapter 2, “Mechanical Behavior ofMaterials Under Tensile Loads.”

Elastic Behavior

Most structures are designed so that the ma-terials of construction undergo elastic loadingsunder normal service conditions. These loadsproduce elastic or reversible strains in the struc-tural materials. The upward movement of a wingas an airplane takes off and the sway of a tallbuilding in a strong wind are examples in whichthe elastic strains are readily apparent. Bendingof an automobile axle and stretching of a bridgewith the passing of a car are less noticeable ex-amples of elastic strains. The magnitude of thestrain is dependent on the elastic moduli of thematerial supporting the load. Although elasticmoduli are not generally determined by tensiletesting, tensile behavior can be used to illustratethe importance of elastic properties in the selec-tion and use of metals and alloys.




Fig. 1 Schematic representation of the elastic portions of thestress-strain curves for iron, copper, and aluminum

Young’s modulus for iron (207 GPa, or 30 �106 psi) is approximately three times that of alu-minum (69 GPa, or 10 � 106 psi) and almosttwice that of copper (117 GPa, or 17 � 106 psi).This variation in elastic behavior is illustrated inFig. 1. Because of its higher value of Young’smodulus, an iron component will deflect lessthan an “identical” copper or aluminum com-ponent that undergoes an equivalent load. In atensile test, for example, the elastic tensilestrains in 12.8 mm (0.505 in.) diam tensile barsof iron, copper, and aluminum loaded to 455 kg(1000 lb) will be 1.6 � 10�4 mm/mm (in./in.)for iron, 2.9 � 10�4 mm/mm (in./in.) for cop-per, and 5 � 10�4 mm/mm (in./in.) for alumi-num.

The ability of a material to resist elastic de-formation is termed “stiffness,” and Young’smodulus (E) is one measure of that ability. En-gineering applications that require very rigidstructures, such as microscopes, antennas, sat-ellite dishes, and radio telescopes, must be con-structed from either very massive componentsor selected materials that have high values ofelastic moduli. The elastic modulus of iron ishigher than those of many metals and alloys, andthus iron and iron alloys are frequently used forapplications that require high stiffness.

The equation that defines Young’s modulus,r � Ee, is based on the observation that tensilestrain (e) is linearly proportional to the appliedstress (r). This linear relationship provides anadequate description of the behavior of metalsand alloys under most practical situations. How-ever, when materials are subjected to cyclic orvibratory loading, even slight departures fromtruly linear elastic behavior may become impor-tant. One measure of the departure from linearelasticity is the anelastic response of a material.

Anelasticity

Anelasticity is time-dependent, fully revers-ible deformation. The time dependence resultsfrom the lack of instantaneous atom movementduring the application of a load. There are sev-eral mechanisms for time-dependent deforma-tion processes, including the diffusive motion ofalloy and/or impurity atoms. This diffusive mo-tion may simply be atoms jumping to nearbylattice sites made favorable by the application ofa load.

Tensile loading of an iron-carbon alloy willproduce elastic strains in the alloy, and its body-centered-cubic structure will be distorted to be-come body-centered-tetragonal. Carbon, in solidsolution, produces a similar distortion of the ironlattice. There is one basic difference between thedistortions introduced by tensile loads and thoseintroduced by dissolving carbon. The averagedistortion of a metallic lattice during a tensiletest is anisotropic: each unit cell of the structureis elongated in the direction of the tensile loadand, because of Poisson’s ratio, the material alsocontracts in the lateral direction. In contrast, theaverage lattice distortion resulting from the so-lution of carbon is isotropic even though eachindividual carbon atom produces a localized an-isotropic distortion.

Carbon atoms, in solid solution in iron, arelocated at the interstitial sites shown schemati-cally in Fig. 2. Because the dissolved carbon at-oms are too big for the interstitial sites, a carbonatom at site X would push the iron atoms A and

Fig. 2 Interstitial sites in an iron lattice. The large spheres atthe corners and center of the cube represent iron at-

oms, and the small spheres (X, Y, and Z) represent interstitial sitesfor carbon. There are duplicate interstitial sites at the corners ofthe cube or unit cell.

Tensile Testing of Metals and Alloys / 117

B apart and cause the unit cell to elongate in thex direction. Similarly, a carbon atom at site Ywould push iron atoms B and C apart and causeelongation in the y direction, and a carbon atomat site Z would cause elongation in the z direc-tion. Within any given unstressed iron or alphagrain, carbon atoms are randomly distributed inX, Y, and Z sites. Thus, although each unit cellis distorted in one specific direction, the over-alldistortion of the unstressed grain is basically iso-tropic, or equal in all directions.

The application of a tensile stress causes spe-cific interstitial sites to be favored. If the tensilestress is parallel to the x direction, type X sitesare expanded and become favored sites for thecarbon atoms. Type Y sites become favored ifthe stress is in the y direction, and type Z sitesare favored when stresses are in the z direction.During a tensile test, carbon atoms will migrateor diffuse to the sites made favorable by the ap-plication of the tensile load. This migration istime and temperature dependent and can be thecause of anelastic deformation.

The sudden application of the tensile loadmay elastically strain the iron lattice at such ahigh rate that carbon migration to favored sitescannot occur as the load is applied. However, ifthe material remains under load, the time-depen-dent migration to favored sites will produce ad-ditional lattice strain because of the tendency forthe interstitial carbon to push iron atoms in the

direction of the applied stress. These additionalstrains are the anelastic strains in the material.Similarly, if the load is suddenly released, theelastic strains will be immediately recoveredwhereas recovery of the anelastic strains will re-quire time as the interstitial carbon atoms relo-cate from the previously favorable sites to forma uniform distribution in the iron lattice. Thetime dependence of the elastic and anelasticstrains is shown schematically in Fig. 3.

The combination of the elastic and anelasticstrains may cause Young’s modulus, as deter-mined in a tensile test, to be loading-rate (orstrain-rate) dependent and may produce damp-ing or internal friction in a metal or alloy sub-jected to cyclic or vibratory loads. Anelasticstrains are one cause of stress relaxation in atensile test when the test specimen is loaded andheld at a fixed displacement. This stress relaxa-tion is frequently called an “elastic aftereffect”and results in a time-dependent load drop be-cause the load necessary to maintain the fixeddisplacement will decrease as atoms move to fa-vored sites and anelastic deformation takesplace. This elastic aftereffect, illustrated in Fig.4, demonstrates the importance of time or load-ing rate on test results.

The total reversible strain that accompaniesthe application of a tensile load to a test speci-men is the sum of the elastic and anelasticstrains. Rapid application of the load will cause

Fig. 3 A relationship between elastic and anelastic strains. The elastic strains develop as soon as the load is applied, whereas theanelastic strains are time dependent.


Fig. 5 Loading-rate effects on Young’s modulus

Fig. 4 The elastic aftereffect. The tensile specimen wasloaded to a stress of r0 and then held. The time-de-

pendent drop in stress results from a decrease in the load requiredto maintain a fixed displacement. This decrease results from an-elastic strains that increase the length of the test specimen. Whenthe anelastic straining process is complete, the stress has relaxedby a value of rmax.

the anelastic strain to approach zero (the testtime is not sufficient for anelastic strain), thusthe total strain during loading will equal the trueelastic strain. Very slow application of the sameload will allow the anelastic strain to accompanythe loading process, thus the total reversiblestrain in this test will exceed the reversible strainduring rapid loading. The measured value ofYoung’s modulus in the low-strain-rate test willbe lower than that measured in the high-strain-rate test, and the measured modulus of elasticitywill be strain-rate dependent. This dependencyis illustrated in Fig. 5. The low value of Young’smodulus is termed the “relaxed modulus,” andthe modulus measured at high strain rates istermed the “unrelaxed modulus.”

Damping

Tensile tests and cyclic loadings frequentlyare made at strain or loading rates that are inter-mediate between those required for fully relaxedbehavior and those required for fully unrelaxedbehavior. Therefore, on either loading or un-loading, the initial or short-time portion of thestress-strain curve will produce unrelaxed be-havior whereas the later, longer-time portions ofthe curve will produce more relaxed behavior.The transition from unrelaxed to relaxed behav-ior produces a loading-unloading hysteresis inthe stress-strain curve (Fig. 6).

This hysteresis represents an energy loss dur-ing the load-unload cycle. The amount of energyloss is proportional to the magnitude of the hys-

teresis. Such energy losses that may be attributedto anelastic effects within the metal lattice aretermed “internal friction.” Internal friction playsa major role in the ability of a material to absorbvibrational energy. Such absorption may causethe temperature of a material to rise during theloading-unloading cycle. One measurement ofthe susceptibility of a material to internal frictionis the damping capacity. Because anelasticityand internal friction are dependent on time andtemperature, the damping capacity of a metal oralloy is both temperature and strain-rate depen-dent.

Internal friction and damping play major rolesin the response of a metal or alloy to vibrations.Materials tested under conditions that cause sig-nificant internal friction during loading-unload-ing cycles undergo large energy losses and aresaid to have high damping capacities. Such ma-terials are useful for the absorption of vibrations.Gray cast iron, for example, has a very highdamping capacity and is frequently used for thebases of instruments and equipment that must beisolated from room vibrations. Lathes, presses,and other pieces of heavy machinery also use

Fig. 6 Hysteresis in the loading-unloading curve


Fig. 7 Effect of accuracy of measurement on the determina-tion of the proportional limit

cast iron bases to minimize transmission of ma-chine vibrations to the floor and surroundingarea. However, a high damping capacity is notalways a useful material quality. Bells, for ex-ample, are constructed from materials with lowdamping capacities because both the length ofbell ring and the loudness of the tone will in-crease as the damping capacity decreases.

Anelasticity, damping, stress relaxation, andthe elastic moduli of most metals and alloys aredependent on the microstructure of the materialas well as on test conditions. These propertiesare not typically determined by tensile-testingtechniques. However, these properties, as wellas the machine parameters, influence the shapeof the stress-strain curve. Therefore, an aware-ness of these phenomena may be useful in theinterpretation of tensile-test data.

The Proportional Limit

The apparent stress necessary to produce theonset of curvature in the tensile stress-strain re-lationship is the proportional limit. The propor-tional limit is defined as the maximum stress at

which strain remains directionally proportionalto stress. Departures from proportionality maybe attributed to anelasticity and/or the initiationof plastic deformation. The ability to detect theoccurrence of these phenomena during a tensiletest is dependent on the accuracy with whichstress and strain are measured. The measuredvalue of the proportional limit decreases as theaccuracy of the measurement increases (Fig. 7).Because the measured value of proportionallimit is dependent on test accuracy, the propor-tional limit is not generally reported as a tensileproperty of metals and alloys. Furthermore, val-ues of proportional limit have little or no utilityin the selection, qualification, and use of metalsand alloys for engineering service. A far morereproducible and practical stress is the yieldstrength of the material.

Yielding and the Onset of Plasticity

The yield strength of a metal or alloy may bedefined as the stress at which that metal or alloyexhibits a specified deviation from the propor-tionality between stress and strain. Very smalldeviations from proportionality may be causedby anelastic effects, but these departures fromlinear behavior are fully reversible and do notrepresent the onset of significant plastic (non-reversible) deformation or yielding. Theoreticalvalues of yield strength, rtheor, are calculatedfrom equations such as

Er �theor 2p

Based on these calculations, yielding should nottake place until the applied stress is a significantfraction of the modulus of elasticity. These es-timates for yielding generally overpredict themeasured yield strengths by factors of at least100, as summarized in Table 1.

Table 1 Young’s modulus and theoretical and measured yield strengths of selected metals at 20 �C(68 �F)

Yield strength

Young’s modulus Theoretical Measured(a)

Metal GPa 106 psi GPa 106 psi MPa ksi

Aluminum 70.3 10.2 11 1.6 26 4Nickel 199 28.9 32 4.6 234 34Silver 82.7 12.0 13 1.9 131 19Steel (mild) 212 30.7 34 4.9 207 30Titanium 120 17.4 19 2.7 172 25

(a) Measured values of yield strength are dependent on the metallurgical condition of the material.


The discrepancy between the theoretical andactual yield strength results from the motion ofdislocations. Dislocations are defects in the crys-tal lattice, and the motion of these defects is aprimary mechanism of plastic deformation inmost metals and alloys.

There are three very broad categories of crys-tal defects in metallic solids:

1. Point defects, including vacancies and alloyor impurity atoms

2. Line defects of dislocations3. Area defects, including grain and twin

boundaries, phase boundaries, inclusion-ma-trix interfaces, and even external surfaces

The characterization of these defects in anyparticular material may be accomplishedthrough metallography. Optical metallography isused to characterize area defects or grain struc-ture, as shown in Fig. 8.

Transmission electron microscopy is used tocharacterize line defects or dislocation substruc-ture, as shown in Fig. 9. More specialized me-tallographic techniques, such as field ion mi-croscopy, are used to characterize the pointdefects. Interaction among defects is common,and most techniques that alter the yieldstrengths of metals and alloys are dependent ondefect interactions to alter the ease of disloca-tion motion.

Dislocation mobility is dependent on the alloycontent, the extent of cold work, the size, shape,and distribution of inclusions and second phaseparticles, and the grain size of the alloy. Thestrength of most metals increases as alloy con-tent increases, because the alloy (or impurity)atoms interact with dislocations and inhibit sub-sequent motion. Thus, this type of strengtheningresults from the interaction of point defects withline defects. Such strengthening was discoveredby ancient metallurgists and was the basis forthe Bronze Age. The strength, and therefore theutility, of copper was significantly increased bydissolving tin to form bronze. The yield strengthof the copper-tin alloys (bronze) was sufficientlyhigh for the manufacture of tools and spearpoints. This strengthening mechanism was notdiscovered by the native Americans, and on theAmerican Continents, copper was used for jew-elry but not for more practical purposes. Bronzes(Cu-Sn alloys), brasses (Cu-Zn alloys), Monels(Ni-Cu alloys), and many other alloy systemsare dependent on solid-solution strengthening tocontrol the yield strength of the material. Theeffects of nickel and zinc additions on the yieldstrength of copper are illustrated in Fig. 10.

Cold work is another effective technique forincreasing the strength of metals and alloys. Thisstrengthening mechanism is effective becausethe number of dislocations in the metal increases

Fig. 8 Optical photomicrograph of type 304 stainless steel. The apparent defects include grain boundaries, twin boundaries, andinclusions. 100�


as the percentage of cold work increases. Theseadditional dislocations inhibit the continued mo-tion of other dislocations in much the same man-ner as increased traffic decreases the mobility ofcars along a highway system. Cold work is anexample of strengthening because of line defectsinteracting with other line defects in a crystallattice. Many manufactured components dependon cold work to raise their strength to the re-

quired level. Rolling, stamping, forging, draw-ing, swaging, and even extrusion may be usedto provide the necessary cold work. The effectsof cold work on the hardness and strength of a70%Cu-30%Zn alloy, iron and copper are illus-trated in Fig. 11. The yield and tensile strengthsfollow nearly identical trends, with the yieldstrength increasing slightly faster than the tensilestrength.

Grain and phase boundaries also block dis-location motion. Thus, the yield strength of mostmetals and alloys increases as the number ofgrain boundaries increases and/or as the per-centage of second phase in the structure in-creases. A decrease in the grain size increases

Fig. 9 Dislocations. (a) Transmission electron micrograph oftype 304 stainless steel showing dislocation pileups at

an annealing twin boundary. (b) Schematic representation of dis-locations on a slip plane

Fig. 11 Effects of cold work on the hardnesses and strengthsof brass, iron, and copper

Fig. 10 Effects of nickel and zinc contents on the yieldstrengths of copper alloys


the number of grain boundaries per unit volume,thus increasing the density of area defects in themetal lattice. Because interactions between areadefects and line defects inhibit dislocation mo-bility, the yield strengths of most metals and al-loys increase as the grain size decreases and asthe number of second-phase particles increases.The effects of grain size are illustrated in Fig.12. Because of these and other strengtheningmechanisms, any given alloy may show a widerange of yield strengths. The range will be de-pendent on the grain size, percentage of coldwork, distribution of second-phase particles, andother relatively easily quantified, microstruc-tural parameters. The values of these microstruc-tural parameters depend on the thermomechan-ical history of the material; thus a knowledge ofthese very important metallurgical variables isalmost a necessity for intelligent interpretationof yield-strength data and for the design and util-ization of metallic structures and components.

The most common definition of yield strengthis the stress necessary to cause a plastic strain of0.002 mm/mm (in./in.). This strain represents areadily measurable deviation from proportion-ality, and the stress necessary to produce thisdeviation is the 0.2% offset yield strength (seeChapter 3, “Uniaxial Tensile Testing,” for a de-tailed description of the 0.2% offset yieldstrength). A significant amount of dislocationmotion is required before a 0.2% deviation fromlinear behavior is reached. Therefore, in a stan-dard tensile test, the 0.2% offset yield strengthis almost independent of test-machine variables,gripping effects and reversible nonlinear strainssuch as anelasticity. Because of this indepen-dence, the 0.2% offset yield strength is a repro-ducible material property that may be used inthe characterization of the mechanical properties

of metals and alloys. However, it is vital to re-alize that the magnitude of the yield strength, orany other tensile property, is dependent on thedefect structure of the material tested. Therefore,the thermomechanical history of the metal or al-loy must be known if yield strength is to be ameaningful design parameter.

The Yield Point

The onset of dislocation motion in some al-loys, particularly low-carbon steels tested atroom temperature, is sudden, rather than a rela-tively gradual process. This sudden occurrenceof yielding makes the characterization of yield-ing by a 0.2% offset method impractical. Be-cause of the sudden yielding, the stress-straincurve for many mild steels has a yield point, andthe yield strength is characterized by lower yieldstress. The yield point develops because of in-teractions between the solute (dissolved) atomsand dislocations in the solvent (host) lattice. Thesolute-dislocation interaction in mild steels in-volves carbon migration to and interaction withdislocations. Because the interaction causes theconcentration of solute to be high in the vicinityof the dislocations, the yield point is said to de-velop because of segregation of carbon to thedislocations.

Many of the interstitial sites around disloca-tions are enlarged and are therefore low-energyor favored sites for occupancy by the solute at-oms. When these enlarged sites are occupied, ahigh concentration or atmosphere of solute is as-sociated with the dislocation. In mild steels, thesolute segregation produces carbon-rich atmo-spheres at dislocations. Motion of the disloca-tions is inhibited because such motion requires

Fig. 12 The effects of grain size on the strengths and ductilities of metals and alloys


the separation of the dislocations from the car-bon atmospheres. As soon as the separationtakes place, the stress required for continued dis-location motion decreases and, in a tensile test,the lower yield strength is reached. This yieldingprocess involves dislocation motion in localizedregions of the test specimen. Because disloca-tion motion is plastic deformation, the regionsin which dislocations moved represent deformedregions or bands in the metal. These localized,deformed bands are called Luders bands (seeFig. 4 in Chapter 2). Once initiated, additionalstrain causes the Luders bands to propagatethroughout the gage length of the test specimen.This propagation takes place at a constant stresswhich, is the lower yield strength of the steel.When the entire gage section has yielded, thestress-strain curve begins to rise because of theinteraction of dislocations with other disloca-tions, and strain-hardening initiates.

The existence of a yield point and Ludersband is particularly important because of the im-pact of the sudden softening and localized strain-ing on processing techniques. For example, sud-den localized yielding will cause jerky materialflow. Jerky flow is undesirable in a drawingoperation because the load on the drawingequipment would change rapidly, causing largeenergy releases that must be absorbed by theprocessing equipment. Furthermore, localizedLuders strains will produce stretch marks instamped materials. These stretch marks aretermed “stretcher strains” and are readily appar-ent on stamped surfaces. This impairs the sur-face appearance and reduces the utility of thecomponent. If materials that do not have yieldpoints are stamped, smooth surfaces are devel-oped because the strain-hardening processspreads the deformation uniformly throughoutthe material. Uniform, continuous deformationis important in many processing and finishingoperations; thus, it is important to select a com-bination of material-processing conditions thatminimize the tendency toward localized yield-ing.

Grain-Size Effects on Yielding

The metals and alloys used in most structuralapplications are polycrystalline. The typical me-tallic object contains tens of thousands of mi-croscopic crystals or grains. The size of thegrains is difficult to define precisely because the3-D shape of the grain is quite complex. If the

grain is assumed to be spherical, the grain di-ameter, d, may be used to characterize size.More precise characterizations of grain size in-clude the mean grain intercept, and the ratiol,of grain-boundary surface to grain volume, Sv.These two parameters may be establishedthrough quantitative metallographic techniques.The grain structure of the metal or alloy of in-terest is examined at a magnification, X, and aline of a known length l is overlaid on the mi-crostructure. The number of grain-boundary in-tersections with that line in measured, dividedby the length of the line, and multiplied by themagnification. The resulting parameter, Nl, is theaverage number of grain boundaries intersectedper unit length of line. This value for Nl is relatedto and Sv throughl

l � 1/Nl

and

S � 2Nv l

Unfortunately, for historical reasons, the param-eter d is the most common measure used to char-acterize the influence of grain size on the yieldstrengths of metals and alloys. This influence isfrequently quantified through the Hall-Petch re-lationship whereby yield strength, ry, is relatedto grain size through the empirical equation

�1/2r � r � kdy 0

The empirical constants r0 and k are the latticefriction stress and the Petch slope, respectively.A graphical representation of this relationship isshown in Fig. 12(a).

Grain boundaries act as barriers to dislocationmotion, causing dislocations to pile up behindthe boundaries. This pileup of dislocations con-centrates stresses at the tip of the pileup, andwhen the stress is sufficient, additional disloca-tions may be nucleated in the adjacent grain. Themagnitude of the stress at the tip of a dislocationpileup is dependent on the number of disloca-tions in the pileup. The number of dislocationsthat may be contained in a pileup increases withincreasing grain size because of the larger grainvolume. This difference in the number of dis-locations in a pileup makes it easier for new dis-locations to be nucleated in a large-grain metalthan in a fine-grain metal of comparable purity,and this difference in the ease of dislocation nu-cleation extrapolates directly to a difference in


Fig. 14 Effects of grain size and cold work on the flow stress of titanium

Fig. 13 Stress-strain curve for nickel

yield strength. Based on this model for grain-size strengthening, the effects of grain sizeshould exist even after the yield strength is ex-ceeded.

Strain Hardening and theEffect of Cold Work

A stress-strain curve for relatively pure nickel(Fig. 13) shows that the 0.2% offset yieldstrength of this metal was approximately 235MPa (34 ksi). The stress necessary to cause con-tinued plastic deformation increased as the ten-sile strain increased. After a strain of approxi-mately 1%, the stress necessary to producecontinued deformation was 330 MPa (48 ksi),and after 10% strain the necessary stress had in-creased to approximately 415 MPa (60 ksi).

The stress necessary for continued deforma-tion is frequently designated as the flow stressat that specific tensile strain. Thus, at 1% strain,the flow stress is 330 MPa (48 ksi), and the flowstress at 10% strain is 415 MPa (60 ksi). Thisincreasing flow stress with increasing strain isthe basis for increasing the strength of metalsand alloys by cold working. The effects of grainsize on the strength of the alloy are retainedthroughout the cold working process (Fig. 14).

The fact that the grain-size dependence ofstrength is retained throughout the strain-hard-ening process demonstrates the possibility forinteractions among the various strengtheningmechanisms in metals and alloys. For example,cold work causes strength increases through theinteraction between point defects and disloca-tions, and these effects are additive to the effectsof alloying. This is apparent in Fig. 15(a), wherethe incremental increase in strength resulting


Fig. 15 Effects of cold work on the tensile properties of cop-per and yellow brass. (a) Tensile strength. (b) Elon-

gation. (c) Reduction in areaFig. 16 Effects of cold work on the tensile stress-strain curves

of low-carbon steel bars

rolled specimen were elongated and flattened,thus changing from the semispherical grains inFig. 17(a) to the pancake-shape grains in Fig.17(b). A rod-drawing process would have pro-duced needle-shape grains in this same alloy. Inaddition to the changes in grain shape, the graininterior is distorted by cold forming operations.Bands of high dislocation density (deformationbands) develop, twin boundaries are bent, andgrain boundaries become rough and distorted(Fig. 18). Because the deformation-inducedchanges in microstructure are anisotropic, thetensile properties of wrought metals and alloysfrequently are anisotropic. The strain-hardenedmicrostructures and the associated mechanicalproperties that result from cold work can be sig-nificantly altered by annealing. The microstruc-tural changes that are introduced by heating tohigher temperatures are dependent on both thetime and temperature of the anneal. This tem-perature dependence is illustrated in Fig. 19 andresults because atom motion is required for theanneal to be effective.

The sudden drop in hardness seen in the Cu-5%Zn alloy in Fig. 19 results from recrystalli-zation, or the formation of new grains, in thealloy. Plastic deformation of metals and alloysat temperatures below the recrystallization tem-perature is cold work, and plastic deformation attemperatures above the recrystallization tem-perature is hot work. Metals and alloys, in ten-sile tests above the recrystallization temperature,

from zinc additions to copper becomes largerwhen the alloy is cold worked.

Furthermore, strength is not the only tensileproperty affected by the cold working process.Ductility decreases with increasing cold work(Fig. 15b and c), and, if cold working is too ex-tensive, metals and alloys will crack and fractureduring the working operation. The over-all ef-fects of cold work on strength and ductility areillustrated in Fig. 16, which compares the tensilebehavior of steel rods that were cold drawn vari-ous amounts before being tested to fracture.

Note that the increase in strength and decreasein ductility cause the area under the stress-straincurve to decrease. This is significant becausethat area represents the work or energy requiredto fracture the steel bar, and the tensile-test re-sults demonstrate that this energy decreases asthe percentage of cold work increases.

Cold working, whether by rolling, drawing,stamping, or forging, changes the microstruc-ture. The resulting grain shape is determined bythe direction of metal flow during processing, asillustrated in Fig. 17. The grains in the cold


Fig. 17 Effect of cold rolling on grain shape in cartridge brass. (a) Grain structure in annealed bar. (b) Grain structure in same barafter 50% reduction by rolling. Diagram in the lower left of each micrograph indicates orientation of the view relative to

the rolling plane of the sheet. 75�

do not show significant strain hardening, and thetensile yield strength becomes the maximumstress that the material can effectively support.See Chapter 13, “Hot Tensile Testing,” for in-formation on the effects of elevated tempera-tures on tensile properties.

Ultimate Strength

The ability to strain harden is one of the gen-eral characteristics in mechanical behavior thatdistinguish metals and alloys from most otherengineering materials. Not all metallic materials

Fig. 18 Grain structure of severely deformed Cu-5%Zn alloy


Fig. 19 Effect of annealing on hardness of cold rolled Cu-5%Zn brass. Hardness can be correlated with

strength, and the strengths of this alloy would show similar an-nealing effects. Fig. 20 Stress-strain curve for brittle material

exhibit this characteristic. Chromium, for ex-ample, is very brittle and fractures in a tensiletest without evidence of strain hardening. Thestress-strain curves for these brittle metals aresimilar to those of most ceramics (Fig. 20). Frac-ture occurs before significant plastic deforma-tion takes place.

Such brittle materials have no real yieldstrength, and the fracture stress is the maximumstress that the material can support. Most metalsand alloys, however, undergo plastic deforma-tion prior to fracture, and the maximum stressthat the metal can support is appreciably higherthan the yield strength. This maximum stress(based on the original dimensions) is the ulti-mate or tensile strength of the material.

The margin between the yield strength and thetensile strength provides an operational safetyfactor for the use of many metals and alloys instructural systems. Other than this safety margin,the actual value of tensile strength has very littlepractical use. The ability of a structure to with-stand complex service loads bears little relation-ship to tensile strength, and structural designsmust be based on yielding.

Tensile strength is easy to measure and is fre-quently reported because it is the maximumstress on an engineering stress-strain curve. En-gineering codes may even specify that a metalor alloy meet some tensile-strength requirement.Historically, tensile strengths, with experience-based reductions to avoid yielding, were used indesign calculations. As the accuracy of mea-

surement of stress-strain curves improved, util-ization of tensile strength diminished, and by the1940s most design guidelines were based onyielding. There is a large empirical database thatcorrelates tensile strength with hardness, fatiguestrength, stress rupture, and mechanical proper-ties. These correlations, historical code require-ments, and the fact that structural designs incor-porating brittle materials must be based ontensile strength provide the technical basis forthe continuing utilization of tensile strengths asdesign criteria.

Cold work and other strengthening mecha-nisms for metals and alloys do not increase ten-sile strength as rapidly as they increase yieldstrength. Therefore, as evident in Fig. 16,strengthening processes frequently are accom-panied by a reduction in the ability to undergoplastic strain. This reduction decreases the abil-ity of the material to absorb energy prior to frac-ture and, in many cases, is important to success-ful materials utilization. Analysis of the tensilebehavior of metals and alloys can provide in-sight into the energy-absorbing abilities of thematerial.

Toughness

The ability to absorb energy without fractur-ing is related to the toughness of the material.Most, if not all, fractures of engineering mate-rials are initiated at pre-existing flaws. Theseflaws may be small enough to be elements of themicrostructure or, when slightly larger, may bemacroscopic cracks in the material or, in the ex-treme, visually observable discontinuities in the


Fig. 21 Stress-strain curves for materials showing various de-grees of plastic deformation or ductility. (a) Brittlema-

terial. (b) Semibrittle material. (c) Ductile material

structure. A tough material resists the propaga-tion of flaws through processes such as yieldingand plastic deformation. Most of this deforma-tion takes place near the tip of the flaw. Becausefracture involves both tensile stress and plasticdeformation, or strain, the stress-strain curve canbe used to estimate material toughness. How-ever, there are specific tests designed to measurematerial toughness. Most of these tests are con-ducted with precracked specimens and includeboth impact and fracture-mechanics type studies(see Mechanical Testing and Evaluation, Vol-ume 8 of ASM Handbook, for descriptions ofthese tests). Toughness calculations based ontensile behavior are estimates and should not beused for design.

The area under a stress-strain curve (normal-ized to specimen dimensions) is a measure ofthe energy absorbed by the material during a ten-sile test. From that standpoint, this area is arough estimate of the toughness of the material.Because the plastic strain associated with tensiledeformation of metals and alloys is typicallyseveral orders of magnitude greater than the ac-companying elastic strain, plasticity or disloca-tion motion is very important to the develop-ment of toughness. This is illustrated by thestress-strain curves for a brittle, a semibrittle,and a ductile material shown schematically inFig. 21.

Brittle fracture (see Fig. 21a), takes place withlittle or no plastic strain, and thus the area underthe stress-strain curve, A is given by

A � (1/2)re

and, because all the strain is elastic,

r � Ee

Combining these equations gives

2A � (1/2)(r )Ef

where rf is the fracture stress. If the fracturestress for this material were 205 MPa (30 ksi)and Young’s modulus were 205 GPa (30 � 106

psi), the fracture energy, estimated from thestress-strain curve, would be 1.2 � 10�3 J/mm3

(15 lbf • in./in.3) per cubic inch of gage sectionin the test specimen. If the test specimen wereductile (Fig. 21c), the area under the stress-straincurve could be estimated from

A � (r � r )(e /2)y t f

where ry is yield strength, rt is tensile strength,and ef is strain to fracture. Estimation of the frac-ture energy from the typical tensile properties ofmild steel test specimens, ry � 205 MPa (30ksi), rt � 415 MPa (60 ksi), and ef � 0.3, gives1.12 J/mm3 (13,500 lbf • in./in.3) of gage sectionin the test specimen.

The ratio of the energy for ductile fracture tothe energy for brittle fracture is 900. This ratio


Fig. 22 Comparison of the stress-strain curves for high- andlow-toughness steels

is based on the calculations shown above andwill increase with increasing strain to fractureand with increasing strain hardening. These areaand energy relationships are only approxima-tions. The stresses used in the calculations arebased on the original dimensions of the testspecimen. The utility of such toughness esti-mates is the ease with which testing can be ac-complished and the insight that the estimatesprovide into the importance of plasticity to theprevention of fracture. This importance is illus-trated by considering the area under the stress-strain curve shown in Fig. 21(b). Assuming that,for this semibrittle material, the yield strengthand tensile strength are both 205 MPa (30 ksi)(no significant strain hardening) and that frac-ture takes place after a plastic strain of only 0.01mm/mm (in./in.), the area under the stress-straincurve is 410 J (300 lbf • in.) per unit area. Thisarea is 20 times higher than the area under thestress-strain curve for brittle fracture shown inFig. 21(a). This calculation demonstrates that aplastic strain of only 0.01% can have a remark-able effect on the ability of a material to absorbenergy without fracturing.

Toughness is a very important property formany structural applications. Ship hulls, cranearms, axles, gears, couplings, and airframes areall required to absorb energy during service. Theability to withstand earthquake loadings, systemoverpressures, and even minor accidents willalso require material toughness. Increasing thestrength of metals and alloys generally reducesductility and, in many cases, reduces toughness.This observation illustrates that increasing thestrength of a material may increase the proba-bility of service-induced failure when materialtoughness is important for satisfactory service.This is seen by comparing the areas under thetwo stress-strain curves in Fig. 22.

The cross-hatched regions in Fig. 22 illustrateanother tensile property—the modulus of resil-ience, which can be measured from tensilestress-strain curves. The ability of a metal or al-loy to absorb energy through elastic processes isthe resilience of the material. The modulus ofresilience is defined as the area under the elasticportion of the stress-strain curve. This area is thestrain energy per unit volume and is equal to

2A � (1/2)(r /E)y

Increasing the yield strength and/or decreas-ing Young’s modulus will increase the modulusof resilience and improve the ability of a metal

or alloy to absorb energy without undergoingpermanent deformation.

Ductility

Material ductility in a tensile test is generallyestablished by measuring either the elongationto fracture or the reduction in area at fracture. Ingeneral, measurements of ductility are of interestin three ways:

1. To indicate the extent to which a metal canbe deformed without fracture in metalwork-ing operations such as rolling and extrusion.

2. To indicate to the designer, in a general way,the ability of the metal to flow plastically be-fore fracture. A high ductility indicates thatthe material is ‘forgiving’ and likely to de-form locally without fracture should the de-signer err in stress calculation or the predic-tion of severe loads.

3. To serve as an indicator of changes in im-purity level or processing conditions. Ductil-ity measurements may be specified to assessmaterial quality even though no direct rela-tionship exists between the ductility mea-surement and performance.

Tensile ductility is therefore a very usefulmeasure in the assessment of material quality.Many codes and standards specify minimumvalues for tensile ductility. One reason for thesespecifications is the assurance of adequatetoughness without the necessity of requiring amore costly toughness specification. Mostchanges in alloy composition and/or processingconditions will produce changes in tensile duc-


Fig. 24 True stress-strain curves for austenitic and mild steelsFig. 23 Comparison of engineering and true stress-strain

curves

tility. The “forgiveness” found in many metalsand alloys results from the ductility of these ma-terials. Although there is some correspondencebetween tensile ductility and fabricability, themetalworking characteristics of metals and al-loys are better correlated with the ability tostrain harden than with the ductility of the ma-terial. The strain-hardening abilities of many en-gineering alloys have been quantified throughthe analysis of true stress-strain behavior.

True Stress-Strain Relationships

Conversion of engineering stress-strain be-havior to true stress-strain relationships may beaccomplished using the techniques representedby Eq 8 through 13 in Chapter 1, “Introductionto Tensile Testing.” This conversion, summa-rized graphically in Fig. 23, demonstrates thatthe maximum in the engineering stress-straincurve results from tensile instability, not from adecrease in the strength of the material. The dropin the engineering stress-strain curve is artificialand occurs only because stress calculations arebased on the original cross-sectional area. Bothtesting and analysis show that, for most metalsand alloys, the tensile instability corresponds tothe onset of necking in the test specimen. Neck-ing results from strain localization; thus, oncenecking is initiated, true strain cannot be calcu-lated from specimen elongation. Because ofthese and other analytical limitations of engi-neering stress-strain data, if tensile data are usedto understand and predict metallurgical responseduring the deformation associated with fabrica-

tion processes, true stress-true strain relation-ships are preferred.

The deformation that may be accommodated,without fracture, in a deep drawing operationvaries with the material. For example, austeniticstainless steels may be successfully drawn to50% reductions in area whereas ferritic steelmay fail after only 20 to 30% reductions in areain similar drawing operations. Both types ofsteel will undergo in excess of 50% reduction inarea in a tensile test. This difference in draw-ability correlates with the strain-hardening ex-ponent (n) and therefore is apparent from theslope of the true stress-strain curves for the twoalloys (Fig. 24). A detailed discussion on thestrain-hardening exponent, or coefficient, can befound in Chapter 6, “Tensile Testing for Deter-mining Sheet Formability.”

The strain-hardening exponents, or n valuesfor ferritic and austenitic steels, are typically0.25 and 0.5, respectively. A perfectly plasticmaterial would have a strain-hardening expo-nent of zero and a completely elastic solid wouldhave a strain-hardening exponent of one. Mostmetals and alloys have strain-hardening expo-nents between 0.1 and 0.5. Strain-hardening ex-ponents correlate with the ability of dislocationsto move around or over dislocations and otherobstacles in their path. Such movement istermed “cross slip.” When cross slip is easy, dis-locations do not pile up behind each other andstrain-hardening exponents are low. Mild steels,aluminum, and some nickel alloys are examplesof materials that undergo cross slip easily. Thevalue of n increases as cross slip becomes moredifficult. Cross slip is very difficult in austeniticstainless steels, copper, and brass and the strain-hardening exponent for these alloys is approxi-mately 0.5.


Fig. 25 Effects of temperature and strain rate on the strengthof copper

Tensile specimens, sheet or plate material,wires, rods, and metallic sections have spot-to-spot variations in section size, yield strength,and other microstructural and structural inhom-ogeneities. Plastic deformation of these materi-als initiates at the locally weak regions. In theabsence of strain hardening, this initial plasticstrain would reduce the net section size and fo-cus continued deformation in the weak areas.Strain hardening, however, causes the flowstress in the deformed region to increase. Thisincrease in flow stress increases the load nec-essary for continued plastic deformation in thatarea and causes the deformation to spreadthroughout the section. The higher the strain-hardening exponent, the greater the increase inflow stress and the greater the tendency for plas-tic deformation to become uniform. This ten-dency has a major impact on the fabricability ofmetals and alloys. For example, the maximumreduction in area that can be accommodated ina drawing operation is equal to the strain-hard-ening exponent as determined from the truestress-strain behavior of the material. Because ofsuch correlations, the effects of process variablessuch as strain rate and temperature can be eval-uated through tensile testing. This provides a ba-sis to approximate the effects of process vari-ables without direct, in-process assessment ofthe variables.

Temperature and Strain-Rate Effects

The yield strengths of most metals and alloysincrease as the strain rate increases and decreaseas the temperature increases. This strain-ratetemperature dependence is illustrated in Fig. 25.These dependencies result from a combinationof several metallurgical effects.

For example, dislocations are actually dis-placements and therefore cannot move fasterthan the speed of sound. Furthermore, as dislo-cation velocities approach the speed of sound,cross slip becomes increasingly difficult and thestrain-hardening exponent increases. This in-crease in the strain-hardening exponent in-creases the flow stress at any given strain, thusincreasing the yield strength of the material. Adecrease in ductility and even a transition fromductile to brittle fracture may also be associatedwith strain-rate-induced increases in yieldstrength. In many respects, decreasing the tem-perature is similar to increasing the strain rate.The mobility of dislocations decreases as the

temperature decreases, and thus, for most metalsand alloys, the strength increases and the ductil-ity decreases as the temperature is lowered. Ifthe reduction in dislocation mobility is suffi-cient, the ductility may be reduced to the pointof brittle fracture. Metals and alloys that show atransition from ductile to brittle when the tem-perature is lowered should not be used for struc-tural applications at temperatures below thistransition temperature.

Dislocation motion is inhibited by interac-tions between dislocations and alloy or impurity(foreign) atoms. The effects of these interactionsare both time and temperature dependent. Theinteraction acts to increase the yield strength andlimit ductility. These processes are most effec-tive when there is sufficient time for foreign at-oms to segregate to the dislocation and whendislocation velocities are approximately equal tothe diffusion velocity of the foreign atoms.Therefore, at any given temperature, disloca-tion-foreign atom interactions will be at a max-imum at some intermediate strain rate. At lowstrain rates, the foreign atoms can diffuse as rap-idly as the dislocations move and there is littleor no tendency for the deformation process toforce a separation of dislocations from their sol-ute atmospheres. At high strain rates, once sep-aration has been effected, there is not sufficienttime for the atmosphere to be re-established dur-ing the test. Atom movement increases with in-creasing temperature, thus the strain rates thatallow dislocation-foreign atom interactions tooccur are temperature dependent. Because theseinteractions limit ductility, the elongation in atensile test may show a minimum at intermediatetest temperatures where such interactions aremost effective (Fig. 26).


Fig. 27 Illustration of strain aging during an interrupted ten-sile test. (a) Specimen reloaded in a short period of

time. (b) Time between loading and unloading is sufficientFig. 26 An intermediate-temperature ductility minimum in

titanium

The effects of time-dependent dislocation for-eign atom interactions on the stress-strain curvesof metals and alloys are termed “strain aging”and “dynamic strain aging.” Strain aging is gen-erally apparent when a tensile test, of a materialthat exhibits a sharp yield point, is interrupted.If the test specimen is unloaded after beingstrained past the yield point, through the Ludersstrain region and into the strain-hardening por-tion of the stress-strain curve, either of two be-haviors may be observed when the tensile test isresumed (Fig. 27). If the specimen is reloadedin a short period of time, the elastic portion ofthe reloading curve (line d-c in Fig. 27a) is par-allel to the original elastic loading curve (line a-b in Fig. 27a) and plastic deformation resumesat the stress level (level c) that was reached justbefore the test was interrupted.

However, if the time between unloading andreloading is sufficient for segregation of foreignatoms to the dislocations, the yield point reap-pears (Fig. 27b) and plastic strain is not reini-tiated when the unloading stress level (point c)is reached. This reappearance of the yield pointis strain aging, and the strength of the strain-aging peak is dependent on both time and tem-perature because solute-atom diffusion and seg-regation to dislocations are required for the peakto develop. If tensile strain rates are in a rangewhere solute segregation can occur during thetest, dynamic strain aging is observed. Segre-gation pins the previously mobile dislocationsand raises the flow stress, and when the new,higher flow stress is reached the dislocations areseparated from the solute atmospheres and theflow stress decreases. This alternate increase anddecrease in flow stress causes the stress-straincurve to be serrated (Fig. 28).

Serrated flow is common in mild steels, insome titanium and aluminum alloys, and in other

Fig. 28 Dynamic strain aging or serrated yielding in an aluminum alloy tested at room temperature


metals that contain mobile, alloy or impurity ele-ments. This effect was initially studied in detailby Portevin and LeChatelier and is frequentlycalled the Portevin-LeChatelier effect. Process-ing conditions must be selected to avoid strain-aging effects. This selection necessarily involvesthe control of processing strain rates and tem-peratures.

Special Tests

The tensile test provides basic informationconcerning the responses of metals and alloys tomechanical loadings. Test temperatures andstrain rates (or loading rates) generally are con-trolled because of the effects of these variableson the metallurgical response of the specimen.The tensile test typically measures strength andductility. These parameters are frequently sen-sitive to specimen configuration, test environ-ment, and the manner in which the test is con-ducted. Special tensile tests have beendeveloped to measure the effects of test/speci-men conditions on the strengths and ductilitiesof metals and alloys. These tests include thenotch tensile test and the slow-strain-rate tensiletest.

Notch Tensile Test. Metals and alloys in en-gineering applications frequently are required towithstand multiaxial loadings and high stressconcentrations owing to component configura-tion. A standard tensile test measures materialperformance in smooth bar specimens exposedto uniaxial loads. This difference between ser-vice and test specimens may reduce the abilityof the standard tensile test to predict materialresponse under anticipated service conditions.Furthermore the reductions in ductility generallyinduced by multiaxial loadings and stress con-centrations may not be apparent in the test re-sults. The notched tensile test therefore was de-veloped to minimize this weakness in thestandard tensile test and to investigate the be-havior of materials in the presence of flaws,notches, and stress concentrations.

The notched tensile specimen generally con-tains a 60� notch that has a root radius of lessthan 0.025 mm (0.001 in.) (see Fig. 23 in Chap-ter 3). The stress state just below the notch tipapproaches triaxial tension, and for ductile met-als this stress state generally increases the yieldstrength and decreases the ductility. This in-crease in yield strength results from the effect ofstress state on dislocation dynamics. Shear

stresses are required for dislocation motion. Puretriaxial loads do no produce any shear stress;thus, dislocation motion at the notch tip is re-stricted and the yield strength is increased. Thisrestriction in dislocation motion also reduces theductility of the notched specimen. For low-duc-tility metals, the notch-induced reduction in duc-tility may be so severe that failure takes placebefore the 0.2% offset yield strength is reached.

The sensitivity of metals and alloys to notcheffects is termed the “notch sensitivity.” Thissensitivity is quantified through the ratio ofnotch strength to smooth bar tensile strength.Metals and alloys that are notch sensitive haveratios less than one. Smooth bar tensile data forthese materials are not satisfactory predictors ofmaterial behavior under service conditions.Tough, ductile metals and alloys frequently arenotch-strengthened and have notch sensitivityratios greater than one, thus the standard tensiletest is a conservative predictor of performancefor these materials.

Slow-Strain-Rate Testing. Test environ-ments also may have adverse effects on the ten-sile behavior of metals and alloys. The charac-terization of environmental effects on materialresponse may be accomplished by conductingthe tensile test in the environment of interest (forexample, sodium chloride solutions). Becausethe severity of environmental attack generallyincreases with increasing time, tensile tests de-signed to determine environmental effects fre-quently are conducted at very low strain rates.The low strain rate increases the test time andmaximizes exposure to the test environment.This type of testing is termed either “slow-strain-rate testing” (SSRT) or “constant-exten-sion-rate testing” (CERT). Exposure to the ag-gressive environment may reduce the strengthand/or ductility of the test specimen. These re-ductions may be accompanied by the onset ofsurface cracking and/or a change in the fracturemode. A CERT or SSRT study that shows det-rimental effects on the tensile behavior will es-tablish that the test material is susceptible to en-vironmental degradation (Fig. 29a).

This susceptibility may cause concern overthe utilization of the material in that environ-ment. Conversely, the test may show that thetensile behavior of the material is not influencedby the environment and is therefore suitable forservice in that environment (Fig. 29b). CERTand SSRT may be used to screen materials forpotential service exposures and/or investigatethe effects of anticipated operational changes on


Fig. 30 Typical slow-strain-rate test apparatus

Fig. 29 Typical CERT and SSRT results showing (a) material susceptibility to environmental degradation and (b) materialcompatibilitywith the environment

the materials used in process systems. In eitherevent, the intent is to avoid materials utilizationunder conditions that may degrade the strengthand ductility and cause premature fracture. Inaddition to the tensile data per se, evidence ofadverse environmental effects may also be foundthrough examination of the fracture morpholo-gies of CERT and SSRT test specimens.

Figure 30 shows a typical SSRT or CERT test-ing machine. Various types of corrosion cellsmay be required to control the test conditionsfor specific studies. Standard tensile specimens(ASTM E 8) are generally recommended for usewith specified conditions of gage lengths, radii,and so on, unless specialized studies are beingconducted. Notched or precracked specimensare also used for certain tests. More detailed in-formation SSRT/CERT testing can be found inthe article “Evaluating Stress-Corrosion Crack-ing” in Corrosion: Fundamentals, Testing, andProtection, Volume 13A of ASM Handbook.

Fracture Characterization

Tensile fracture of ductile metals and alloysgenerally initiates internally in the necked por-tion of the tensile bar. Particles such as inclu-sions, dispersed second phases, and/or precipi-tates may serve as the nucleation sites. Thefracture process begins by the development ofsmall holes, or microvoids, at the particle-matrixinterface (Fig. 31).

Continued deformation enlarges the micro-voids until, at some point in the testing process,the microvoids contact each other and coalesce.This process is termed “microvoid coalescence”and gives rise to the dimpled fracture surfacetopography characteristic of ductile failure pro-cesses (Fig. 32).

The surface topography of a brittle fracturediffers significantly from that of microvoid co-alescence. Brittle fracture generally initiates atimperfections on the external surface of the ma-terial and propagates either by transgranularcleavagelike processes or by separation alonggrain boundaries. The resultant surface topog-raphy is either faceted, perhaps with the riverlikepatterns typical of cleavage (Fig. 33a), or inter-granular, producing a “rock candy”-like appear-ance (Fig. 33b). The test material may be inher-ently brittle (such as chromium or tungsten), or


Fig. 32 Scanning electron micrograph illustrating ductile fracture surface topography. This fracture topography is identified as mi-crovoid coalescence.

Fig. 31 Photomicrograph illustrating fracture initiation at particles. Particle is small sphere near the center of the micrograph.

brittleness may be introduced by heat treatment,lowering the test temperature, the presence of anaggressive environment, and/or the presence ofa sharp notch on the test specimen.

The temperature, strain rate, test environment,and other conditions, including specimen sur-

face finish for a tensile test, are generally wellestablished. An understanding of the effects ofsuch test parameters on the fracture character-istics of the test specimen can be very useful inthe determination of the susceptibility of metalsand alloys to degradation fabrication and during


Fig. 33 Scanning electron micrographs illustrating transgranular and intergranular fracture topographies. (a) Transgranularcleavage-like fracture topography. Direction of crack propagation is from grain A through grain B. (b) Intergranular fracture topography

service. Typically, any heat treatment or testcondition that causes the fracture process tochange from microvoid coalescence to a morebrittle fracture mode reduces the ductility andtoughness of the material and may promote pre-mature fracture under selected service condi-tions. Because the fracture process is very sen-sitive to both the metallurgical condition of thespecimen and the conditions of the tensile test,characterization of the fracture surface is an im-portant component of many tensile-test pro-grams.

Summary

The mechanical properties of metals and al-loys are frequently evaluated through tensiletesting. The test technique is well standardizedand can be conducted relatively inexpensivelywith a minimum of equipment. Many materialsutilized in structural applications are required tohave tensile properties that meet specific codesand standards. These requirements are generallyminimum strength and ductility specifications.Because of this, information available from atensile test is frequently under utilized. A ratherstraightforward investigation of many of themetallurgical interactions that influence the re-sults of a tensile test can significantly improvethe usefulness of test data. Investigation of theseinteractions, and correlation with metallurgical/

material/service variables such as heat treat-ment, surface finish, test environment, stressstate, and anticipated thermomechanical expo-sures, can lead to significant improvements inboth the efficiency and the quality of materialsutilization in engineering service.

ACKNOWLEDGMENT

This chapter was adapted from M.R. Louthan,Jr., Tensile Testing of Metals and Alloys, TensileTesting, 1st ed., P. Han, Ed., ASM International,1992, p 61–104

SELECTED REFERENCES

● C.R. Brooks, Plastic Deformation and An-nealing, Heat Treatment, Structure andProperties of Nonferrous Alloys, AmericanSociety for Metals, 1982, p 1–73

● G.E. Dieter, Mechanical Metallurgy, 3rd ed.,McGraw-Hill, New York, 1986

● T.M. Osman, Introduction to the MechanicalBehavior of Metals, Mechanical Testing andEvaluation, Vol 8, ASM Handbook, ASMInternational, 2000, p 3–12

● T.H. Courtney, Fundamental Structure-Prop-erty Relationships in Engineering Materials,Materials Selection and Design, Vol 20,ASM Handbook, ASM International, 1997, p336–356

CHAPTER 8

Tensile Testing of Plastics

Table 1 ASTM and ISO mechanical test standards for plastics

ASTM standard ISO standard Topic area of standard

Specimen preparation

D 618 291 Methods of specimen conditioningD 955 294-4 Measuring shrinkage from mold dimensions of molded thermoplasticsD 3419 10724 In-line screw-injection molding of test specimens from thermosetting compoundsD 3641 294-1,2,3 Injection molding test specimens of thermoplastic molding and extrusion materialsD 4703 293 Compression molding thermoplastic materials into test specimens, plaques, or sheetsD 524 95 Compression molding test specimens of thermosetting molding compoundsD 6289 2577 Measuring shrinkage from mold dimensions of molded thermosetting plastics

Mechanical properties

D 256 180 Determining the pendulum impact resistance of notched specimens of plasticsD 638 527-1,2 Tensile properties of plasticsD 695 604 Compressive properties of rigid plasticsD 785 2039-2 Rockwell hardness of plastics and electrical insulating materialsD 790 178 Flexural properties of unreinforced and reinforced plastics and insulating materialsD 882 527-3 Tensile properties of thin plastic sheetingD 1043 458-1 Stiffness properties of plastics as a function of temperature by means of a torsion testD 1044 9352 Resistance of transparent plastics to surface abrasionD 1708 6239 Tensile properties of plastics by use of microtensile specimensD 1822 8256 Tensile-impact energy to break plastics and electrical insulating materialsD 1894 6601 Static and kinetic coefficients of friction of plastic film and sheetingD 1922 6383-2 Propagation tear resistance of plastic film and thin sheeting by pendulum methodD 1938 6383-1 Tear propagation resistance of plastic film and thin sheeting by a single tear methodD 2990 899-1,2 Tensile, compressive, and flexural creep and creep-rupture of plasticsD 3763 6603-2 High-speed puncture properties of plastics using load and displacement sensorsD 4065 6721-1 Determining and reporting dynamic mechanical properties of plasticsD 4092 6721 Dynamic mechanical measurements on plasticsD 4440 6721-10 Rheological measurement of polymer melts using dynamic mechanical proceduresD 5023 6721-3 Measuring the dynamic mechanical properties of plastics using three-point bendingD 5026 6721-5 Measuring the dynamic mechanical properties of plastics in tensionD 5045 572 Plane-strain fracture toughness and strain energy release rate of plastic materialsD 5083 3268 Tensile properties of reinforced thermosetting plastics using straight-sided specimensD 5279 6721 Measuring the dynamic mechanical properties of plastics in torsion

ENGINEERING PLASTICS are either ther-moplastic resins (which can be repeatedly re-heated and remelted) or thermosetting resins(which are cured resins with cross links that de-polymerize upon exposure to elevated tempera-tures above the glass transition temperature).The glass transition temperature (Tg) is definedas the temperature at which an amorphous poly-mer (or the amorphous regions in a partiallycrystalline polymer) changes from a hard andrelatively brittle condition to a viscous or rub-bery condition.

The testing of plastics includes a wide varietyof chemical, thermal, and mechanical tests (Ta-ble 1). This chapter reviews the tensile testingof plastics, which has been standardized inASTM D 638, “Standard Test Method for Ten-sile Properties of Plastics,” and other compara-ble standards. Tensile testing embraces variousprocedures by which modulus, strength, andductility can be assessed. Tests specifically de-signed to measure phenomena as varied ascreep, stress relaxation, stress rupture, fatigue,and impact resistance can all be classified as ten-




sile tests provided that the stress system is pre-dominantly tensile, but by common usage theterm “tensile test” is usually taken to mean a testin which a specimen is extended uniaxially at auniform rate. Ideally, the specimen should beslender, of constant cross section over a sub-stantial gage length, and free to contract laterallyas it extends; a tensile stress then develops overtransverse plane sections lying within the gageregion, and the specimen extends longitudinallyand contracts laterally. A procedure was initiallydeveloped for tests on metals but was subse-quently adopted and adapted for tests on rub-bers, fibers, and plastics. In the case of plastics,their viscoelastic nature and the probable aniso-tropy of their end products (including test spec-imens) are factors that strongly influence boththe conduct of the tests and the interpretation ofthe results.

Practical tensile testing often conforms to one(e.g., ASTM D 638) or another of several stan-dard methods or to a code of practice, with var-iants dictated by local circumstances. Most ofthe stipulations set out in the standardized prac-tices embody the collective wisdom of earliertensile-test practitioners and fall into four dis-tinct groupings:

● Stipulations relating to the specimen-ma-chine system

● Stipulations relating to the derivation of ex-citation-response relationships from the rawdata

● Stipulations relating to the precision of thedata

● Stipulations relating to the physical interpre-tation of the data.

The stipulations in the first group are the primaryones, because, unless the specimen-machinesystem functions properly, no worthwhile datacan be generated. The stipulations in the otherthree groups are supplementary but are never-theless essential in that they enable the outcomeof the machine-specimen interaction to be trans-lated progressively into mechanical-propertiesdata for the specimen under investigation.

Viscoelasticity and anisotropy cast their influ-ences over all these groups. Viscoelasticity in-fluences the excitation-response relationships,complicates the analysis of data, and affectssome practical aspects of the test. Anisotropydoes the same things, but also introduces an un-certainty about the utility of any specific datumbecause it varies from point to point in a speci-men, and from specimen to specimen in a sam-

ple, depending on the processing conditions andother factors. These variations can be large, andtherefore questions arise as to how such mate-rials should be evaluated and whether or not re-sults from tests on a particular specimen canever be definitive. If a test has been properlyexecuted, the properties data should be precise,but they may be precise without being accurateand may be accurate without being definitive.

In one particular respect, tensile testing suf-fers from a fundamental and inescapable defi-ciency that is common to many types of me-chanical tests: the experimenter has no optionbut to measure force and deformation, whereasthe physical characteristics of the specimen andthe material should be expressed in terms ofstress and strain. The translations of force intostress and deformation into strain are sources oferrors and uncertainties, so much so that thetransformed results may bear little relation to thestrict truth, although this does not render themuseless. Note No. 2 in Section 1, “Scope,” ofASTM D 638 states, appropos of other factorsbut appropriate nevertheless, that “This testmethod is not intended to cover precise physicalprocedures. . . . Special additional tests shouldbe used where more precise physical data arerequired.”

Fundamental Factors thatAffect Data from Tensile Tests

Viscoelasticity. Plastics are viscoelastic—that is, the relationships between the stress stateand the strain state are functions also of time.Linear viscoelasticity, the simplest case, is rep-resented by the relationship

� �n m� r � ea � b� n � mn m�t �tn�0 m�0

where r is stress, e is strain, and t is time, anda and b are characterizing coefficients. Whenmost of the coefficients are set to zero, the equa-tion describes simple behavior. If only a0 and b0differ from zero, the equation represents linearelastic behavior, and if only a0 or b1 differs fromzero, it represents Newtonian viscosity, but asother coefficients differ from zero the differen-tial terms progressively enter the equation andthe relationships between stress and strain thenbecome time-dependent. In simple cases, theviscoelasticity can be visualized as the mechan-

Tensile Testing of Plastics / 139

Fig. 1 Visualizations of simple viscoelastic systems

ical behavior of assemblies of Hookean springsand Newtonian dashpots (which are representa-ble by the same equation), the two simplest as-semblies being a series combination and a par-allel combination of one spring and one dashpot.The former, known as a Maxwell element, isused primarily to represent or demonstrate thetime-dependence of the stress that arises when astrain is applied suddenly, and the latter, knownas a Voigt element, demonstrates the time-de-pendence of the strain that develops when astress is applied suddenly (see Fig. 1).

Due allowance must be made for viscoelas-ticity during both the practical execution of thetest and the interpretation of the results, becausethe ramifications of viscoelasticity extend overvirtually all the mechanical behavior. Thus, forexample, after the specimen has been mountedin the grips, the clamping stresses may relax tothe point where it is not held securely. There areseveral such specimen-machine interactions, butappropriate practical measures alleviate theirconsequences, and serious malfunctions gener-ally can be avoided. In contrast, possibilities ofmisinterpretation of the results are not so easilycircumvented, because viscoelasticity is an in-escapable feature of almost every response

curve. In general, the response of a viscoelasticbody to an applied stress or strain is a functionof the stress history or the strain history. There-fore, the moduli, which are defined in variousways depending on the time-form of the exci-tation, are functions of elapsed time and/or fre-quency (see Fig. 1). Furthermore, plastics arenonlinearly viscoelastic—that is, at constanttime the relationship between stress and strain isnonlinear. The relaxation modulus, which is de-rived from an experiment in which a strain sup-posedly is applied instantaneously and held con-stant thereafter, is a function of the strainmagnitude as well as of the elapsed time; simi-larly, the creep compliance is a function of thestress magnitude and the elapsed time. Thesetwo procedures are ideal in that they enable non-linearity and time-dependence to be separatedexperimentally, but the apparently simple pro-cedure of conventional tensile testing is not sim-ple; the force or the stress that develops in thecourse of the test is governed by both thechanges in strain and the passage of time.

A single tensile test provides merely one sec-tion across a relationship that for plastics is acomplex one between stress, strain, and strainrate, and it follows that inferences drawn from


that single curve are correspondingly limited intheir scope. For instance, such a curve containsno direct indication of load-bearing capabilityunder loads sustained over any period greaterthan the duration of that particular tensile test.Tensile-testing practice accommodates this andrelated deficiencies pragmatically by regardingdeformation rate as a critical variable. A com-prehensive evaluation entails the use of severalrates, which should range over several decades,although this raises certain practical issues. Verylow rates may be prohibited on the grounds ofuneconomical deployment of expensive appa-ratus, and very high rates pose technical de-mands on machine power and sensor responsethat may be resolved more effectively by use ofimpact tests.

The viscoelasticity, in combination with cer-tain features of the test system itself, influencesthe choice of data for subsequent conversion intoproperty values. Thus, the modulus, which is amultivalue property if the material is viscoelas-tic, must be qualified by specification of the cur-rent stress (or strain) and the stress (or strain)history up to a specific point in time. For rampexcitations—i.e., the constant deformation-rateconditions of a tensile test—modulus can be de-fined as the slope of either the tangent at, or thesecant to, any desired point on a stress-straincurve. As such, each single datum is one pointonly in a viscoelastic function; it has no specialmerit, although, of the various options, the tan-gent at the origin is possibly the best in theorybecause the strain-dependence should be negli-gible there. However, mechanical inertias in thetesting machine and finite response times of thesensors combine with the viscoelasticity to dis-tort the observed force-deformation relationship.They reduce the initial slope, obscure the origin,and obscure or distort abrupt changes in slopethat may signify structural changes in the de-forming specimen, thereby detracting from theusefulness of the test and introducing the poten-tial for errors in the measurements.

Strength is also a multivalue property, the vis-coelasticity intruding both directly, as a time-dependence (rate-dependence) or the equivalenttemperature-dependence, and indirectly, as afactor influencing the nature of the failure orfracture, through the sensitivity to strain rate andtemperature of the ductile-brittle transition. Thistransition is usually a gradual one, with the duc-tility decreasing progressively as the deforma-tion rate is increased or as the temperature islowered. The practicalities of the evaluation of

tensile properties are such that temperature usu-ally is varied in preference to extension rate; Fig.2 shows typical results from which it may beinferred that the shapes of the stress-straincurves of plastic materials are not uniquely char-acteristic, and it follows also that uncertaintiescan arise over the point at which a characterizingdatum such as a strength or a yield strain shouldbe extracted from the response curve.

In summary, the viscoelastic nature of plasticsentails specific precautions concerning somepractical aspects of the test and the analysis ofthe results. In the first category, mounting of thespecimen in the grips and mounting of strainsensors on the specimen require special atten-tion. In the second category, the response curvemust be recognized as offering only a limitedinsight into the mechanical behavior of the sam-ple under investigation, and the data must beused with appropriate caution. See also Fig. 3.

Anisotropy in Plastic Specimens. Test spec-imens, whether directly molded or cut fromlarger pieces, are often anisotropic—partly be-cause plastics are viscoelastic in their moltenstate and very viscous, so that the shaping pro-cesses cause molecular alignments, and partlybecause ordered structural entities may developduring the cooling stage.

The property values derivable from suchspecimens often differ from what might be ex-pected on the basis of isotropic idealizations,and, because of their limited range, the data usu-ally generated are not definitive in that they donot adequately quantify the tensor array of mod-ulus or strength and do not show how that arrayvaries with processing conditions, flow geome-try, and specimen geometry. Some of the rami-fications have been troublesome in evaluationprograms in the past, because certain conse-quential results have seemed to be anomalous.Two situations are particularly important: onerelates to the position of the failure site, and theother relates to the strength of notched speci-mens.

The first situation involves tensile specimensof dumbbell or similar shape, which often areinjection molded through an endgate (see Fig. 5in Chapter 11, “Tensile Testing of Fiber-Re-inforced Composites,” for a typical tensile testspecimen). The pattern of molecular and fiberorientation is then predominantly longitudinal inthe outer layers of the parallel-sided section butis more complex in the core and at the ends ofthe specimen. At the end remote from the gate,the larger cross section causes diverging flow


Fig. 2 Influence of temperature on the nature of the stress-strain relationship. Strain rate has a similar effect, with increasing ratebeing equivalent to decreasing temperature. Source: Ref 1

during the molding operation and thereforesome lateral molecular orientation, which maylower the longitudinal strength locally to such alevel that the specimen breaks there rather thanat the smaller cross section in the gage region.

The second situation involves notched speci-mens. A molded notch may not affect strengthto the same degree, or even in the same sense,that would be inferred from stress-concentrationtheory, because the local flow geometry near thecrack tip may enhance the strength and therebymitigate the effect of the stress concentration.On the other hand, the flow geometry may re-duce the strength in the critical direction. A ma-chined notch also interacts with the flow ge-ometry in that the geometrical details governwhere the tip lies in relation to the orientationpattern. Results are likely to be less ambiguousthan those for molded notches but still at quan-titative variance with predictions based on con-cepts of stress concentration or stress-field in-tensity.

A secondary consequence, but one of greatpractical importance, is that the essentially sim-ple functional operation of the test machine iscompromised, particularly in relation to thespecimen-machine interaction. The force is

transmitted to the specimen mainly by means ofshear stresses at or near the grips, and the spec-imen is required to extend with lateral contrac-tion but no extraneous distortion. However, apredominantly axial molecular orientation or fi-ber alignment confers a relatively high tensilestrength but a relatively low shear strength alongthe longitudinal direction, with the result thatshear failure near the grips may ensue beforetensile failure occurs in the gage region. Modi-fied grips, reinforcing plates attached to the endsof specimens, and changed specimen profilescan all reduce the risk of malfunction, but suchsteps may be detrimental in other respects. If thepredominant orientation lies at some angle to thetensile axis, the specimen will distort into a sig-moid, the exact form of which will depend onwhether or not the clamped ends are free to ro-tate; in either case, the observed force and ex-tension will not convert into correct values oftensile modulus or tensile strength. In general,these effects are far more pronounced in speci-mens of continuous-fiber plastic-matrix com-posites than in simple plastic specimens (includ-ing those containing short fibers); but even ifthere is no gross malfunction in tests on plastics,


Fig. 3 Influence of the inherent nature of plastics on tensile-testing practice

there is a high probability of mildly erroneousdata being generated.

The influences of flow geometry and flow ir-regularities on derived property values are per-vasive and can distort an investigator’s percep-tion of properties, trends, etc. Corrective actionto avoid misconceptions entails expansion of theevaluation programs to cover samples with dif-ferent flow geometries and, in some instances,

modified test configurations—e.g., differentspecimen profiles. The choice of samples andspecimens is a complex issue that has never beenresolved adequately. Specimens machined fromvarious judiciously chosen positions in largeritems are possibly a wiser choice than the widelyused injection-molded endgated bars. The latterare popular because they are economical in theuse of material and manpower, but the pre-


Fig. 4 Yielding and post-yield tensile behavior: (a) uniformextension; (b) yielding followed by necking rupture; (c)

yielding followed by “cold drawing” and work hardening

dominantly axial molecular orientation of thinmoldings confers higher tensile moduli andstrengths than those exhibited by most end prod-ucts. The pattern of orientation varies with thethickness of the bar; axial orientation arisesmainly in the outer layers, and hence, as thethickness increases, the measured values of ten-sile modulus and strength decrease.

In summary, anisotropy can cause extraneousdistortions in specimens under test, failure at ornear the grips, unsuspected errors in data, andodd trends with respect to notch geometry, spec-imen profile, etc. (see also Fig. 3). In many in-stances, the evaluation program should be ex-panded, possibly with modified test procedures.

Plasticity, Necking Rupture, and WorkHardening. There is much experimental evi-dence, from creep studies and from tensile teststhemselves, that with increasing strain the de-formation processes become progressively dom-inated by molecular mechanisms that either areirreversible or are reversible but have very pro-tracted recovery times. The over-all character ofthe deformation processes becomes “viscous”rather than “elastic,” and the specimen then ei-ther extends uniformly or yields by means of anecking mechanism approximately in confor-mance with plasticity theory. Figure 4 gives aschematic impression of likely yielding andpost-yield behavior. A material that has yieldedis usually radically different in nature from whatit was prior to yielding. The difference may bemerely a reordered molecular state, but it alsomay be the presence of larger-scale discontinu-ities such as voids, crazes, or interphase cracks,all of which have various and different impli-cations for the service performance of end prod-ucts.

The yield stress, defined by some identifiablefeature on the force-deformation curve, dependson the deformation rate, as does the probabilitythat failure will occur before a neck is estab-lished. The higher the deformation rate, thehigher the yield stress and the greater the chancethat brittle or pseudobrittle failure will intervene.There are two principal reasons for the latter re-lationship. The temperature and the anisotropymay be such that the ductile-brittle transition istraversed as the deformation rate is increased, orthe neck may form but fail to stabilize becauseof the particular microstructure of the polymeror composition of the plastic. The molecular ar-chitecture, the molecular weight, and the degreeof branching all affect the propensity of the mol-ecules to align in the neck and the consequential

strength there. Similarly, the development ofmacroscopic discontinuities—e.g., microvoids,phase separations, and crazes—may be detri-mental, although not necessarily, because theligaments may be strengthened by favorably ori-ented molecules. Another factor is the local tem-perature, which will rise if the heat generated byvirtue of the inherent loss processes exceedswhat can be lost to the environment and whichmay reach a critical point at which the yieldstress has fallen to such a level that the neckcannot support the prevailing force. If the neckstabilizes satisfactorily it will travel along theparallel-sided section of the specimen either atan approximately constant force or with a pro-gressively increasing force if the molecular as-sembly is such that further orientation can occur.

The various features of time-dependent plas-ticity, necking rupture, inhomogeneous defor-mation, and work hardening affect the practicalexecution of tests in that a high extensibility im-poses particular requirements on the grips andthe deformation sensors, but, more importantly,these features affect the ways in which the de-rived data should be presented and interpreted(see Fig. 3). Thus, a yield stress identified bysome features on the force-deformation curveshould not be regarded as unambiguously defin-itive, because there is a zone in which the ma-terial is neither wholly viscoelastic nor whollyplastic and, additionally, the material in the neckis not necessarily a continuum. At a more mun-dane level, if a specimen has necked, the stressand the strain at failure are not readily calculablefrom the force and deformation data.


Stipulations inStandardized Tensile Testing

The Specimen-Machine System. The super-ficially simple nature of the tensile test concealsa demanding mechanical requirement. The spec-imen must be extended uniformly at any one ofseveral prescribed rates, which, when translatedinto a design specification, entails:

● Adequate power in a testing machine to en-sure that the stiffest specimens can be ex-tended at the designated rates

● Alignment of the line of action with the axisof symmetry of the specimen, to minimizethe variation of stress across the specimencross section

● Secure and balanced clamping of the speci-men to ensure that it neither slips in the gripsnor suffers extraneous forces

● High-quality specimens of the correct sizeand profile for the intended purpose and witha fine surface finish

These four design features are interconnected tosome degree and are all influenced by the vis-coelastic nature of the specimens.

The provision of adequate power poses no di-rect problem, but there may be secondary diffi-culties in that a powerful machine is likely to bemassive and to have inertias and frictions in theactuator and the likages that are troublesomewhen the active forces are small—i.e., at lowspecimen strain or when the specimen has a lowmodulus or a low strength. The issue is whethera single machine is suitable for testing all classesof plastics at all conceivable strain rates and overthe entire strain range to failure. If there is arange of machines at the investigator’s disposal,the choice should be governed by the characterof the specimen and should be such that thespecimen is matched to the machine. The spec-imen should never dominate the machine, be-cause in such an event the signals being ex-tracted from the test would reflect a complexcombination of machine and specimen charac-teristics. On the other hand, if the machine isexcessively dominant, it may impose inadver-tent and undesirable constraints on the speci-men.

Accurate alignment of the specimen in themachine is not easily achieved, because the ma-chine, the specimen, and the clamping of the oneto the other are all prone to asymmetries that cancause misalignment. There are various design

choices ranging from sufficient degrees of free-dom to allow a misaligned specimen to settleinto an aligned position as it begins to extend,at one extreme, to total constraint at the other.The former method relies on the specimen beingsufficiently stiff to be essentially unaffected bythe adjustment forces, which is unlikely to bethe case for a plastic material. Similarly, how-ever, the friction inherent in a fully constrainedsystem may constitute a large error in the mea-sured force.

Machine factors are largely outside the con-trol of a user, but, to varying degrees, specimen-preparation procedures, choice of grips, and op-erational checks, all of which affect and/orcontrol the axiality of the alignment, are discre-tionary. Specimens must be symmetrical abouttheir longitudinal axes. One machined from alarger item can be very accurately symmetrical.A directly molded specimen can be similarly ac-curate, but inappropriate molding conditions ora badly designed mold can produce distortedspecimens. Specimens molded from novel ornewly developed materials, for which the pro-cessing conditions may not have been opti-mized, are prone to such distortion, but force ofcircumstance may dictate the data generatedfrom such specimens must be used, despite theimperfections, as a basis for judgments crucialto the further progression of a research or de-velopment program. When this is the case, thejudgments should be suitably circumspect.

Even if the specimen is satisfactorily sym-metrical, it may be clamped unsymmetricallyunless special precautions are taken to positionit properly in the grips. Use of a hole in eachspecimen end and corresponding pins in thegrips is the simplest solution, and has provedvery satisfactory for tensile creep tests. Theholes also facilitate the machining operation bydefining the axis of symmetry. Ideally, the forceshould be transmitted to the specimen throughthe pins rather than through the faces of thegrips, but this imposes special requirements onthe specimen geometry to limit the chance ofshear failure at the pins (see the subsection onanisotropy in plastic specimens), and the lessideal conventional clamping, ostensibly actingacross the entire width of the specimen, is com-monly preferred.

Misalignment is relatively unimportant if thestrength of a ductile material is being measured,because limited plastic deformation suffices tocorrect the fault and the test progresses unim-paired thereafter. On the other hand, misalign-


ment is a source of error if the strength of abrittle material or the modulus of any type ofmaterial is being measured, because the mis-alignment causes the specimen to bend or un-bend, as the case may be, as it is extended in thetest. The stress is then nonuniform over the crosssection, and one face of the specimen bears astress higher than the average stress; the mea-sured strength is then likely to be an underesti-mate of the true strength. The error in the mod-ulus measurement may be positive or negative,depending on the positioning of the strain sen-sor, and can even be eliminated if the strain oneach face of the specimen is measured.

To some degree, there is a conflict of objec-tives in the design and operation of the grips.Secure clamping is desirable so that the speci-men does not slip relative to the grips, or entirelyout of the grips, during a test, but it simulta-neously prevents self-aligning movement andthereby preserves any initial misalignment. Onbalance, total constraint is the preferred option.In this case, hydraulic grips are probably themost satisfactory because they exert a pressurethat is uniform over the entire face and that re-mains constant as the specimen extends and cor-respondingly thins. Simple mechanical gripsmay have to be over-tightened initially, and con-sequently the specimen may be severely dis-torted. Such distortion can be reduced or elimi-nated by the use of reinforcing tabs on the endsof the specimens, but this is a tedious measurethat is not widely used for tests on plastics.

The specimen-machine system cannot be ex-pected to operate satisfactorily, however welldesigned it may be, unless the quality of thespecimen is commensurate with the expecta-tions. Methods of specimen production includedirect molding, die cutting, and machining witha router or milling cutter. Certain proceduresmust be followed with each method if the sym-metry required for axial stressing is to be at-tained: the cooling systems of molding cavitiesshould be so designed that any residual strainsare in equilibrium, specimens being machinedshould be supported so that they do not distortunder the machining forces, etc. The surface fin-ish is also important, because imperfections mayact as stress concentrators and cause the speci-men to fail prematurely. Unsuitable moldingconditions can produce surface textures and im-perfections ranging from the visually obvious tothe submicroscopic. Die cutters are fast in opera-tion but often produce specimens with poor edgefaces. In general, milling cutters and routers pro-

duce better surface finishes than die cutters, butthis depends on the cutting speed, which shouldbe high but not so high that generated heat soft-ens or melts the surface.

The various elements of the specimen-ma-chine interaction that affect the over-all opera-tion efficiency in the tensile testing of plasticsare summarized in Fig. 5.

Derivation of Excitation-Response Rela-tionships. Many investigators require only asingle datum from a tensile test and naturallytend to regard the derivation procedure as a sim-ple operation, which it may be when the testingmachine is set up with a single objective inmind. The over-all operation, however, is a morecomplex matter, the single datum being only asmall element in the total response of the spec-imen. The excitation-response relationship pro-vides numerical values of various mechanicalproperties—e.g., modulus and yield strength;also, in its entirety it gives an over-all impres-sion of “tensile characteristics” although, as waspointed out in the section on viscoelasticity, eachcurve provides only one section across a com-plex relationship between stress, strain, andstrain rate. The particular type of excitation usedin tensile testing was originally chosen for itsmechanical simplicity; it loosely approximates aramp function of strain versus time, which is notparticularly tractable analytically even for a lin-ear viscoelastic body and is even less tractablefor a nonlinear one. Thus, because of both prac-tical and theoretical limitations, it is unlikely thatthe observable response can ever be translatedinto fundamental quantities at the molecularlevel—for example, relaxation time spectra.

However, irrespective of the details, infor-mation can be obtained from a test only if thereare suitable sensors to convert the excitation andresponse into numerical or analog data. Thesesensors, which are described in Chapter 4, “Ten-sile Testing Equipment and Strain Sensors,”must have sensitivities and response times thatare appropriate for the intended purpose of thetest. The sensitivity should be such that the sen-sor discriminates at, say, 1% of full scale display,and the response time should be such that thefine structure of response is detected eventhough this generally entails the likelihood thatextraneous vibrations in the machine will be in-corporated as noise in the signal. The observablequantities are limited to force and deformation,and the former is actually measured as defor-mation in a transducer.

The force is always measured directly and ac-curately provided that the machine and the trans-


Fig. 5 Sources of experimental error in the specimen-machine system

ducer are adequately stiff. The deformation upto the yield point may be measured directly bymeans of an extensometer attached to the spec-imen, strain gages bonded to it, or an indepen-dent optical device operating without physicalcontact. These methods entail careful and some-times expensive subsidiary operations, and, fur-thermore, only the remote optical devices arepracticable beyond the yield point. Conse-quently, for certain classes of test, they may bedispensed with, the deformation then being mea-sured indirectly as actuator movement, with pos-sible corrections for extraneous effects causedby clamping and the specimen profile.

Strain gages and clip-on extensometers havetheir respective advantages and disadvantages.

The former are more troublesome to mount onthe specimen and measure the strain over onlya small zone, but, on the other hand, they can beso positioned as to measure strain along which-ever direction is of interest. Clip-on gages pro-vide an average strain over a larger span. Theyare less versatile in relation to strain axis but canmeasure transverse strains, and therefore thechange in volume during a test can be deter-mined by either type of sensor. Such informationprovides insight into pre-yield mechanisms.

In the case of modulus measurement, thestrains involved are small and the over-all de-formation is homogeneous; force translates eas-ily into stress with only small errors, and defor-mation can be measured over a defined gage


length. In principle, deformation measurementsshould be accurate in such situations, but clip-on extensometers may slip if the retaining springforce is small or may indent the specimen if thespring force is large, and bonded strain gagesmay affect the surface strain that they are in-tended to measure if the stiffness of the speci-men is low. Even so, with minor reservations,the modulus can be measured to a satisfactoryprecision. Coefficients of variation of about 0.03are commonplace, and coefficients of 0.02 areattainable.

In the case of strength tests, the over-all pre-cision of the measurements is lower—primarilybecause the calculation of stress is inevitably anapproximation, and secondarily because extra-neous defects in the specimen may promote fail-ure or induce brittleness. If the failure is brittle,the calculated strength can be based on the initialcross-sectional area, but this measured quantitymay be neither precise nor accurate because ofnonaxial loading, defects in the specimen, orvariable anisotropy. Coefficients of variation of0.10 for the interspecimen variability are com-monplace, and the values may be a substantialunderestimate of the true strength. If the failureis ductile, the estimate of area is likely to beerroneous, and if the deformation is also inho-mogeneous, as is common, the calculation offailure stress is further confounded. The nominalyield stress calculated on the basis of the initialcross section is likely to be precise, with a co-efficient of variation of about 0.03, but nothighly accurate because of the complexity of theassociated phenomena. In contrast, the nominalbreaking stress of a specimen that extends be-yond the yield point is little more than a nor-malized breaking force and is physically mean-ingless.

The deformation or strain at failure is simi-larly a dubious quantity. It is usually inferredfrom the movement of the actuator, becausestrain gages and extensometers normally are notused in tests that are intended to progress to fail-ure of the specimen. With brittle fracture, theerror in the inferred deformation is usually large,because extraneous deformations at and near thegrips constitute a relatively large proportion ofthe over-all movement of the actuator. Thissource of error is less influential when the failureis ductile, but the measured deformation usuallydoes not then translate directly into strain. Evenso, the commonly quoted extension to fractureis a useful quantity because it relates loosely tothe stability of the neck, the propensity of the

specimen for subsequent work hardening, andthe incidence of defects in the specimen. Thereare no quantitative rules for underpinning ofjudgments on these matters, and the investigatormust assess new results against a background ofwhichever accrued data are appropriate. Thesame is true, to varying degrees, of most of thedata relating to failure; they are accommodatedwithin a framework of comprehension that en-ables useful information to be extracted despiteuncertainties about the physical credentials ofthe experimental data. This framework of com-prehension is based on the collective experienceof many previous investigators, accumulationsof data, established correlations between test re-sults and service performance, perceptions ofquality, and other knowledge. It follows that thereliability of such rationalizations dependsheavily on the quality of the database.

The principle sources of error that are en-countered in this phase of the testing operationare summarized in Fig. 6. In combination, thevarious sources of error summarized in Fig. 3,5, and 6 often lead to coefficients of variation of0.10 or higher; at this level, the imprecision issuch that ten nominally identical specimensshould be tested for the derivation of a propertyvalue (most standard specifications stipulate aminimum of five).

Physical Interpretation of Data. The force-determination relationships of specimens areconverted by calculation and inference intostress-strain relationships for the constituent ma-terial. At low strains, this stress-strain relation-ship defines various moduli, and, provided thatappropriate procedural precautions are taken, theaccuracy of the modulus data can be high. If thespecimens are brittle, the precision of the mea-sured strength may also be high, but the accu-racy is likely to be low because of the deleteriouseffects of imperfections in the specimens. As thestrain increases—beyond, say, 0.02—the con-versions become progressively more approxi-mate, and therefore, even though the original testresults may have been precise, the final strengthdata are unlikely to be accurate. Even so, theapproximations and oversimplifications entailedin this stage are minor impediments in compar-ison with those involved in the train of inferenceleading from the over-all bulk values derivedfrom the test to the local values prevailing at thesite of fracture of failure. The theories of fracturemechanics and plasticity, taken in conjunctionwith a mathematical model of the local situation,provide some conversion rules, and it is possi-


Fig. 6 Faulty techniques and errors in the derivation of raw data and property values

ble, therefore, for an investigator to gain an in-sight into micromechanical behavior from ma-cromechanical data. Some procedures, however,are too cumbersome for routine use, and are alsoquestionable to the extent that some doubt per-sists about the over-all quality of the data gen-erated by them.

The features on a force-determination curvethat are taken as identifying important eventssuch as yielding or the onset of critical crackgrowth may have been chosen more for theirmacroscopic convenience than for their physicalvalidity, one practical consequence being the en-hancement of precision at the expense of accu-racy or realism. The diagram in Fig. 7 summa-

rizes the possible ambiguity over theidentification of the “yield point” in even thesimplest case—i.e., when the force-determina-tion curve passes through a maximum. The pos-sible error in the measured yield stress is likelyto be small because of the shape of the force-deflection curve as the yield point is approached;on the other hand, for the same reason, an esti-mate of the yield strain is likely to be imprecise.Where there is no maximum, the characterizingpoint may be less easily identified and will al-most certainly be associated with differentphysical manifestations; the derived yield stressmay be as prone to error as the derived yieldstrain. Similarly with brittle failure, the error in


Fig. 7 Simple force-deformation curve. The maximum force usually is taken as signifying the onset of yielding, but it merely marksthe point at which the specimen, as a structure, becomes less resistant to further deformation. Thus, the yield stress and the

yield strain are not unambiguously quantifiable.

the critical stress-field intensity factor may belarge because of the shape of the rising flank ofthe curve and because the selected feature maynot mark the critical point; for instance, the dom-inant peak may denote the over-all collapse ofthe specimen as a load-bearing structure ratherthan the point at which the growth of the crackbecomes critical.

If an investigator needs to clarify such pointsor to study the phenomena in greater detail, sup-plementary tests can be helpful. Photography ofthe specimen at specific moments or continuallythroughout the test enables correlations to be es-tablished between the features on the force-de-formation curve and the physical events in thespecimen. The simplest expedient is nothingmore than a supplementary tensile test at an ex-tension rate sufficiently low for the correlationsto be established through visual inspection of theextending specimen; such a test can even be in-

terrupted temporarily to permit a more intensescrutiny, although when an interrupted tensiletest is resumed the subsequent force-deforma-tion relationship will differ from that of an un-interrupted test because of viscoelastic relaxa-tion during the static period.

As the extension progresses beyond the yieldregion, the link between the observed force-de-formation relationship and the inferred stress-strain relationship becomes progressively moretenuous. The causes are the aforementioned ap-proximations entailed in the translations of forceinto stress and deformation into strain, devel-oping inhomogeneities in the specimen and mo-lecular and structural rearrangements in the ma-terial. In the post-yield region, the measurablequantities are the ultimate strength, commonlydefined as force divided by initial cross-sec-tional area; the elongation to fracture, derivedfrom the actuator movement; the shape of the


Table 2 Room-temperature tensile properties of selected engineering plastics

Tensile strength(a) Tensile modulus(a)

Thermoplastic MPa ksi Tensile elongation at break(a), % kPa psi

Styrene 46 6.7 2.2 320 46Styrene-acrylonitrile (SAN) 72 10.5 3.0 390 56Acrylonitrile-butadiene-styrene (ABS) 48 7 8.0 210 30Flame-retardant ABS 40 5.8 5.1 240 35Polypropylene (PP) 32 4.7 15.0 130 19Glass-coupled PP 32 4.7 15.0 130 19Polyethylene (PE) 30 4.3 9.0 100 15Acetal (AC) 61 8.8 60.0 280 41Polyester 55 8 200.0 280 40Flame-retardant polyester 61 8.9 60.0 280 40Nylon 6 81 11.8 200.0 280 40Flame-retardant Nylon 6 85 12.3 60.0 290 42Nylon 6/6 79 11.4 300.0 130 19Flame-retardant Nylon 6/6 67 9.7 35.0 130 19Nylon 6/12 61 8.8 150.0 200 29Polycarbonate (PC) 62 9 110.0 240 34.5Polysulfone (PSU) 70 10.2 75.0 250 36

(a) ASTM D 638 test method

curve immediately after necking; and the over-all slope of the curve. These are all character-izing quantities for the force-deformation curve,but it is important that they be regarded as noth-ing more. These quantities have to be trans-formed into characterizing quantities for thespecimen as an engineering entity, and the reli-ability of this operation depends on the validityof the mathematical model that is chosen to sim-ulate the mechanical behavior of the specimen.There must be a second transformation, intocharacterizing data for the material. This is themore difficult of the two, because the flow ge-ometry and processing conditions inherent in theproduction of specimens impose particular statesof molecular order, aggregation, etc., that governthe anisotropy and the levels of the property val-ues. Thus, even though data may be precise andaccurate, they may not be representative of thematerial properties as manifested in the majorityof end products, and therefore they may be ei-ther unsuitable for some purposes or misleading.

Thermoplastics differ in their sensitivities toflow geometry and processing conditions. Highmolecular weights, discrete second phases, andlarge crystal entities tend to worsen the aniso-tropy, and the consequential ranges of propertyvalues can be large—for example, a factor oftwo for modulus and a factor of three forstrength. However, such large ranges normallydo not appear as overt variabilities, because thespecimen-preparation routines have been stan-dardized and restricted in the interests of repro-ducibility and operational economy rather thanin the interests of practical relevance. Further-

more, the data so generated usually lie near theupper limit of attainable values and are thereforepotentially misleading.

The nebulous nature of the post-yield data andthe potential variation in all data do not detractunduly from the usefulness of the data, becausethere are many semiquantitative correlations be-tween the characterizing features and propertyvalues on the one hand and certain attributes andproperties of end products on the other. For ex-ample, even though elongation to fracture varieswith the shape of the specimen and cannot beequated accurately with strain, a high value isgenerally a desirable attribute that is indicativeof probable toughness in service items. Inter-sample differences often can be attributed tospecific factors such as molecular weight and theincidence of flaws, contaminants, defects, etc.,but results must always be judged in the contextof the particular evaluation program and setagainst an established pattern of data. The over-all success depends on the quality of the infra-structure and the database.

Utilization of Data from Tensile Tests

Materials Evaluation. Tensile tests are mul-tipurpose, the data derived from them beingcommonly used for purposes ranging from qual-ity control to research. Property tables, such asshown in Table 2, feature modulus, tensilestrength, and elongation to fracture derived fromtensile tests, but for only one standard defor-mation rate and one temperature (23 �C, or 73


�F), whereas an emerging body of opinion con-tends that data for other rates and temperaturesshould be provided by the data generators.

The current minimum evaluation scheme fallsfar short of what is now being called for for-mally, and even the latter calls for less than whatcould be derived from tensile tests, namely:

● The tensile modulus (tangent and secant) atvarious strains below the yield point

● The lateral contraction ratios● The yield stress and, in some instances, the

yield strain● The “load drop” after yielding● The slope of force versus deformation after

the yield point● The ultimate strength (based on initial cross-

sectional area)● The elongation to fracture.

As discussed in previous sections, these quan-tities are measurable to different levels of pre-cision, have variously dubious claims to thestatus of physical properties, and all relate to thespecimen rather than to the material from whichit has been made. It follows that they should beinterpreted with caution. Above all, an evalua-tor/investigator should bear two points in mindwhenever the results/data are being communi-cated to others:

● Data at one deformation rate and one tem-perature may not be adequately representa-tive of the tensile properties and fall short ofprospective recommendations on data gen-eration and presentation.

● Whatever the range of test conditions andwhatever the information extracted from thetest, the data relate to the specimen; the prop-erties of the sample and of the material mustbe inferred.

Despite these reservations, the types of datapresented in the seven-item list above serve avariety of purposes satisfactorily, although theyare also subject to misinterpretation and misuse.Misinterpretation by the investigator can resultfrom:

● Reliance on a single datum, and failure tomake use of the entire force-deformation re-lationship

● Failure to impose independent checks on in-ferences drawn from the data.

Misuse by the investigator and others can resultfrom:

● Disregard of the possible uniqueness of eachsample

● Insufficient regard for the potentially dele-terious effects of unfavorable flow geome-tries

● Disregard of the boundaries beyond whichparticular data are invalid or irrelevant.

Materials Comparisons and Selection. Theelementary table of properties on which manycomparisons are based features tensile modulus,tensile yield strength, ultimate tensile strength,and ultimate elongation. It is currently criticizedfor its various shortcomings, but it may owe itssimple form to the fact that, for some purposes,many data on each of many properties or pseu-doproperties may be confusing rather than en-lightening. On the other hand, judgments insome areas require special or selective data, andjudgments in other areas require data that extendfar beyond the confines of “single-point” data.Thus, the criteria by which a material is chosenin preference to others vary with circumstance,in accordance with often subjective rules. At-tempts have been made, and are being made, toautomate the operation, which entails a pseu-doquantification of the judgment processes, butthis latter step is generally a difficult one becausethe specification for the end product often asksfor a combination of property values or charac-teristics that are mutually exclusive.

One such dilemma arises regularly in the per-petual search for an optimum balance betweenmodulus and ductility, which relate, respec-tively, to stiffness and toughness in an end prod-uct. Practical experience has provided the roughworking rule, which also has a basis in theory,that the two properties are reciprocally related,and it follows, therefore, that an acceptable bal-ance at one temperature and deformation ratemay not be sustained under different conditions.Currently, the two requisite measurements oftenare made by independent techniques that usespecimens of different shapes, but the tensile testoffers the advantage of them being measured onone specimen in one operation.

Decisions about the data formats and logicpathways for materials comparison and selectionlie generally outside the scope and influence ofthe evaluators/investigators, although theseworkers can nevertheless exert an indirect influ-ence through the tactics and strategies that theyadopt for testing and evaluation. It is desirable,in the longer term, that any such steps should beformalized by modifications of existing standardtest methods, but this is always a protracted pro-cess because of the necessary consultation stage,


and as an interim measure limited but useful en-hancements of the data can be achieved by strictobservance of those strictures of the standardsthat relate to the qualifying information that de-scribes and specifies the test sample. This sug-gestion is not likely to recommend itself to peo-ple heavily engaged in testing, because thequalifying data can be more voluminous than theactual property data, although there is a growingrealization that the latter are virtually uselesswithout the former.

Design Data. The principle underlying de-sign calculations is that the behavior of a struc-ture under a system of forces can be deducedfrom a formula combining relevant materialproperties with an appropriate form factor. Theproperty values used should be appropriate forthe practical situation to which the design cal-culation relates—i.e., service temperature, pat-tern of loading, flow geometry, and other influ-ential factors should all be considered. Adistinction is drawn between “design data” andsingle-point property data, the implication beingthat the former have a higher status. However,this distinction is an artificial one because evena single datum, such as a modulus or a strengthderived from a tensile test, may be used in adesign calculation provided that adjustments aremade to allow for the differences between thelaboratory test conditions and the service/designsituation.

At least some of the adjustment factors canbe derived from other tensile tests. Thus, aniso-tropy and other consequences of specific pro-cessing conditions and flow geometries can beassessed by tests on appropriately chosen spec-imens and samples. On the other hand, adjust-ments that allow for long loading times, inter-mittent loading, or similar situations must bebased on independent creep, creep-rupture, andfatigue tests that are specifically structured toidentify and quantify the response of specimensto such loading patterns.

The degree of adjustment varies with thepolymer architecture, the composition of theplastic, and the operative factor. If the strengthof a standard injection-molded endgated tensilebar is taken as a reference point, an unfavorableflow geometry can reduce the strength to 50%of the reference value, and a long loading periodcan reduce it to 20% of the reference value, forexample. To use unadjusted data in a design forservice conditions radically different from thoseof the test would be to misuse them.

Summary

Tensile testing produces information aboutthe mechanical behavior of specimens subjectedto a predominantly tensile stress. The scope andquality of that information depend mainly on thedegree of practical finesse that is deployed. Themain factors that can affect the outcome of thetest program are:

● Sample and specimen selection● Machine design and function● Specimen preparation● Choice and mounting of sensors● Specimen-machine interaction● Translation of sensor signals into properties

data● Trains of inference.

However, the over-all test procedure and thestrategy depend on the purpose of the test; com-prehensive evaluations are expensive, and cur-tailed evaluations are relatively uninformative.

The over-all balance of the machine-specimensystem affects the precision, and to some degreethe accuracy, of the raw data. The choices ofsample, specimen geometry, specimen positionand alignment with respect to the sample, andnumber of specimens tested affect the precision,accuracy, and fitness-for-purpose of the deriveddata.

The raw data take the form of a relationshipbetween force and deformation, which can beconverted into approximations of a stress-strainrelationship and other properties. The raw dataand the transformed data relate only to the spe-cific conditions of the test.

The mean value of a measured quantity andthe standard deviation as derived from a smallsubset of nominally identical specimens are ap-proximations of the true mean and standard de-viation of a large set of nominally identical spec-imens.

A tensile test provides data relating to thespecimen tested. Tensile-property values de-rived from one type of specimen drawn from asample do not fully characterize the tensile prop-erties of the entire sample, and the tensile prop-erty values of one sample do not usually sufficeto characterize the tensile properties of the con-stituent material. Finally, tensile properties alonedo not characterize the mechanical behavior ofa specimen, sample, or material, although theyconstitute invaluable indicators.


ACKNOWLEDGMENT

This chapter was adapted from S. Turner, Ten-sile Testing of Plastics, Tensile Testing, 1st ed.,P. Han, Ed., ASM International, 1992, p 105–133

REFERENCE

1. S. Turner, Mechanical Testing, EngineeringPlastics, Vol 2, Engineered Materials Hand-book, ASM International, 1988, p 544–558

SELECTED REFERENCES

● A.-M.M. Baker and C.M.F. Barry, Effects ofComposition, Processing, and Structure on

Properties of Engineering Plastics, MaterialsSelection and Design, Vol 20, ASM Hand-book, ASM International, 1997, p 434–456

● J. Rietveld, Viscoelasticity, EngineeringPlastics, Vol 2, Engineered Materials Hand-book, ASM International, 1988, p 412–422

● M.L. Weaver and M.E. Stevenson, Introduc-tion to the Mechanical Behavior of Nonme-tallic Materials, Mechanical Testing andEvaluation, Vol 8, ASM Handbook, ASM In-ternational, 2000, p 13–25

● Mechanical Testing of Polymers and Ceram-ics, Mechanical Testing and Evaluation, Vol8, ASM Handbook, ASM International,2000, p 26–48

CHAPTER 9

Tensile Testing of Elastomers

ELASTOMERS comprise a subclass of thelarger group of materials, based on very largemolecules, called polymers. Various commonplastics such as polystyrene and polyethylene,and other materials such as household films andwraps, are polymer-base materials but are notcalled elastomers because of their limited capac-ity for reversible stretching. Elastomers mustdisplay the ability to stretch and recover that istypical of a rubber band.

Although the terms “elastomer” (from “elasticpolymer”) and “rubber” at one time had slightlydifferent meanings, they have become synony-mous for all practical purposes. These terms areused to designate the mixture of polymers andother ingredients that makeup a rubber formu-lation. Each unique formulation is called a“compound,” much as a mixture of metals isknown as an “alloy.”

Manufacturing of Elastomers (Ref 1)

The manufacture of rubbers or elastomers in-volves three major processing steps: mixing orcompounding, shaping, and vulcanizing orcrosslinking.

Compounding. The properties of elastomersare typically adjusted by compounding, that is,the incorporation of additives that improve prop-erties, aid processing, or reduce cost. A typicalformulation might include the elastomer base it-self; fillers for reinforcement, hardness control,or cost reduction; a plasticizer to improve low-temperature properties; antioxidants; and thecrosslinking system.

The actual mixing process depends on thetype of elastomer. A high-viscosity elastomersuch as natural rubber requires the use of a pow-erful mixer such as a Banbury mixer or rubber

mill, whereas a more liquid material can be pro-cessed using ordinary rotary mixers.

Shaping. The compounded elastomer can beshaped using molding, extrusion, or calendering.Compression molding, transfer molding, and in-jection molding can be used to produce formsranging from cable connectors and champagnestoppers to tires. Hoses are the major exampleof elastomers formed by extrusion. Calenderingis used to produce sheet rubber products such asconveyor belts, protective liners, and floor tiles.

Vulcanization is generally carried out afterthe elastomer is in its final shape, frequentlywhile it is in a mold, at temperatures between135 and 200 �C (275 and 390 �F). Vulcanizationis necessary to transform the raw elastomer intoa useful material by providing crosslinks be-tween the long chains of the polymer molecules.As described in the section “Factors InfluencingElastomer Properties” in this chapter, vulcani-zation has a profound effect on the properties ofelastomers.

Properties of Interest

A test of the tensile strength of an elastomercan yield readings of several different proper-ties. In some cases, these properties are totallyindependent of each other. In other cases, theyare interrelated. At times, some will be of moreinterest than others, depending on what is beinginvestigated or controlled. Typical properties ofsome of the more common elastomers are listedin Table 1.

Ultimate Tensile Strength. Naturally, thefirst property of interest determined in a tensiletest is the ultimate tensile strength. For elasto-mers, a class of materials that contain substantialnumbers of very different polymers, tensilestrength can range from as low as 3.5 MPa (500




Table 1 Properties of common elastomers

Mechanical properties Service temperature(continuous use)

Common nameSpecificgravity

ShoreDurometerhardness

Tensile strength,MPa (ksi)

Modulus, 100%,MPa (psi)

Elongation,%

min,�C (�F)

max,�C (�F)

Butadiene rubber 0.91 45A–80A 13.8–17.2 (2.0–2.5) 2.1–10.3 (300–1500) 450 �100 (�150) 95 (200)Natural rubber,

isoprene rubber0.92–1.037 30A–100A 17.2–31.7 (2.5–4.6) 3.3–5.9 (480–850) 300–800 �60 (�75) 70 (160)

Chloroprene rubber 1.23–1.25 30A–95A 3.4–24.1 (0.5–3.5) 0.7–20.7 (100–3000) 100–800 �50 (�60) 107 (225)Styrene-butadiene

rubber0.94 30A–90D 12.4–20.7 (1.8–3.0) 2.1–10.3 (300–1500) 450–500 �60 (�75) 120 (250)

Acrylonitrile-butadiene(nitrile) rubber

0.98 30A–100A 6.9–24.1 (1.0–3.5) 3.4 (490) 400–600 �50 (�60) 120 (250)

Isobutylene-isoprene (butyl)rubber

0.92 30A–100A �13.8 (�2.0) 0.3–3.4 (50–500) 300–800 �45 (�50) 150 (300)

Ethylene-propylene(-diene) rubber

0.86 30A–90A 3.4–24.1 (0.5–3.5) 0.7–20.7 (100–3000) 100–700 �55 (�70) 150 (300)

Silicone rubber 1.1–1.6 20A–90A 10.3 (1.5) . . . 100–800 �117 (�178) 260 (500)Fluoroelastomer 1.8–1.9 55A–95A 10.3–13.8 (1.5–2.0) 1.4–13.8 (200–2000) 150–250 �50 (�60) 260 (500)

Source: Ref 1

psi) to as high as 55.2 MPa (8.0 ksi); however,the great majority of common elastomers tendto fall in the range from 6.9 to 20.7 MPa (1.0 to3.0 ksi).

Ultimate Elongation. The second propertynoted is ultimate elongation, which is the prop-erty that defines elastomeric materials. Any ma-terial that can be reversibly elongated to twiceits unstressed length falls within the formalASTM definition of an elastomer. The upper endof the range for rubber compounds is about800%, and although the lower end is supposedto be 100% (a 100% increase of the unstressedreference dimension), some special compoundsthat fall slightly below 100% elongation still areaccepted as elastomers.

Modulus. The third characteristic that may beof interest is referred to in the rubber industry asthe modulus of the compound, but a specific des-ignation such as 100% modulus or 300% mod-ulus is used. That is due to the fact that the num-ber generated is not an engineering modulus inthe normal sense of the term, but rather is thestress required to obtain a given strain. There-fore, the “100% modulus,” also referred to asM-100, is simply the stress required to elongatethe rubber to twice its reference length.

Tension Set. A final characteristic that can bemeasured, but that is used less often than theother three, is called “tension set.” Often, whena piece of rubber is stretched to final rupture, therecovery in length of the two sections resultingfrom the break is less than complete. It is pos-sible to measure the total length of the original

reference dimension and calculate how muchlonger the total length of the two separate sec-tions is. This is expressed as a percentage. Someelastomers will exhibit almost total recovery,whereas others may display tension set as highas 10% or more. Tension set may also be mea-sured on specimens stretched to less than break-ing elongation.

Factors InfluencingElastomer Properties

Because elastomers are enormously differentin molecular structure from other materials suchas metals, and in fact are complex organic com-posites of numerous ingredients of very differ-ing characteristics, it is not surprising that theytend to exhibit a wide range of characteristics.Some of the important factors that influenceelastomer properties include:

● Structuring of the molecular matrix● Compounding● Specimen preparation● Specimen type● Vulcanization parameters● Temperature

Molecular Structure. Very often the pro-cessing of the mixture that makes up the elas-tomer results in some level of orientation of themolecules involved. This structuring of the mo-lecular matrix is commonly referred to as the

Tensile Testing of Elastomers / 157

“grain” of the rubber, and tensile properties usu-ally differ to a detectable degree with and acrossthe grain. This anisotropy may not be significantor even exist in actual elastomeric components,depending on both the specific compound andits processing history. When the grain directioncan be determined from knowledge of the pro-cessing, tensile testing is done parallel to thegrain.

Compounding. Over 20 different types ofpolymers can be used as bases for elastomericcompounds, and each type can have a significantnumber of contrasting subtypes within it. Prop-erties of different polymers can be markedly dif-ferent: for instance, urethanes seldom have ten-sile strengths below 20.7 MPa (3.0 ksi) whereassilicones rarely exceed 8.3 MPa (1.2 ksi). Nat-ural rubber is known for high elongation, 500 to800%, whereas fluoroelastomers typically haveelongation values ranging from 100 to 250%.

Literally hundreds of compounding ingredi-ents are available, including major classes suchas powders (carbon black, clays, silicas), plas-ticizers (petroleum-base, vegetable, synthetic),and curatives (reactive chemicals that change thegummy mixture into a firm, stable elastomer). Arubber formulation can contain from four or fiveingredients to 20 or more. The number, type, andlevel of ingredients can be used to change dra-matically the properties of the resulting com-pound, even if the polymer base remains exactlythe same.

Thus, the same base material—polychloro-prene (widely known as neoprene), for exam-ple—can be used by the rubber chemist to makecompounds as soft as a baby-bottle nipple or ashard as a hockey puck, with tensile strengthsranging from less than 6.9 MPa (1.0 ksi) to morethan 20.7 MPa (3.0 ksi) and elongation valuesfrom 150 to 600%. Considering the wide vari-eties of starting polymers and ingredientchoices, it is understandable that extremelybroad contrasts in properties are found amongelastomers.

Specimen Preparation. In addition, tensileproperties of elastomers are sensitive to factorsinvolved in specimen preparation. The majorityof the time, specimens are cut from moldedsheets of rubber. This is done using sharpeneddies of a specific dumbbell shape, and thesmoothness and sharpness of the die are impor-tant. Any nick or tiny tear along the edge of thecut specimen can act as a crack initiator and leadto premature failure of the specimen. Inappro-priately low levels of ultimate tensile strength

and elongation can be observed in such in-stances.

Similarly, lack of thoroughness in mixing ofthe ingredients can lead to poor dispersion, andcareless mixing can cause incorporation of smallforeign particles in the rubber. Either case willagain lead to lower and less precise test results.

Specimen Type. Use of specimens other thanthe standard type called for in the ASTM pro-cedures (see below) is sometimes necessary.Pieces from large moldings can be cut out andground to reasonable flatness and appropriatethickness, or strips of small tubing can be tested.Correlation between such specimens and stan-dard types is not always precise. Ground speci-mens do not have the smooth, molded surfacesof laboratory specimens, and therefore it is verylikely that cracks will propagate from surfaceimperfections in the early stages of strain, lead-ing to tensile rupture at lower elongations. Be-cause the stress-strain curve is terminated at alower strain, the associated tensile force is au-tomatically lower as well, and thus nonstandardspecimens seem to display lower values of elon-gation and tensile strength than lab specimens ofidentical material.

Vulcanization. Differences in test results be-tween lab specimens and specimens cut from ac-tual parts may also be caused partly by anothervariable—the level of vulcanization of the elas-tomer, also called its “state of cure.” It is difficultto determine whether or not the state of cure fora lab specimen is truly the same as that for aspecimen cut from a large article.

Vulcanization, which is the formation ofchemical crosslinks between the long chains ofthe polymer molecules, is usually accomplishedthrough exposure to some level of heat overtime. Although different thermal cycles mayyield rubber articles that appear and feel thesame, their properties can vary appreciably. Thevarious tensile properties will change in differ-ent degrees with increasing thermal treatment,so that there is seldom an optimum state of curein the sense of all of the compound propertiesreaching their ideal levels simultaneously. Forinstance, tensile strength may reach a maximumfollowing some particular curing cycle, whereaselongation at that point is well along a steeplydecreasing curve.

Thus, the optimum curing cycle for moldingof a given compound must be determinedthrough various means too diverse to be ex-plained here, and that curing cycle must then beused consistently for test specimens made of that


compound. Otherwise, differences in tensileproperties that do not truly relate to any real dif-ference in the formulation will very likely beobserved.

At times, a compound will be tested at its nor-mal cure level, and then a second set of samplesnot only will be molded with the standard curingcycle, but will then undergo an additional phaseof high-temperature exposure prior to thermaltesting. This thermal aging, usually done in anoven at a combination of temperature and timeappropriate to the particular type of elastomer,will result in definite changes in the polymer ma-trix.

Such changes are reflected in alteration of thetensile-test results. Reduction in elongation istypical, but ultimate tensile strength may in-crease or decrease. The degree of change of ten-sile properties resulting from thermal aging isfrequently used as an indicator of the com-pound’s ability to withstand aging and/or lowerthermal exposure over long time periods. Onerule of thumb is that the time required at a giventemperature for a compound’s tensile strength todrop to about half its original level representsthe functional life of the compound at that tem-perature.

A more subtle effect on standard test resultsis the effect of time delay between vulcanizationand testing of the elastomer. Various complexprocesses continue to take place in the polymericmatrix for some time after molding is com-pleted, which can affect tensile properties.Therefore, normal procedures call for a mini-mum delay of 8 h between molding and testing.However, in certain production situations forwhich such a delay is not tolerable, a correlationcould be developed between “warm testing” re-sults—i.e., from tests run within a short time ofthe sample being vulcanized—and those fromstandard procedures.

Test Temperature. Aside from the types ofspecimen-preparation effects mentioned above,there are also significant effects from differingtest conditions. The great bulk of testing is doneat room temperature and a standard rate of elon-gation, but occasionally special conditions willbe called for. For instance, knowledge of tensilestrength at some elevated temperature is some-times desired. Raising or lowering test tempera-ture usually has an inverse effect on tensilestrength that can be very substantial, changing itby a factor of two or more.

ASTM Standard D 412

The official standard for tensile testing ofelastomers is ASTM D 412 (Ref 2). It specifiestwo principal varieties of specimens: the morecommonly used dumbbell-type die cut from astandard test slab 150 by 150 by 20 mm (6 by 6by 0.8 in.), and actual molded rings of rubber.The second type was standardized for use by theO-ring industry. For both varieties, several pos-sible sizes are permitted, although, again, moretests are run on one of the dumbbell specimens(cut using the Die C shape described in ASTMD 412) than on all other types combined.Straight specimens are also permitted, but theiruse is discouraged because of a pronounced ten-dency to break at the grip points, which makesthe results less reliable. Unless otherwise spec-ified, the standard temperature for testing elas-tomer specimens is 23 � 2 �C (73.4 � 3.6 �F).

The power-driven equipment used for testingis described, including details such as the jawsused to grip the specimen, temperature-con-trolled test chambers when needed, and thecrosshead speed of 500 mm/min (20 in./min).The testing machine must be capable of mea-suring the applied force within 2%, and a cali-bration procedure is described. Various otherdetails, such as die-cutting procedures and de-scriptions of fixtures, are also provided.

The method for determining actual elongationcan be visual, mechanical, or optical, but is re-quired to be accurate within 10% increments. Inthe original visual technique, the machine op-erator simply held a scale behind or alongsidethe specimen as it was being stretched and notedthe progressive change in the distance betweentwo lines marked on the center length of the dog-bone shape. The degree of precision that couldbe attained using a hand-held ruler behind apiece of rubber being stretched at a rate of over75 mm/s (3 in./s) was always open to question,with 10% being an optimistic estimate.

More recent technology employs extensome-ters, which are comprised of pairs of very lightgrips that are clamped onto the specimen andwhose motion is then measured to determine ac-tual material elongation. The newest technologyinvolves optical methods, in which highly con-trasting marks on the specimen are tracked byscanning devices, with the material elongationagain being determined by the relative changesin the reference marks.

Normal procedure calls for three specimensto be tested from each compound, with the me-


dian figure being reported. Provision is alsomade for use of five specimens on some occa-sions, with the median again being used.

Techniques for calculating the tensile stress,tensile strength, and elongation are described forthe different types of test specimens. The com-mon practice of using the unstressed cross-sec-tional area for calculation of tensile strength isused for elastomers as it is for many other ma-terials. It is interesting to note that if the actualcross-sectional area at fracture is used to calcu-late true tensile strength of an elastomer, valuesthat are higher by orders of magnitude are ob-tained.

Test Method Precision. In recent years, at-tention has been given to estimating the preci-sion and reproducibility of the data generated inthis type of testing. Interlaboratory test compar-isons involving up to ten different facilities havebeen run, and the later versions of ASTM D 412contain the information gathered.

Variability of the data for any given com-pound is to some degree related to that particularformulation. When testing was performed onthree different compounds of very divergenttypes and property levels, the pooled value forrepeatability of tensile-strength determinationswithin labs was about 6%, whereas reproduci-bility between labs was much less precise, atabout 18%. Comparable figures for ultimateelongation were approximately 9% (intralab)and 14% (interlab).

Surprisingly, the same comparisons for M-100 (100% modulus) showed much less preci-sion, with intralab variation of almost 20% andinterlab variation of over 31%. The theory hadbeen held for some time that, because tensilestrength and ultimate elongation are failureproperties, and as such are profoundly affectedby details of specimen preparation, tensile mod-ulus figures would be more narrowly distributed.Because the data given above clearly do not sup-port such a theory, some other factor must be atwork. Possibly it is the lack of precision withwhich the 100% strain point is observed, but inany case it was important to determine the actualrelationship between the precision levels of thedifferent property measurements.

Significance andUse of Tensile-Testing Data

Tensile Strength. The meaning of tensilestrength of elastomers must not be confused with

the meaning of tensile strength of other materialssuch as metals. Whereas tensile strength of ametal may be validly and directly used for a va-riety of design purposes, this is not true for elas-tomers. As stated early in ASTM D 412, “Ten-sile properties may or may not be directly relatedto the end use performance of the product be-cause of the wide range of performance require-ments in actual use.” In fact, it is very seldom ifever that a given high level of tensile strengthof a compound can be used as evidence that thecompound is fit for some particular application.

It is important to note that the tensile prop-erties of elastomers are determined by a singleapplication of progressive strain to a previouslyunstressed specimen to the point of rupture,which results in a stress-strain curve of someparticular shape. The degree of nonlinearity andin fact complexity of that curve will vary sub-stantially from compound to compound.

In Fig. 1, tensile-test curves from five verydifferent compounds, covering a range of basepolymer types and hardnesses, are displayed.The contrasts in properties are clearly visible,such as the high elongation (�700%) of the softnatural rubber compound compared with themuch lower (about 275%) elongation of a softfluorosilicone compound. Tensile strengths aslow as 2.4 MPa (350 psi) and as high as 15.5MPa (2.25 ksi) are observed. Different shapes inthe curves can be seen, most noticeably in thepronounced curvature of the natural rubber com-pound.

Figure 2 demonstrates that, even within a sin-gle elastomer type, contrasting tensile-propertyresponses will exist. All four of the compoundstested were based on polychloroprene, coveringa reasonably broad range of hardnesses, 40 to 70Shore A Durometer. Contrasts are again seen,but more in elongation levels than in final tensilestrength. Two of the compounds are at the sameDurometer level, and still display a noticeabledifference between their respective stress-straincurves. This shows how the use of differing in-gredients in similar formulas can result in someproperties being the same or nearly the samewhereas others vary substantially.

It should be noted that successive strains topoints just short of rupture for any given com-pound will yield a series of progressively dif-ferent stress-strain curves; therefore, the tensile-strength rating of a compound would certainlychange depending on how it was flexed prior tofinal fracture.

Thus, the real meaning of rubber tensilestrength as determined using the official proce-


Fig. 2 Tensile-test curves for four polychloroprene compounds

Fig. 1 Tensile-test curves for five different elastomer compounds

dures is open to some question. However, someminimum level of tensile strength is often usedas a criterion of basic compound quality, be-cause the excessive use of inexpensive ingredi-ents to fill out a formulation and lower the costof the compound will dilute the polymer to thepoint that tensile strength decreases noticeably.For example, neoprene compounds are capableof achieving tensile strengths up to 20.7 MPa

(3.0 ksi) or higher when compounded usinggood technical practice.

In many cases, use of legitimate compoundingtechniques to optimize specific performancecharacteristics will result in neoprene com-pounds whose tensile strengths range from 10.3to 17.2 MPa (1.5 to 2.5 ksi). The fact that therange has a lower end well below 20.7 MPa (3.0ksi) does not in any way imply that the com-


pounds are deficient in some sense, but it is gen-erally accepted that a tensile strength of a neo-prene compound below 10.3 MPa (1.5 ksi) isevidence that the compound is low in polymercontent and therefore its ability to provide goodperformance over time is questionable.

Various specifications on elastomers, includ-ing government and industrial standards, call forminimum tensile strengths at different levels fordifferent types of polymers. Such minima rangefrom perhaps 4.8 MPa (700 psi) for silicones toover 21 MPa (3.0 ksi) for urethanes.

Because elastomeric elements are hardly everused in tension, tensile strength of compoundsis not a useful property measurement for pre-dicting performance. Also, because tensilestrength does not correlate with other importantcharacteristics such as stress relaxation and fa-tigue resistance, it is principally used as a qual-ity-control parameter relating to consistency.

Elongation is the unique defining property ofelastomers, and its meaning is somewhat moreapplicable to end uses. However, because ser-vice conditions normally do not require therubber to stretch to any significant fraction of itsultimate elongative capacity, ultimate elongationstill does not provide a precise indication ofserviceability.

It is commonly accepted that as the elongationof a compound declines, that material’s abilityto tolerate strain, including repetitive strain, gen-erally decreases. Thus, if two compounds basedon the same elastomer but having quite contrast-ing elongation values are compared in fatigueproperties when both are subjected to equalstrain levels, the formula with the higher elon-gation might well be expected to have the longerlife.

Just as with tensile strength, certain minimumlevels of ultimate elongation are often called outin specifications for elastomers. The particularelongation required will relate to the type ofpolymer being used and the stiffness of the com-pound. For example, a comparatively hard (80Durometer) fluoroelastomer might have a re-quirement of only 125% elongation, whereas asoft (30 Durometer) natural rubber might havea minimum required elongation of at least 400%.

Tensile modulus, better described as thestress required to achieve a defined strain, is ameasurement of a compound’s stiffness. Whenthe stress-strain curve of an elastomer is drawn,it can be seen that the tensile modulus is actuallya secant modulus—that is, a line drawn from thegraph’s origin straight to the point of the specific

strain. However, if an engineer really needs tounderstand what forces will be required to de-form the elastomer in a small region about thatstrain, he or she would be better off drawing aline tangent to the curve at the specific level ofstrain, and using the slope of that line to deter-mine the approximate ratio of stress to strain inthat region. This technique can be utilized in re-gard to actual elastomeric components as wellas lab specimens.

Tension set is used as a rough measurementof the compound’s tolerance of high strain. Thisproperty is not tested very often, but for someparticular applications such a test is considereduseful. It could also be used as a quality-controlmeasure or compound development tool, butmost of the types of changes it will detect in acompound will also show up in tests of tensilestrength, elongation, and other properties, and soits use remains infrequent.

Summary

Tensile properties of elastomers vary widely,depending on the particular formulation, andscatter both within and between laboratories isappreciable compared with scatter in tensile test-ing of metal alloys. ASTM D 412 is the definingspecification, and presents detailed instructionson specimen preparation, equipment, test con-ditions, etc. The meaning of the data is compar-atively limited in regard to the utility of anycompound for a specific application. Tensile-testdata are used effectively as quality-control pa-rameters and general development tools for therubber technologist.

ACKNOWLEDGMENT

This chapter was adapted from R.J. Del Vec-chio, Tensile Testing of Elastomers, Tensile Test-ing, P. Han, Ed., ASM International, 1992, p135–146

REFERENCES

1. R. Tuszynski, Elastomers, Engineered Ma-terials Handbook, Desk Edition, ASM Inter-national, 1995, p 282–286

2. ASTM D 412, “Standard Test Methods forVulcanized Rubber and Thermoplastic Elas-


tomers—Tension,” Annual Book of ASTMStandards, Vol 09.01, ASTM International

SELECTED REFERENCES

● A.K. Bhowmick and H.L. Stephens, Ed.,Handbook of Elastomers, 2nd ed., MarcelDekker, 2000

● A.K. Bhowmick, M.M. Hall, and H.A. Ben-arey, Ed., Rubber Products ManufacturingTechnology, Marcel Dekker, 1994

● A.N. Gent, Ed., Engineering with Rubber,Hanser Publishers, 1992

● W.F. Harrington, Elastomeric Adhesives,Engineered Materials Handbook, Vol 3, Ad-hesives and Sealants, ASM International,1990, p 143–150

● J.E. Mark, B. Erman, and F.R. Eirich, Ed.,Science and Technology of Rubber, 2nd ed.,Academic Press, 1994

● B.M. Walker and C.P. Rader, Ed., Handbookof Thermoplastic Elastomers, 2nd ed., VanNostrand Reinhold, 1988

CHAPTER 10

Tensile Testing of Ceramics andCeramic-Matrix Composites

THE ADVANCED CERAMIC MATERIALSdescribed in this chapter include both noncom-posite, or monolithic, ceramics (for example,oxides, carbides, nitrides, and borides) and ce-ramic-matrix composites (CMCs). Ceramic-ma-trix composites can be broadly classified intotwo types: discontinuously reinforced CMCs(for example, particulate- or whisker-reinforcedmaterials) and continuous fiber-reinforced ma-terials. These advanced ceramic materials ex-hibit superior mechanical properties, corrosion/oxidation resistance, or electrical, optical, and/or magnetic properties when compared totraditional ceramics (ceramics products that useclay or have a significant clay component in thebatch).

Rationale for Use of Ceramics

Advanced ceramics have been shown to havesignificant potential as structural materials. Thisis especially true for various specialized appli-cations—particularly those involving high usetemperatures. Ceramic materials have severalreal or potential advantages for such specializedapplications that make them very appealing andpossibly very competitive with existing struc-tural materials. These advantages include thefact that ceramics can be made from noncriticalraw materials (for example, aluminum, boron,carbon, nitrogen, oxygen, silica, and so on), incontrast to the scarce materials (nickel, cobalt,chromium, niobium, and so on) required forhigh-temperature superalloys. Another advan-tage is a potential for low cost, based in part onlow-cost raw materials. Other advantages arebased on the intrinsic properties characteristic ofceramics, including high stiffness (elastic mod-

ulus), high hardness, low thermal expansion,low density, chemical stability, thermal stability,and good electromagnetic properties (which areimportant for electromagnetic windows andelectronic materials). The combination of lowdensity, high stiffness, high strength and tough-ness (in composites), high use temperature, andchemical stability make some ceramics andCMCs most appealing as high-temperaturestructural materials. In such applications, thesematerials can be expected to have propertiessuch as stiffness-to-weight and strength-to-weight ratios that far surpass those achievablewith competitive materials such as superalloysor intermetallics (for example, NiAl).

Intrinsic Limitations of Ceramics

Unfortunately, some of the desirable intrinsicproperties of ceramics also lead to some highlyundesirable characteristics. The most significantof these derives from the ionic/covalent bondingtypical of most ceramics, which severely limitsplastic deformation. This limited plasticitygreatly reduces the energy absorbed during frac-ture. The fracture energy then approaches thevery low values of the cleavage energy. The lowfracture energy or fracture toughness further re-sults in several undesirable traits. Monolithic ce-ramics are typically flaw-sensitive, failing as aresult of defects that are undetectable by con-ventional NDE techniques. The same flaw sen-sitivity also gives rise to great variability instrength, as a result of variations in the flawpopulation, and thus very low values of designstrength. The low fracture energy also impliesthat monolithic ceramics will typically fail cat-astrophically—i.e., they will exhibit no stable




crack propagation below the critical stress-inten-sity value, KIc. The effect here is most severewith respect to the tensile properties of ceramics.Ceramics typically are much higher in compres-sive strength than in tensile strength, and do notfail in shear modes, because KIIc and KIIIc aremuch higher than KIc.

As a result of the severe flaw sensitivity, lackof plastic deformation and relatively high stiff-ness of ceramics, the tensile strengths of ceram-ics are typically measured indirectly, rather thanin direct tensile tests, as is common for otherengineering materials. The results of direct ten-sile tests are relatively clear, assuming that fail-ure occurs in appropriate locations and modes.In that case, the strength value derived from adirect uniaxial tensile test reflects the true tensilestrength of the material. For most ceramics,however, “tensile” strength is measured indi-rectly by one of two types of flexural or bendingtests. In these tests, the specimen is subjected toa complex stress state including tension, com-pression, shear, and significant stress gradients.In interpreting the results of these flexure tests,the maximum tensile stress present in the spec-imen at failure is usually reported as the “ten-sile” strength of the ceramic. Although such test-ing is straightforward, and calculation of thefailure stress simple, many complications are in-volved. This is particularly true with fiber-re-inforced CMCs, for which the results can bevery misleading in terms of the true tensilestrength of the material tested.

In addition to the widely used flexure tests(three-point, or modulus of rupture, and four-point), there are also other indirect tensile tests,each with its advantages and disadvantages, aswill be discussed. Most of these tests have beendeveloped with the intention of overcomingsome of the difficulties associated with directtensile tests or the complications inherent inflexure tests. In addition, especially in recentyears, some modifications of tensile-test fixturesand specimens have become available, whichmake direct tensile testing of some ceramicsmore tractable.

Overview of ImportantConsiderations for TensileTesting of Advanced Ceramics

There are four key considerations that mustbe taken into account when carrying out tensile

tests on advanced monolithic ceramics andCMCs. These include:

● Effects of flaw type and location on tensiletests

● Separation of flaw populations● Design strength and scale effects● Lifetime predictions and environmental ef-

fects

Effects of Flaw Type andLocation on Tensile Tests

One of the complications of tensile testing isthe physical location of the flaws that lead tofailure. Most ceramics (and other materials) con-tain both surface and volume flaws. Surfaceflaws typically result from finishing operationsand/or damage during service (for example,damage by foreign objects). Volume flaws typ-ically are intrinsic to the material microstructureor are processing defects (voids, inclusions,etc.). It is important that any “tensile” test char-acterize the effects of all of these defects (or atleast the most severe in terms of performance)on strength. Unfortunately, many of the indirecttensile tests, including flexure tests, produce se-vere stress gradients that may bias failure towardone type of flaw, most typically toward surfacedefects. Thus a flexure test on a ceramic materialmay detect primarily the flaws associated withthe machining required to produce the test spec-imen, rather than the volume flaws associatedwith the processing of the material. It is quiteimportant here, in trying to assess the “tensile”strength of a material, to be aware of these dif-ferent flaw types and locations, and their effectson the results of different test procedures.

Separation of Flaw Populations

Assessment of the importance of differenttypes and locations of flaws ideally is based onidentification of the actual flaw types using frac-tography (Ref 1, 2). This is generally a time-consuming and sometimes very difficult task, es-pecially if scanning electron microscopy isrequired. An alternative although less determin-istic approach is to use data-analysis proceduressuitable for separating multimodal distributionsof strength data into their constituent parts. Insome cases, this can be done effectively, al-though some uncertainties are always associatedwith this purely mathematical approach to sepa-rating the effects of different flaw populations ina material.

Tensile Testing of Ceramics and Ceramic-Matrix Composites / 165

Fractography, as performed on ceramics andsome ceramic composites, is typically done us-ing reflected light microscopy for the largerflaws, but more often requires scanning electronmicroscopy for resolution of the small flaws (10to 30 lm, or 0.39 to 1.2 mils) that are typical ofmonolithic ceramics. Recommended proceduresfor fractographic analysis are outlined in ASTMC 1322, “Standard Practice for Fractography andCharacterization of Fracture Origins in Ad-vanced Ceramics.”

Many data-analysis procedures for character-izing strength distributions can be found in theapplied mathematics and statistics literature.Commercial computer programs that performsome types of data analysis are widely available,although there are some pitfalls here as well.Different techniques for fitting the same distri-bution function to a set of data can produce dif-ferent results for both the function’s parametersand the errors in the parameters. These differ-ences can then lead to problems with the use ofthe strength data, such as with lifetime predic-tions, predictions of failure probabilities, or es-timates of scale effects on strength.

Design Strength and Scale Effects

For ceramics, determination of designstrength and prediction of scale effects are twoof the most important uses of strength data andthus two of the most important reasons for per-forming some type of tensile testing and the as-sociated data analysis. For the designer, one ofthe key requirements is the specification of de-sign strength as a function of service conditions(temperature and environment) and time. Pre-sumably, the designer can specify quite accu-rately these service conditions (stress, tempera-ture, and so on) as well as the desired lifetimeof the component. Thus, accurate and hopefullyconservative design-strength values can be in-corporated into design codes to help ensure thatcomponents will perform as desired.

One aspect of the design process that is moresignificant for ceramics than for other, less brit-tle materials is the effect of specimen or com-ponent size on strength. The qualitative effecthere is that larger specimens or components, onaverage, will have lower strengths and less scat-ter in strength values than small specimens. Thisresults from presence in the larger componentsof greater numbers of flaws and a greater prob-ability of the presence of more severe flaws. Ifdesign-strength data based on testing of rela-tively small specimens are to be used for pre-

dicting the performance of larger components, itis necessary to account for the scale effect onstrength. This is typically done through the useof Weibull strength distributions, which weredeveloped in the 1940s (Ref 3–5) and have sincebeen widely used for characterizing a variety ofmaterial and component properties. Note thatvariations in size between laboratory test speci-mens and actual components can be quite large,with very large effects on design strengths. Thedifference in stressed volume between a metaltensile-test specimen and a solid-fuel rocket-mo-tor casing, and the difference in gage length be-tween a laboratory tensile-test specimen of anoptical fiber and a transatlantic communicationcable, both may be on the order of 106. Becausetesting of actual components in these and othercases is clearly impractical, accurate and con-servative techniques for predicting such scale ef-fects on strength and other significant propertiesare essential.

Lifetime Predictions andEnvironmental Effects

An issue that is also related to the nature offlaw and strength distributions is the predictionof component lifetimes from initial strength dis-tributions and knowledge of service conditions.This relies even more heavily on accurateknowledge of the nature of the initial flaw dis-tribution, because the nature of subsequent de-layed failure depends strongly on the type andlocation of the initial flaw that leads to failure.Surface flaws can easily react with the environ-ment, leading to delayed failure in modes suchas stress-corrosion cracking. Volume flaws maybe stable and may not lead to delayed failureunder long-term loading. However, such flawsmay also react with the remainder of the mate-rial—for instance, with an inclusion that differschemically from the rest of the material—or mayreact with the environment diffusing into thebulk of the material. Such changes in volumeflaws may subsequently lead to failure of thematerial. It is clearly important to have detailedknowledge of the nature of the initial flaw popu-lation, the manner in which the flaws evolve dur-ing service, how they interact with the serviceenvironment and the applied loads, and whichof them control the service life of the material.

Tensile Testing Techniques

Tensile testing techniques, as applied to ce-ramics and CMCs, fall into four basic categories,


each of which has its own advantages, problems,and complications. These categories are:

● True direct uniaxial tensile tests at ambienttemperatures

● Indirect tensile tests (for example, three- andfour-point flexural tests)

● Other tests where failure is presumed to re-sult from tensile stresses

● High-temperature tensile tests

Applicable standards for some of these tests in-clude:

● ASTM C 1273, “Standard Test Method forTensile Strength of Monolithic AdvancedCeramics at Ambient Temperatures”

● ASTM C 1275, “Standard Test Method forMonotonic Tensile Behavior of ContinuousFiber-Reinforced Advanced Ceramics withSolid Rectangular Cross-Section Test Spec-imens at Ambient Temperature”

● ASTM C 1161, “Standard Test Method ofFlexural Strength of Advanced Ceramics atAmbient Temperature”

● ASTM C 1211, “Standard Test Method forFlexural Strength of Advanced Ceramics atElevated Temperatures”

Direct Tensile Tests

In terms of analysis of test results, the moststraightforward tests are the direct tensile testscovered in ASTM C 1273 and C 1275. In thesetests, the gage length of the specimen is nomi-nally in a state of uniaxial tensile stress. Con-sequently, both the volume and surface of thegage length are subject to the same simple stressstate, which is assumed to be constant through-out the gage volume; that is, it is normally as-sumed that both the surface and the volume ofthe gage section of the test specimen are sub-jected to a state of uniform uniaxial tension.

Test Specimen Geometries. There are twobasic types of tensile specimen geometries. Onetype of specimen that can be prepared usingreadily available machine tools is the flat or“dog-bone” specimen shown in Fig. 1(a) andFig. 2. Such specimens can be prepared readilyusing milling machines with carbide tooling forsome materials and diamond tooling for others.It is also feasible, in some cases, to mold spec-imens directly into the desired shape (for ex-ample, by injection molding), which permitstesting of materials with as-fabricated surfaces.These may be preferable to the machined sur-faces typical of specimens prepared by grinding,

where actual components are not surface fin-ished.

The other type of specimen normally used isa cylindrical specimen (Fig. 1b and 2), typicallywith a reduced gage section and ends machinedto suit some gripping arrangement. Such speci-mens are typically prepared (in the case of met-als and polymers) by machining to the desiredshape on a template-controlled profile lathe. Inthe case of ceramics and CMCs, the analogousprocedure uses diamond grinding in the samemode to produce a cylindrical specimen of thedesired shape. Again, it is possible, and some-times desirable, to produce such specimens di-rectly by a molding process, or by machining inthe green state prior to firing, when an as-firedsurface finish is appropriate for testing.

Gripping and Load Transfer in Direct Ten-sile Tests. Gripping of both flat and cylindricalspecimens can be accomplished in various man-ners, depending on the particular material beingtested. Success in using various gripping tech-niques will depend on the relative values of ten-sile strength, shear strength, hardness, and so on,of the material being tested. The dog-bone spec-imens can be gripped in conventional mechani-cal grips (Fig. 3a) or hydraulic or pneumaticgrips (Fig. 3b), using friction alone to transmitthe load to the specimen. Conventional mechan-ical wedge-action grips (Fig. 3c) can also beused successfully in some cases, although thehigh and uncontrollable clamping pressure mayresult in crushing or shear failure in the grip sec-tion for some materials. Pneumatic or hydraulicgrips are generally preferable, because the grip-ping pressure can be controlled precisely, andbecause deformation of the specimen does notproduce any change in the gripping pressure.

The success in load transfer through frictiondepends on achieving a reasonable friction co-efficient between the specimen and the gripfaces without causing the specimen to fail incompression. As an illustration of this, considergripping a cylindrical aluminum oxide specimenwith a 6.4 mm (0.25 in.) diameter in the gagesection and a 12.7 mm (0.5 in.) diameter smoothshank. If the tensile strength is assumed to beapproximately 350 MPa (50 ksi), a tensile testwill require a load of 10,900 N (2450 lbf ) tofracture the specimen. With a coefficient of fric-tion of 0.13 between the specimen and the gripfaces, the lateral clamping force would have tobe 83,980 N, or 18,880 lbf. This clamping forceis easily achievable with commercially availablehydraulic grips.


Fig. 1 Specimen configurations for direct tensile testing of advanced ceramics. (a) Flat plate or “dog-bone” direct tensile specimenwith large ends for gripping and reduced gage section. (b) Cylindrical tensile specimen with straight ends for collet grips and

reduced gage section. Tapers and radii at corners of both specimens may be critical, as is machining finish. See Fig. 2 for examples ofmore complex specimen geometries.

The compressive stress on the shank of thespecimen is based on the area of the specimensurface inserted into the grip. For this example,if the specimen is inserted into the grip to a depthof 25 mm (1 in.), the compressive stress is about83 MPa (12 ksi), or well within the capability ofthe material.

It is very important to verify that the specimengeometry of the material being tested is appro-priate for that material’s strength. A combinationof reducing the cross-sectional area of the gagesection and increasing the length of insertioninto the grips may be necessary to allow fric-tional gripping on some ceramic materials. Ifthese specimen geometry enhancements are not

possible because of limitations in the material,the use of frictional gripping may not be appro-priate.

The problems of frictional gripping are gen-erally severe for most ceramics, which typicallyhave high hardnesses and low friction coeffi-cients against other hard materials. This grippingtechnique is also particularly difficult with somefiber-reinforced CMCs, which combine hightensile strength, high hardness, and low shearstrength. The problems are doubly complicatedfor the CMCs because the low shear strengthlimits the load transfer, as well as providing thepossibility of shear failure in the grip section athigh gripping pressures. There is a relatively


Fig. 2 Tensile specimens used for monolithic ceramics (each is in correct proportion to the others); all dimensions in mm. Upperrow for round specimens; lower row for flat specimens. Source: G.D. Quinn, NIST

simple technique for minimizing these problemswith CMCs, namely the use of large ratios ofgrip area to gage section cross-sectional area;however, this technique introduces other prob-lems as well, primarily in terms of the effects ofmachining damage on the relatively large sur-face area of the gage section versus the intrinsicflaws in the relatively small volume of a highlyreduced gage section.

Gripping of cylindrical specimens can also bedone by means of friction, using wedge-type orcollet grips, but this involves the same problemsas those detailed above, plus the additional dif-ficulties of requiring precise machining of spec-imen ends to mate with collets, and strict re-quirements in regard to specimen straightness.In the case of tapered specimen ends, which areused to increase load transfer, or in the case ofthe buttonhead specimen discussed below, ma-chining can be even more critical.

Load transfer for flat plate or dog-bone spec-imens can also be effected by means of pins in-serted through the grip section of the specimen(Fig. 3d), or such pinned ends can be combinedwith frictional gripping. Load transfer throughpins requires, again, a balance between the loadthat can be transmitted through the bearing area,rbAb, and the load required to produce tensilefailure, r • Agage. In most cases, this requires theuse of multiple pins for load transfer. The use ofmultiple pins requires great precision both in thetest apparatus and in machining of the specimen(precise hole location and diameter to ensureequal distribution of loading).

One approach sometimes taken to overcomesome of these difficulties in specimen grippingand load transfer is bonding of the ceramic orcomposite specimen to grips of a more forgivingmaterial. A low-shear-strength, high-tensile-strength, unidirectional CMC specimen can be


Fig. 3 Gripping systems for direct tensile tests. (a) Mechanical grips with screw clamping. (b) Pneumatic (or hydraulic) grips withforce applied through lever arrangement and pneumatic pressure, ensuring constant clamping force. (c) Wedge-action, self-

tightening mechanical grips; clamping pressure is roughly proportional to the tensile load in the specimen. (d) Pinned grips with loadtransfer by means of pins through grip and specimen. (e) Specimen configuration (buttonhead) for self-aligning commercial grip systems(all dimensions in millimeters; ground surface finish, 2 to 3 lm).

bonded to metallic grips that are a good matchfor the CMC in terms of Young’s modulus (tominimize stress concentration). Provided thatsufficient gripping area is available for loadtransfer through the adhesive, there is then littledifficulty in applying load by conventionalmeans to the now-metallic gripping area of thespecimen (note that conventional epoxy adhe-sives have shear strengths that exceed those ofsome continuous-fiber CMCs). This procedure,which works very well, unfortunately is not use-ful for the more important high-temperature ten-sile tests, as will be discussed later.

The last technique to be discussed here is onethat has come into use in commercial test fix-tures for tensile testing of ceramics, based on asystem developed by personnel at Oak RidgeNational Laboratory (Ref 6–8). These test fix-tures utilize complex systems for eliminatingsome of the major sources of errors in tensiletesting of ceramics with low strains to failure.Both use what is referred to as a “buttonhead”specimen (see Fig. 3e), to which the load istransferred through enlarged regions on thespecimen ends. Although these specimens haveoperational advantages, such as minimal re-


Fig. 4 Errors in tensile testing derived from load applied off-center and at angle to centerline of gage section; errors for two effectscombined are roughly additive.

quirements for specimen alignment in the testfixtures, there are severe restrictions on theamount of load that can be transmitted throughthe buttonhead. The result has been that this typeof gripping/load transfer has been very success-ful with materials of moderate tensile strength,and with long-term, low-stress tests such ascreep and stress-rupture tests, but tends to failfor materials with high tensile strengths. Theo-retical analysis of the requirements and limita-tions of this test are extremely difficult, as a re-sult of the complex contact-stress problem at thebuttonhead/grip interface. Thus, little guidance,aside from practical experience, can be utilizedfor determining when this type of test will besuccessful, and when the large investment in thegrips themselves is appropriate.

Experimental Problems and Errors. Onemajor source of error that is inherent in directtensile tests has been eliminated to a major ex-tent by the introduction of self-aligning grip sys-tems. This error is associated with eccentricities

in load application (see Fig. 4), which lead to acombined state of tension and bending in the testspecimen. The large magnitudes of the parasiticbending stresses, even for small degrees of mis-alignment, result in significant errors in the cal-culated tensile stress (based on a state of puretension). However, the use of various types ofself-aligning grips, together with appropriatespecimen geometries and careful specimen prep-aration, have largely eliminated these errors (Ref8). The current self-aligning grips, availablefrom the two major testing-machine manufac-turers, use compact hydraulic systems to accom-plish the same effect previously achievedthrough large and costly gas-bearing tensile-testfixtures. The only difficulties with these gripsystems are noted above, involving specimenpreparation, testing of high-strength materials,and the relatively high cost of the grips.

To some extent, the testing problems for cer-tain continuous-fiber CMCs have been allevi-ated. This is particularly true for those CMCs


that have relatively high strain to failure (for ce-ramics) and relatively low modulus. In manycases, the simple gripping techniques used formetals and polymers will suffice for such CMCs,and few special precautions need to be taken,aside from ensuring sufficient gripping area rela-tive to the cross-sectional area of the gage sec-tion (see the discussion above on gripping). Theauthor has, without great difficulty, performedtensile tests on conventional dog-bone speci-mens of CMCs, using ordinary pneumatic gripswith smooth grip faces made of materialsslightly less hard than the CMC itself (for ex-ample, aluminum, copper, or silver) and appro-priately sized grip and gage areas. Such resultssuggest that direct tensile testing of advancedCMCs may be far less difficult than testing ofmonolithic ceramics, and may not require thespecialized test fixtures and specimens neededfor testing of monolithic ceramics.

Summary of Direct Tensile Tests. The ad-vantages and limitations of direct tensile testingof ceramics and ceramic composites are veryclear. The advantages are:

● Direct measurement of the tensile strength ina known and simple stress state

● Stressing of the entire gage-section volumeand surface, sampling both surface and vol-ume flaws in the material being tested

The disadvantages and limitations include:

● The need for large specimens (because of theneed for large gripping areas)

● Complex and precise specimen machiningrequirements for collet grips and especiallyfor buttonhead specimens

● The need for relatively expensive (andbulky) test fixtures and grips

Indirect Tensile Tests

Indirect tensile tests are quite similar, typi-cally involving some complex specimen geom-etry that induces a state of uniaxial tension in aportion of a specimen loaded in a fairly simplemanner. Two examples are the theta specimentest, which is a variant of the diametral com-pression test discussed below, and the trussedbeam test, which is similar to the theta specimentest but involves loading in flexure rather thanin compression (see Fig. 5a and b). Both of thesetests provide the capability for performing whatis very close to a direct tensile test, but withoutthe need for expensive tensile-test fixtures. Both

are also amenable to use at high temperatures,without the great complications that accompanythe use of conventional tensile-testing fixturesand procedures. The primary disadvantages ofthe theta and trussed beam specimens are thedifficulty of machining them, especially with re-spect to the cutouts, and the problem of flawsintroduced through such machining. In somecases, direct molding of specimens in these con-figurations may be possible, eliminating the ma-chining problem altogether, as well as providingsintering, rather than machined, external sur-faces—a possible advantage if actual compo-nents are prepared to net shape with no externalsurface finishing.

It should be noted that a great many othersimilar tests are possible, limited only by the cre-ativity and ability of the experimenter to fabri-cate the test specimen and analyze the stressstate produced. One such example is shown inFig. 5(c), where a thin layer of material to betested is used as the skin on the tensile side of asandwich beam. The only requirement for de-termining the tensile stress at failure is knowl-edge of the elastic properties of the skin and corematerials, and assurance that failure occurs firstin the face sheet loaded in tension. The facesheet on the compressive side can be of virtuallyany high-strength, high-modulus material withknown properties.

Flexure and Other “Tensile” Tests. Thereare a great variety of other tests used to char-acterize the tensile strengths of ceramics andceramic composites, where the gage section ofthe specimen is not in a state of pure, uniaxialtension, but rather in some combined stressstate. Such tests include the three-point andfour-point flexure tests commonly used for ce-ramics, diametral compression tests, C-ringtests, combined-stress-state tests on cylindricalspecimens, and various biaxial tests such asball-on-ring and ring-on-ring tests. When thesetests are used to measure tensile strength, it ispresumed that there is no effect of combinedstresses on failure and that the specimen failsfrom the largest tensile stress present—that is,the principal tensile stress. Historically, this hasbeen a very good assumption for many mono-lithic ceramics with low toughness, identicalelastic behavior in tension and compression,and essentially linear behavior to failure. How-ever, in the case of many of the tougher ceramiccomposites, these assumptions are frequentlyincorrect. Note, however, that the biaxial tests,


Fig. 5 Specimens for indirect tensile tests. (a) Theta specimen, which provides uniaxial tension for central member when specimenis loaded in diametral compression. (b) Trussed beam specimen, which provides approximately uniaxial tension in lower

portion when beam is loaded in four-point bending. (c) Sandwich beam specimen, which loads lower skin in approximately purebending with four-point flexural loading of beam.

in some cases, have been used to evaluate thepossible dependence of strength on stress statein ceramics.

For many toughening mechanisms present inCMCs, such as phase-transformation toughen-ing, crack bridging, and fiber pullout, the behav-ior may be stress-state-dependent. In addition,for many such materials, the behavior in tensionand the behavior in compression are not equal.The worst case of the latter occurs with somecontinuous ceramic-fiber composites, in whichthe compressive failure stress, as a result of fiberbuckling, may be substantially lower than the

tensile strength. The continuous-fiber CMCsalso exhibit, for unidirectional materials, ex-tremely low values of shear strength. This posesthe additional problem of possible shear failurein tests where significant shear stresses are pres-ent, such as the three-point flexure test and theC-ring test. At present, the only solution to thisproblem is the careful monitoring of tests to de-termine the actual mode of failure (for example,compression, shear, or tension). This has beenaccomplished by means of video and telemi-croscopic recording of specimen failure pro-cesses.


Fig. 6 Other “tensile” tests. (a) Four-point flexure test, which loads lower part of central portion of beam in tension, with a stressgradient in the vertical direction. (b) C-ring test, which provides flexural loading of a segment of a tubular component. (c)

Diametral compression, or “Brazilian,” test, which produces equal tensile and compressive stresses at the center of the specimen loadedin diametral compression. (d) Cylindrical specimen internally and externally pressurized and mechanically loaded in tension andcompression, which can produce any desired combination of tensile and compressive stresses in the hoop and axial directions.

In addition to the difficulties encountered intesting of fiber CMCs, there is the problem ofthe effects of shear stresses and combined stressstates on phenomena such as the martensiticphase transformation used to toughen zirconiaand zirconia-containing composites. This phasetransformation is primarily a shear transforma-tion, with substantial volume increase as well.Thus, a stress state with a high dilatational stressand high shear stresses may result in a high de-gree of phase transformation, with consequenteffects on the measured “tensile” stress, in con-trast to the behavior that might be seen in a direct

tensile test with lower dilatational stress and noshear.

Of these various “tensile” tests, by far themost commonly used are the three- and four-point flexure tests. A detailed analysis of the er-rors that occur in the four-point flexure test (thepreferred test; see Fig. 6a and 7) has been per-formed (Ref 9, 10), and standards have been de-veloped (Ref 11) for the use of these tests formonolithic ceramics, together with recommen-dations for both test-specimen geometry and testfixturing. These will not be repeated here, butexperience has shown that use of the recom-


Fig. 7 Flexure strength standard test methods; all dimensions in mm. Source: S. Lampman, ASM International

mended specimen geometry and test fixturesprovides very good characterization of the ten-sile strengths of monolithics in which strengthis controlled by surface flaws. It is also feasible,as with some of the other tests noted, to conductsuch tests at high temperature, using appropriatematerials for the test fixtures, although manyother complications then arise, as will be dis-cussed subsequently. One difficulty with theseflexure tests occurs in the presence of stress gra-dients, with maximum stress occurring at thesurface, leading to preferential failure from sur-face flaws. Another is the presence of shearstresses in regions of the specimen, which is aproblem with some materials relatively weak inshear. A third is the presence of compressivestresses as well, which constitute an additionalproblem for materials, as noted, that fail in com-pression first. A last problem, which may behandled analytically if sufficient information isavailable about material response, is the problemof different stress-strain behavior in tension andcompression. In the case of the flexure testing offiber CMCs, matrix microcracking at a lowstress level leads to an effective decrease inmodulus in a portion of the tensile region of thespecimen. This in turn leads to a shift in the

neutral axis away from the tensile surface and aredistribution of stresses. In this particular case,use of the conventional beam-bending equationsfor maximum tensile stress may produce signifi-cant errors in the calculated stresses (Ref 12).

Another test, which has been used to a lesserextent, is the C-ring test (Fig. 6b), which is es-pecially convenient for testing of materials pro-duced in the form of thin-wall tubes, such asceramic heat exchangers. In such cases, a sliceis taken from the tube, with a portion removedas shown in Fig. 6(b), and is tested in either ten-sion or compression. Testing in tension producesbending and tensile stresses in the interior of thespecimen, as shown, whereas compressive test-ing similarly stresses the exterior of the speci-men in tension. Relatively simple test fixturingsuffices to load the specimen in either case, andextension to high temperatures is also relativelysimple. This test has been analyzed theoretically(Ref 13–15), and the results presumably are ac-curate except for the same limitations of theother flexure tests. These include, as above, theproblems of stress gradients, failure from sur-face flaws, and the presence of significant shearstresses. Other tests that have been used for mea-suring the “tensile” strengths of ceramics in-


clude various biaxial flexure tests (ball-on-ring,ring-on-ring) (Ref 16–18) that are equivalent tothe three- and four-point flexure tests. Thesetests are convenient for materials that normallyare available in the appropriate geometries—forexample, thin plates or disks. These tests arevery similar in most ways to the other flexuretests, except that the stress state is roughly equi-biaxial, thus stressing flaws of all orientations,rather than only those oriented in the worst di-rection relative to the maximum tensile stress,as in a conventional flexure test.

Another type of test that is not widely used inthe technical ceramics community, but more soin the geological area and with building mate-rials, is the diametral compression, or “Brazil-ian,” test, which uses a disk or short cylinderloaded in compression across its diameter (seeFig. 6c). In this test, the maximum tensilestresses are developed at the center of the spec-imen, where equal tensile and compressivestresses are present as shown. In a successful testof this type, the specimen fails by splitting ver-tically at its center. This test is particularly usefulfor materials such as cores from rock sampling,test cylinders of concrete, and similar materials.Typically, exact interpretation of the results interms of the tensile strength of the material isdifficult, because of the difficulty of determiningthe exact source of failure (from the machinedsurfaces or from the bulk of the material). Thereis also the problem, for some materials, of thepresence of an equal compressive stress at thecenter of the specimen, which leads to the de-velopment of very large shear stresses at thissite. Materials with relatively low shearstrengths may thus fail first in shear, rather thanin tension.

Combined-Stress-State Tests Using Mul-tiaxial Cylindrical Specimens. The last type of“tensile” test to be discussed in this section isthe combined-stress-state test employing mul-tiaxial cylindrical specimens. These specimens(Fig. 6d), which can be loaded by various com-binations of internal pressure, external pressure,axial tension or compression, and (when de-sired) torsion, are well suited to production ofalmost any desired stress state in the cylinderwall. As such, they have been used to addressthe problem of the failure criteria for brittle ma-terials through systematic variation of the rela-tive proportions and signs of the principalstresses. However, the major difficulties that areinherent in both preparation and use of suchspecimens have precluded their wide applica-

tion. These tests require large amounts of ma-terial, extensive machining of specimens—typ-ically with a profile lathe and diamond toolpostgrinders for ceramics—and elaborate test fixtur-ing. The extensive machining that is required, inaddition to greatly increasing the cost of testing,introduces the potential for failure to be initiatedby machining-induced flaws, rather than by vol-ume flaws produced during processing. Suchtests also have severe limitations with regard tohigh-temperature testing, as a consequence ofthe required loading arrangements.

Summary of the Advantages and Limita-tions of Flexure and Other “Tensile” Tests.The flexural and other indirect “tensile” tests de-scribed above provide several advantages overdirect tensile tests for ceramic and ceramic com-posite specimens. These include:

● Simple specimen geometries, minimal spec-imen machining and simple test fixturing(flexure, biaxial, diametral compression, andC-ring tests)

● Use of as-fabricated materials (C-ring test)● Capability for testing various stress states

(flexure for tension, shear; biaxial flexureand cylindrical multiaxial specimens forcombined stress states)

The particular disadvantages of these indirecttensile tests include:

● Extensive specimen preparation for multiax-ial cylindrical specimens

● Stress gradients and combined stress statesthat may affect failure modes, especially inceramic-matrix composites, or in other ma-terials that are relatively weak in shear orexhibit different stress-strain behaviors intension and compression

High-Temperature Tensile Tests

High-temperature tensile tests pose severalspecific difficulties and involve several specificrequirements for both specimens and test fix-tures. The particular difficulties depend on thetemperature range involved and the atmospherein which the test is to be conducted. Dependingon the test particulars, suitable types of tests mayinclude direct tensile tests, four-point flexuretests, and C-ring tests, the last two of which aresubject to complications resulting from the stressstates involved. Successful use has also beenmade of the theta specimen test, although thistest has not become particularly popular becauseof the specimen machining involved.


Hot Grip Tests. The complications that in-volve the test temperature range are associatedwith the fixture materials available for transferof load to the specimen (assuming that these fix-tures are in the hot zone of the furnace). Thealternative, which poses its own set of problems,is the use of large specimens and grips outsidethe test furnace. Typical ferrous materials forgrips, pullrods, pushrods, loading anvils, and soon, are limited to approximately 1000 to 1200�C (1830 to 2190 �F) because of severe strengthloss at higher temperatures, as well as chemicalproblems (reaction, oxidation, etc.). The fixturematerials suitable for higher-temperature use in-clude various superalloys, which can be used attemperatures up to about 1200 �C (2190 �F), butmay be expensive, difficult to machine, and sub-ject to oxidation. Other, even more exotic ma-terials include molybdenum, TZM (Mo-0.5Ti-0.08Zr-0.03C) thoria-dispersed nickel, andcarbon or carbon-carbon composites. Some ofthese materials—for example, molybdenum andcarbon/carbon—can be used at extremely hightemperatures (up to about 2000 �C, or 3630 �F),but only in vacuum or inert atmospheres. Ce-ramics have also been used for high-temperaturefixtures and grips, and may generally be used ina range of atmospheres. Unfortunately, some ofthe applications (for example, pullrods) are lim-ited by the relatively low tensile strengths (200to 400 MPa, or 30 to 60 ksi) of most of theavailable ceramics. The use of ceramics is alsolimited to temperatures of about 1500 to 1700�C (2730 to 3090 �F) by the ceramics availablein suitable forms for test fixtures and grips, suchas aluminum oxide, silicon carbide, and siliconnitride. Finally, the use of ceramic grips and fix-turing is severely limited by the difficulties andvery high cost associated with machining testfixtures from suitable ceramic materials, whichare hard and brittle.

Direct Tensile Tests. Assuming the desire towork with hot grips, or hot fixtures, to avoidsome of the difficulties associated with coldgrips, the selection of tests is very limited. Directtensile tests can be performed only up to thetemperature limitations of the grip materials, as-suming that high-temperature-material analogsof one of the grip types have been acquired. Thistranslates into a temperature limitation of about1000 �C (1830 �F) for typical commercial me-tallic grips available at reasonable cost. Testingat somewhat higher temperatures can be per-formed, albeit at great cost, with ceramic ana-logs of these grips, and testing at temperatures

of approximately 2000 �C (3630 �F) is possiblewith molybdenum grips in an inert atmosphere.

Four-Point Flexure Tests. Relatively appeal-ing alternatives to direct tensile tests include C-ring and four-point flexure tests. Such tests canbe readily performed with ceramic fixtures andpushrods, permitting testing in a variety of at-mospheres at temperatures up to perhaps 1700�C (3090 �F). The MTL four-point test fixture,depicted in Fig. 6(a) and 7, can be duplicated ina variety of ceramics (for example, alumina forthe top and bottom anvil supports and pushrods,and sapphire for the loading-anvil rollers) atrelatively low cost. Four-point flexure tests ofthis type can be used quite successfully,provided that some of the complications notedpreviously (for example, differing stress-strainbehavior in compression and tension, and sig-nificant effects of shear stresses) do not occur.Another complication that may also arise inhigh-temperature flexure testing of ceramics isthe presence of large strains and deflections re-sulting from increases in ductility or other flowprocesses that are operative at high tempera-tures. Such large strains may produce significanterrors in stress values calculated by the use ofbeam-bending theories based on infinitesimalstrains. As mentioned earlier in this chapter, el-evated temperature flexure tests have been stan-dardized in ASTM C 1211.

The C-ring test can also be readily used athigh temperatures—particularly if the ring isloaded in compression by means of appropriateceramic anvils and pushrods (Ref 13, 15). Load-ing in tension with ceramic attachments andpullrods is also possible, because of the rela-tively low loads required to cause failure via thebending stresses in this test. This particular testhas, in fact, been used quite successfully in thedevelopment of ceramics and CMCs for high-temperature heat exchangers, which are fabri-cated from relatively thin-wall tubes. Attemptsto characterize the tensile strengths of such tubesby testing of machined specimens would lead tovery misleading results, because in this casespecimen strength would be controlled primarilyby machining damage, whereas the strength ofthe actual components, with their as-fabricatedsurfaces, is controlled by intrinsic defects.

Cold Grip Tests. In the event that it is feasibleto work with either cooled grips (inside the fur-nace), or cold grips (outside the furnace), thetests that are most suitable are quite different. Inthis case, as shown in Fig. 8, any number of griparrangements can be used, in conjunction with


Fig. 8 Schematic illustration of cold grip tensile-testing ar-rangement with long specimen gripped outside of com-

pact test furnace; commercial systems in this configuration areavailable for testing in air at temperatures up to about 1700 �C(3100 �F).

Fig. 9 Schematic diagram illustrating three-probe linear vari-able differential transformer (LVDT) measurement of

curvature of central portion of four-point flexure system. Theusual assumption of pure bending between inner load points im-plies that the strain is proportional to the curvature of the beam.The curvature is proportional to the difference in displacementsas sensed directly by the LVDT (or other displacement trans-ducer).

furnace, because seals must be provided aroundthe test specimen where it passes into the fur-nace. This is not a major problem with hot griptests, where very effective seals (for example,high-temperature bellows) can be provided atthe points where the pullrods enter the furnace.

Strain Measurement. Historically, measure-ment of strains has been one of the major prob-lems with high-temperature tensile testing of ce-ramics by either direct tensile tests or any of theindirect methods. One of the factors contributingto the difficulty of measuring strains in a high-temperature ceramic tensile specimen is the rela-tively low strain-to-failure in ceramics andCMCs. Frequently the maximum tensile strainachieved in monolithics is less than 0.1%, andeven in the tough-fiber CMCs, the maximumstrain may be only 2 to 3%. Measurement ofsuch small strains is in general a very challeng-ing task, and more so inside a high-temperaturetest furnace. In the past, the typical techniquesused for “strain” measurements have involvedmeasurement of the over-all travel of the loadtrain outside the test furnace or measurement ofthe elongation or deformation of the specimenby means of displacement transducers coupledto the specimen by refractory rods (Ref 19) (seeFig. 9). Also available were dual-channel opticaltracking systems capable of tracking two marksor flags on the specimen, thus providing a non-contact and highly precise method of measuring

a long specimen, with the gage section containedwithin the hot zone of the test furnace. Severalcommercial vendors now offer systems thatcombine small test furnaces, some with hotzones as short as 2.5 to 5 cm (1 to 2 in.), withself-aligning grips (in some cases, water cooled)for the buttonhead specimens. Similarly, a smallfurnace around the gage section of a long, rec-tangular CMC tensile specimen gripped on alu-minum tabs epoxy bonded to the end of the spec-imen has also been used.

This technique is not without its disadvan-tages. It requires large amounts of material fortest specimens, which are typically more than 15cm (5.9 in.) in length, and rather expensive testfixtures and furnaces (assuming that commercialequipment is used). Another unavoidable prob-lem with this cold grip technique, and with theuse of cooled grips in the furnace hot zone, isthat of thermal gradients in the specimen, andincreased requirements for power in the test fur-nace, because of the transfer of heat out of thefurnace through the specimen and into the grips.The cold grip technique also poses some prob-lems with control of the atmosphere inside the


the strain in the gage section of the specimen.However, such optical trackers were extremelyexpensive, rivaling the cost of a complete testmachine, and thus were not used extensively.

The situation with regard to strain measure-ment has improved dramatically in recent years,and several reasonably priced commercial sys-tems for strain measurement inside high-tem-perature furnaces are now available (Ref 7, 20).One such system employs suitable extensions(silica, sapphire, silicon carbide, and so on) tothe clip gages commonly used to measure strainin ambient-temperature tensile tests. These high-temperature clip gages permit accurate measure-ment of strain in a chosen portion of the testspecimen, requiring only two ports in the sideof the furnace for the extension rods. These di-rect-contact extensometers are available at mod-erate cost and are capable of measuring displace-ments and strains with extremely high accuracy.

Also available are various laser-based strain-measurement devices that can be used easily athigh temperatures, requiring only a window inthe side of the furnace through which the spec-imen can be sighted. These laser systems workin several distinct ways. One commercial systemtracks two flags, as did the optical tracking sys-tems previously mentioned, but offers laser tech-nology and modern electronics at a cost com-parable to that of the high-temperature clipgages cited above. The laser systems have theadvantage that the radiation from the hot furnaceinterior does not interfere with the measurement,as it would with an optical tracking system fol-lowing two marks on a specimen inside a hotfurnace. The normal effect at temperaturesabove approximately 1000 �C (1830 �F) is thateverything in the furnace looks the same (colordifferences are only a function of emissivity).With the use of lasers, the sensors can beequipped with narrow band filters that pass onlythe laser wavelength. Additionally, the laser sig-nal can be modulated, with the sensors detectingonly the modulated, ac signal, and not the dcbackground from the thermal radiation insidethe furnace (helium-neon lasers are roughly thesame color as the inside of a furnace at 800 to900 �C, or 1470 to 1650 �F).

Another system that is amenable to use witha great variety of test specimens, even with ex-tremely small-diameter (10 lm, or 0.4 mil) ce-ramic fibers, uses the speckle pattern generatedby the reflection of a coherent laser beam fromthe surface of the specimen. As the specimendeforms, the speckle pattern deforms in a similarmanner, and measurement of the changes in the

speckle pattern permit accurate measurement ofthe strain in any direction on the surface of thespecimen. These speckle interferometric straingages are also reasonable in cost, easy to use,and require, again, only a sight port or smallopening in the test furnace.

With the two types of laser strain gages andthe high-temperature clip gage, there is now lit-tle difficulty in making direct and precise mea-surements of strain in high-temperature tensilespecimens. With some of the other, indirect ten-sile tests, there are also relatively convenientways of measuring strain. For example, for thefour-point flexure test, a convenient and very ac-curate way of measuring strain in the centralportion of the test specimen is the use of a three-probe displacement transducer system (see Fig.9), which effectively measures the curvature ofthe central portion of the beam (which is nor-mally assumed to be in pure bending where thestrain is proportional to the curvature). Accord-ingly, strain measurement is not now consideredto be a significant problem in tensile testing ofceramics.

Atmosphere Control. Control of the atmo-sphere in high-temperature tensile tests of ce-ramics and CMCs continues to be a significantproblem. The situation for test temperatures be-low 1000 to 1200 �C (1830 to 2190 �F) is trac-table, in that hot grips, or cooled grips inside thefurnace, can be used, with effective seals on thepullrods and little restriction of atmosphere im-posed by the grip materials (for example, oxi-dation of metal grips). However, for tempera-tures above 1200 �C (2190 �F), the problems aresevere. The higher-temperature metallic grips(molybdenum) must be used only in inert or re-ducing conditions, and grips fabricated fromgraphite or carbon-carbon composites must beused under inert conditions (vacuum, argon, andso on). If the application requires testing in ox-idizing conditions, as would be the case for gasturbine or hypersonic airframe materials, suchtests may give very misleading results. High-temperature tests under oxidizing conditions (forexample, in air or in simulated gas turbine com-bustion products) require either ceramic fixtures,which limit the type of test that can be performedand the loads that can be achieved in tensiletests, or the use of cold grips outside the furnace.Use of cold grips requires extremely large spec-imens (for experimental materials) and is com-plicated by the problem of sealing the furnaceto provide effective atmosphere control. An ap-pealing alternative, in many cases, is the use offour-point flexure tests with ceramic fixtures and


pushrods, in which it is possible to test to quitehigh temperatures (about 1700 �C, or 3090 �F)in a variety of atmospheres ranging from reduc-ing, through inert, to oxidizing conditions. Ma-terials such as aluminum oxide and sapphire (forload points) will survive atmospheres such asforming gas, argon, nitrogen, vacuum, air, andoxygen, with little effect on the test fixturing,even at very high temperatures.

Recommendations for High-TemperatureTensile Testing of Ceramics. There are someclear choices for high-temperature tensile testingof ceramics, provided that appropriate testequipment and fixturing are affordable. Theclear choice for most monolithic ceramics is theuse of precisely aligned hydraulic grips or self-aligning grip systems, with straight-shank orbuttonhead specimens, a small furnace system,and direct-contact extensometers or optical mea-surement of the specimen strain. Note that thebuttonhead specimens are limited in load levels,as are pinned dog-bone specimens, and may bemore suitable for lower stress level tests such ascreep and fatigue tests.

Some modification of the gripping arrange-ment and grips (and some additional expense)may be necessary for testing of high-strengthmonolithics or CMCs. If test temperatures arealways below 1000 �C (1830 �F), it is possibleto use a much less expensive system, employinghot grips and a large furnace.

For situations where neither true tensile-test-ing system is practical, the most reasonable al-ternative is the use of the four-point flexure testwith displacement transducer measurement ofthe strain in the central (gage) portion of thespecimen. Use of some of the other tests de-scribed should be limited to the special casesapplications for which they are appropriate (forexample, use of the C-ring test for tube segmentsand the diametral compression tests for cylin-drical specimens). The biaxial tests (ball-on-ringand ring-on-ring) may have some limited use-fulness in situations where actual loading is bi-axial and effects of combined stresses are ex-pected to be significant.

Summary

The recommended procedures for ambient-and elevated-temperature tensile testing of ad-vanced monolithic and CMCs are summarizedin the following paragraphs. In addition, a briefdiscussion of data analysis for interpretation ofuniaxial strength is also included.

Recommended Procedures forAmbient-Temperature TensileTesting of Ceramics and CMCs

Monolithic Ceramics and Low-ToughnessCMCs.

1. Direct tensile tests using the currentlyavailable commercial self-aligning grip systemsand strain-measurement techniques. These testsrequire relatively expensive gripping systems,strain-measurement techniques, and large spec-imens with complex machining requirements.Specimen geometry has been established forthese gripping systems to minimize failure in thegripping or transition regions.

2. Where material availability or economicconstraints prevent such testing, four-point flex-ure testing following the ASTM standard C1161; strain measurement preferably is done bymeasuring the displacement in the central por-tion of the test specimen at three points.

High-Toughness CMCs and other Ceram-ics with High Strains to Failure.

1. Direct tensile tests using either the self-aligning grip systems or simpler grip systemstypically used for metals or polymers; strainmeasurement by conventional techniques (clipgages) may be adequate. With the use of themore conventional gripping systems, it may bepossible to work with flat plate specimens,which may be easier to fabricate.

2. Four-point flexure tests in which the detailsof the fracture process are observed carefully, toensure that failure does in fact occur first in atensile mode, and with corrections for neutralaxis shifts resulting from differing tensile andcompressive stress-strain behavior.

Specialized Materials (Such as Heat-Ex-changer Tubes).

1. Direct tensile tests if sufficiently large spec-imens can be obtained from components to min-imize the effects of surface machining damage.

2. Otherwise, C-ring or other similar tests,with the same careful observation and correc-tions recommended for the four-point bend test.

Recommended Procedures forHigh-Temperature TensileTesting of Ceramics and CMCs

Monolithic Ceramics and Low-ToughnessCMCs.

1. Direct tensile tests using the currentlyavailable commercial self-aligning grip systems,with grips outside a compact furnace, and com-


mercial high-temperature strain-measurementtechniques. These tests require relatively expen-sive gripping systems, strain-measurement tech-niques, furnace systems, and large specimenswith complex machining requirements.

2. Where availability of material or financiallimitations make the procedure above impracti-cal, the alternative is four-point flexure with ap-propriate measurement of strain, as above.

High-Toughness CMCs and other Ceram-ics with High Strains to Failure.

1. Direct tensile tests using either self-align-ing cold grip systems or simpler hot grip systemstypically used for metals or polymers, with op-tical or capacitance (clip) gage measurement ofstrain; again, conventional grips may make itpossible to work with the more easily fabricatedflat plate or dog-bone specimen.

2. Four-point flexure tests in which the detailsof the fracture process are observed carefully(this is far more difficult in the confines of ahigh-temperature furnace), to ensure that failuredoes in fact occur first in a tensile mode, andwith corrections for neutral axis shifts resultingfrom differing tensile and compressive stress-strain behavior.

Specialized Materials (Such as Heat-Ex-changer Tubes).

1. Direct tensile tests if sufficiently large spec-imens can be obtained from components to min-imize the effects of surface machining damage.

2. Otherwise, C-ring or other similar tests,with the same careful observation and correc-tions recommended for the four-point bend test.These observations and corrections are difficultto make in a high-temperature test, although C-ring and other indirect tensile tests are otherwiserelatively easy to translate to high-temperaturetests.

Recommended Procedures forData Analysis

The recommended procedures for data anal-ysis and reporting are partly covered in theASTM standards for flexure and tensile testing.Another important source of information fordata analysis is ASTM C 1239, “Standard Prac-tice for Reporting Uniaxial Strength Data andEstimating Distribution Parameters for Ad-vanced Ceramics.” The failure strength of ad-vanced ceramics is treated as a continuous ran-dom variable using this practice. Typically, anumber of test specimens with well-defined ge-ometries are failed under isothermal loading

conditions. The load at which each specimenfails is recorded. The resulting failure stressesare used to obtain parameter estimates associ-ated with the underlying population distribution.ASTM C 1239 is restricted to the assumptionthat the distribution underlying the failurestrengths is the two-parameter Weibull distri-bution with size scaling (see also the discussionof “Design Strength and Scale Effects” earlierin this chapter). Furthermore, C 1239 is re-stricted to test specimens that are primarily sub-jected to uniaxial tensile stresses. This practicealso outlines methods to correct for bias errorsin the estimated Weibull parameters and to cal-culate confidence bounds on those estimatesfrom data sets where all failures originate froma single flaw population (that is, a single failuremode). The methods outlined in C 1239 are notapplicable to samples that fail due to multipleindependent flaw populations (for example,competing failure modes).

Measurements of the strength at failure aretaken for one of two reasons: either for a com-parison of the relative quality of two materials,or the prediction of the probability of failure (or,alternatively, the fracture strength) for a struc-ture of interest. ASTM C 1239 estimates the dis-tribution parameters that are needed for either.In addition, this practice encourages the integra-tion of mechanical property data and fracto-graphic analysis (refer to ASTM C 1322 men-tioned earlier in this chapter).

ACKNOWLEDGMENT

This chapter was adapted from D. Lewis III,Tensile Testing of Ceramics and Ceramic-MatrixComposites, Tensile Testing, P. Han, Ed., ASMInternational, 1992, p 147–181

REFERENCES

1. J.R. Varner, Descriptive Fractography, Ce-ramics and Glasses, Vol 4, Engineered Ma-terials Handbook, ASM International,1991, p 635–644.

2. R.W. Rice, Ceramic Fracture Features, Ob-servations, Mechanisms and Uses, Fractog-raphy of Ceramic and Metal Failures, STP827, ASTM, 1984, p 5–103.

3. S.B. Batdorf, Fundamentals of the Statisti-cal Theory of Failure, Fracture Mechanicsof Ceramics, Vol 3, R.C. Bradt, D.P.H. Has-


selman, A.G. Evans, and F.F. Lange, Ed.,Plenum Press, 1978, p 1–29.

4. D. Lewis, Curve-Fitting Techniques andCeramics, Am. Ceram. Soc. Bull., Vol 57(No. 4), 1978, p 434–437.

5. W. Weibull, A Statistical Distribution Func-tion of Wide Applicability, J. Appl. Mech.,Vol 18, 1951, p 293–297.

6. D.F. Baxter, Jr., Tensile Testing at ExtremeTemperatures, Adv. Mater. Proc., Vol 139(No. 2), 1991, p 22–32.

7. J.C. Bittence, New Emphasis on Automa-tion, Adv. Mater. Proc., Vol 136 (No. 5),1989, p 45–56.

8. K.C. Liu and C.R. Brinkman, Tensile CyclicFatigue of Structural Ceramics, Proc. 23rdAutomotive Technology Development Con-tractor’s Coordination Meeting, Vol 165,Society of Automotive Engineers, Oct1985, p 279–284.

9. F.I. Baratta and W.T. Matthews, “Errors As-sociated with Flexure Testing of Brittle Ma-terials,” U.S. Army Materials TechnologyLaboratory Report MTL TR 87-35, 1987.

10. F.I. Baratta, Requirements for Flexure Test-ing of Brittle Materials, Methods for As-sessing the Structural Reliability of BrittleMaterials, STP 844, ASTM, 1984, p 194–222.

11. G. Quinn, “Flexural Strength of High Per-formance Ceramics at Ambient Tempera-ture,” Department of the Army, MIL-STD-1942(MR), 1984.

12. D.B. Marshall and A.G. Evans, FailureMechanisms in Ceramic Fiber-Ceramic Ma-trix Composites, J. Am. Ceram. Soc., Vol 68(No. 5), 1985, p 225–231.

13. M.K. Ferber, V.J. Tennery, S. Waters, andJ.C. Ogle, Fracture Strength Characteriza-tion of Tubular Ceramics Using a Simple C-Ring Geometry, J. Mater. Sci., Vol 8, 1986,p 2628–2632.

14. O.M. Jadaan, D.L. Shelleman, J.C. Conway,Jr., J.J. Mecholsky, and R.E. Tressler, Pre-diction of the Strength of Ceramic TubularComponents: Part I—Analysis, J. Test.Eval., Vol 19 (No. 3), 1991, p 181–191.

15. D.L. Shelleman, O.M. Jadaan, J.C. Conway,Jr., and J.J. Mecholsky, Jr., Prediction of theStrength of Ceramic Tubular Components:Part II—Experimental Verification, J. Test.Eval., Vol 19 (No. 3), 1991, p 192–201.

16. G. de With and H.H.H. Wagemens, Ball-on-Ring Test Revisited, J. Am. Ceram. Soc.,Vol 72 (No. 8), 1989, p 1538–1541.

17. H. Fessler and D.C. Fricker, A TheoreticalAnalysis of the Ring-on-Ring Loading DiskTest, J. Am. Ceram. Soc., Vol 67 (No. 9),1984, p 582–588.

18. D.K. Shetty, A.R. Rosenfield, and W.H.Duckworth, Statistical Analysis of Size andStress State Effects on the Strength of AnAlumina Ceramic, Methods for Assessingthe Structural Reliability of Brittle Materi-als, STP 844, ASTM, 1984, p 57–80.

19. S.A. Bortz and T.B. Wade, Analysis and Re-view of Mechanical Testing Procedure forBrittle Materials, Structural Ceramics andTesting of Brittle Materials, S.J. Acquavivaand S.A. Bortz, Ed., Gordon and Breach,1968, p 47–139.

20. Laser Gages Creep of Ceramics, Adv. Mater.Proc., Vol 138 (No. 5), 1990, p 75–76.

SELECTED REFERENCES

● J.E. Amaral and C.N. Pollock, Machine De-sign Requirements for Uniaxial Testing ofCeramics Materials, Mechanical Testing ofEngineering Ceramics at High Tempera-tures, B.F. Dyson, R.D. Lohr, and R. Mor-rell, Ed., 1989, p 51–68.

● H.C. Cao, E. Bischoff, O. Sbaizero, M.Ruhle, A.G. Evans, D.B. Marshall, and J.Brennan, Effects of Interfaces on the Me-chanical Properties of Fiber-Reinforced Brit-tle Materials, J. Am. Ceram. Soc., Vol 73(No. 6), 1990, p 1691–1699.

● H. Cao and M.D. Thouless, Tensile Tests ofCeramic-Matrix Composites: Theory andExperiment, J. Am. Ceram. Soc., Vol 73 (No.7), 1990, p 2091–2094.

● D.F. Carroll, S.M. Wiederhorn, and D.E.Roberts, Technique for Tensile Testing Ce-ramics, J. Am. Ceram. Soc., Vol 72 (No. 9),1989, p 1610–1614.

● M.G. Jenkins, M.K. Ferber, R.L. Martin,V.T. Jenkins, and V.J. Tennery, “Study andAnalysis of the Stress State in a Ceramic,Button-Head, Tensile Specimen,” ORNL/TM-11767, Oak Ridge National LaboratoryTechnical Memorandum, Sept 1991.

● C.G. Larsen, Ceramics Tensile Grip, STP1080, J.M. Kennedy, H.H. Moeller, andW.W. Johnson, Ed., ASTM, 1990, p 235–246.

● J.J. Mecholsky, Evaluation of MechanicalProperty Testing Methods for Ceramic Ma-trix Composites, Am. Ceram. Soc. Bull., Vol65 (No. 2), 1986, p 315–322.


● L.C. Meija, High Temperature Tensile Test-ing of Advanced Ceramics, Ceramic Engi-neering and Science Proceedings, Vol 10(No. 7–8), 1989, p 668–681.

● L.G. Mosiman, T.L. Wallenfelt, and C.G.Larsen, Tension/Compression Grips forMonolithic Ceramics and Ceramic MatrixComposites, Ceramic Engineering andScience Proceedings, Vol 12 (No. 7–8),1991.

● T. Ohji, Towards Routine Tensile Testing,Int. J. High. Technol. Ceram., Vol 4, 1988,p 211–225.

● G.D. Quinn, Strength and Proof Testing, Ce-ramics and Glasses, Vol 4, Engineered Ma-terials Handbook, ASM International, 1991,p 599–609

● S.G. Seshadri and K.-Y. Chia, Tensile Test-ing Ceramics, J. Am. Ceram. Soc., Vol 70(No. 10), 1987, p C242–C244.

CHAPTER 11

Tensile Testing ofFiber-Reinforced Composites

Fig. 1 Lamina coordinate system

THE CHARACTERIZATION of engineeringproperties is a complex issue for fiber-reinforcedcomposites due to their inherent anisotropy andinhomogeneity. In terms of mechanical proper-ties, advanced composite materials are evaluatedby a number of specially designed test methods.These test methods are mechanically simple inconcept but extremely sensitive to specimenpreparation and test-execution procedures. Theyinclude:

● Tensile tests● Compression tests● Shear tests● Flexural tests● Fracture tests● Fatigue tests

These test methods are covered by standards de-veloped by ASTM, the International StandardsOrganization (ISO), and the Suppliers of Ad-vanced Composite Materials Association(SACMA).

This chapter is limited to tensile property testmethods. Tensile testing of fiber-reinforcedcomposite materials is performed for the pur-pose of determining uniaxial tensile strength,Young’s modulus, and Poisson’s ratio relative toprincipal material directions. The unidirectionallamina provides the basic building block of themultidirectional laminate. Therefore, character-ization of lamina material properties allows pre-dictions of the properties of laminates. In actualpractice, considerable success has been demon-strated in predicting laminate effective modulusor Poisson’s ratio from ply properties. However,prediction of laminate strength properties fromlamina strength data has proved more difficult,and therefore it is often necessary to resort tocharacterization of laminate strength properties.Thus, basic tensile testing is divided into lamina

and laminate testing. There also are specimendifferences between polymeric-matrix andmetal-matrix composites that require separatediscussions. Basic tensile-test methods for bothpolymeric-matrix and metal-matrix compositesare confined to those materials that behave onthe macroscale as orthotropic bodies.

Fundamentals of TensileTesting of Composite Materials

Unlike homogeneous, isotropic materials, fi-ber-reinforced composites are characterized byproperties that are direction-dependent. Ad-vanced composites, whether of the polymeric-matrix class or the metal-matrix class, often areutilized in the form of a laminate. The lamina,or unidirectionally reinforced ply (Fig. 1), is thebasic building block of the laminate. In order toperform engineering analysis, the heterogeneouslamina consisting of a fiber phase and a matrixphase is treated as a homogeneous, orthotropicmaterial. In addition, laminate modeling as-sumes that plies are in a state of plane stress.

Stress-Strain Relationships for an Ortho-tropic Material. Development of stress-strain




relationships for an orthotropic material requiresthe definition of engineering constants. UsingFig. 1, the unidirectional material is orthotropicwith respect to the x1-x2 axes. The stress-strainrelationships for plane stress are of the forms

1 m12e � r � s (Eq 1a)1 1 2E E1 1

m 112e � � r � r (Eq 1b)2 2E E1 1

1c � s (Eq 1c)12 12G12

where, in the usual manner, the normal stressesand strains in the x1 and x2 directions are denotedby r1, e1, r2, and e2, respectively, whereas theshear stress and strain are denoted by s12 andc12, respectively. In addition, E1, E2, and G12 arethe Young’s modulus parallel to the fibers, theYoung’s modulus transverse to the fibers, andthe shear modulus relative to the x1-x2 plane, re-spectively. The major Poisson’s ratio, as deter-mined from contraction transverse to the fibersduring a uniaxial test parallel to the fibers, isdenoted by �12. For laminates in which the mac-roscopic stress-strain relationships are ortho-tropic, Eq 1 is valid, with the subscripts 1 and 2replaced by x and y, respectively.

Shear Coupling Phenomenon. Componentsof stress and strain can be transformed from onecoordinate system to another. Thus, it is possibleto establish the stress-strain relationship in anycoordinate system. For the unidirectional com-posite in Fig. 1, the constitutive relationshipsrelative to the x-y coordinate system can be writ-ten in the forms

1 m g12 xe � r � r � s (Eq 2a)x x y xyE E Ex x x

m 1 gxy ye � � r � r � s (Eq 2b)y x y xyE E Ey y y

g g 1x yc � r � r � s (Eq 2c)xy x y xyE E Gy x xy

Equations 2a, b, and c correspond to thestress-strain relationships of an anisotropic ma-terial subjected to plane stress. Of particular sig-nificance is the fact that the normal strains arecoupled to the shear stress and the shear strainis coupled to the normal stresses. Such behavioris referred to as the “shear coupling phenome-

non” and requires the definition of two addi-tional elastic properties. In particular, the elasticconstants gx and gy are shear coupling coeffi-cients determined from uniaxial tensile tests inthe x and y directions, respectively—i.e.,

cxyg � (uniaxial tension in the x-direction)x ex

(Eq 3a)

cxyg � (uniaxial tension in the y-direction)y ey

(Eq 3b)

Symmetric Laminates and Laminate No-tation. As shown in Fig. 1, the principal mate-rial directions within each ply of a laminate aredenoted by an x1-x2 axis system. Laminate stack-ing sequences can be easily described for com-posites composed of layers of the same materialwith equal ply thickness by simply listing theply orientations from the top of the laminate tothe bottom. Thus, the notation [0�/90�/0�]uniquely defines a three-layer laminate. The an-gle denotes the orientation of the principal ma-terial axis, x1, within each ply. If a ply were re-peated, a subscript would be used to denote thenumber of repeating plies. Thus, [0�/ /0�] in-90�3dicates that the 90� ply is repeated three times.

Any laminate in which the ply stacking se-quence below the midplane is a mirror image ofthe stacking sequence above the midplane is re-ferred to as a symmetric laminate. For a sym-metric laminate, such as a [0�/ /0�] plate, the90�2notation can be abbreviated by using [0�/90�]s,where the subscript s denotes that the stackingsequence is repeated symmetrically. Angle-plylaminates are denoted by [0�/�45�/�45�]s,which can be abbreviated as [0�/�45�]s. Forlaminates with repeating sets of plies—e.g., [0�/�45�/0�/�45�]s, the abbreviated notation is ofthe form [0�/�45�]2s. If a symmetric laminatecontains a ply that is split at the centerline, a baris used to denote the split. Thus, the laminate[0�/90�/0�] can be abbreviated as [0�/ �]s. For90unsymmetric laminates, a subscript T is oftenused to denote total laminate. For example, thelaminate [0�/90�] can be written as [0�/90�]T.This assures the reader that the laminate is in-deed unsymmetric and that a subscript s was notinadvertently omitted.

Balanced Laminates. Laminates in whicheach ply oriented at an angle of �h (h � 0� or90�) also contains a ply at �h are referred to as

Tensile Testing of Fiber-Reinforced Composites / 185

Fig. 2 Schematic showing typical specimen-mounting methodfor determining single-filament tensile strength

balanced. Such composites are orthotropic rela-tive to the x-y coordinate of the laminate. Thus,Eq 1a, b, and c with the subscripts 1 and 2 re-placed by x and y, respectively, are applicable tobalanced laminates.

Tensile Testing ofSingle Filaments and Tows

Although emphasis in this chapter has beenplaced on tensile testing of laminates, other con-stituent materials are also tested. These includesingle filaments and tows (untwisted bundles ofcontinuous filaments).

Single-filament tensile strength can be de-termined using ASTM D 3379 (Ref 1), whichcan be summarized as a random selection of sin-gle filaments made from the material to betested. Filaments are centerline-mounted on spe-cial slotted tabs (Fig. 2). The tabs are gripped sothat the test specimen is aligned axially in thejaws of a constant-speed movable-crosshead testmachine. The filaments are then stressed to fail-ure at a constant strain rate. For this test method,filament cross-sectional areas are determined byplanimeter measurements of a representativenumber of filament cross sections as displayedon highly magnified photomicrographs. Alter-native methods of area determination include theuse of optical gages, an image-splitting micro-scope, or the linear weight-density method.

Tensile strength and Young’s modulus of elas-ticity are calculated from the load/elongationrecords and the cross-sectional area measure-ments. Note that a system compliance adjust-ment may be necessary for single-filament ten-sile modulus.

Tow tensile testing is carried out usingASTM D 4018 (Ref 2) or an equivalent testmethod. This is summarized as finding the ten-sile properties of continuous filament carbon andgraphite yarns, strands, rovings, and tows by thetensile loading to failure of the resin-impreg-nated fiber forms. This technique loses accuracyas the filament count increases. Strain andYoung’s modulus are measured by an extensom-eter.

The purpose of using impregnating resin is toprovide the fiber forms, when cured, withenough mechanical strength to produce a rigidtest specimen capable of sustaining uniformloading of the individual filaments in the speci-men.

To minimize the effect of the impregnatingresin on the tensile properties of the fiber forms,the resin should be compatible with the fiber, theresin content in the cured specimen should belimited to the minimum amount required to pro-duce a useful test specimen, the individual fila-ments of the fiber forms should be well colli-mated, and the strain capability of the resinshould be significantly greater than the strain ca-pability of the filaments.

ASTM D 4018 method I test specimens re-quire a special cast-resin end tab and grip designto prevent grip slippage under high loads. Al-ternative methods of specimen mounting to endtabs are acceptable, provided that test specimensmaintain axial alignment on the test machinecenterline and that they do not slip in the gripsat high loads. ASTM D 4018 method II testspecimens require no special gripping mecha-nisms. Standard rubber-faced jaws should be ad-equate.

Tensile Testing of Laminates

The basic physics of most tensile test methodsare very similar: a prismatic coupon with astraight-sided gage section is gripped at the endsand loaded in uniaxial tension. The principal dif-ferences between these tensile test coupons arethe coupon cross section and the load-introduc-tion method. The cross section of the couponmay be rectangular, round, or tubular; it may bestraight-sided for the entire length (a “straight-sided” coupon) or width- or diameter-taperedfrom the ends into the gage section (often called“dogbone” or “bow-tie” specimens). Straight-sided coupons may use tabbed load applicationpoints. This section briefly discusses the mostcommon tensile test methods that have beenstandardized for fiber-reinforced composite ma-terials. Reference 3 includes a more detailed dis-


Fig. 3 Specimen for tensile testing of composites as definedin ASTM D 3039. Lg � gage length; LT � tab length;

h � tab bevel angle; W � width. Note: the gage length is com-monly 125 to 150 mm (5 to 6 in.).

cussion and briefly reviews several nonstandardmethods as well.

By changing the coupon configuration, manyof the tensile test methods are able to evaluatedifferent material configurations, including uni-directional laminates, woven materials, and gen-eral laminates. However, some coupon/materialconfiguration combinations are less sensitive tospecimen preparation and testing variations thanothers. Perhaps the most dramatic example ofthis is the unidirectional coupon. Fiber versusload axis misalignment in a 0� unidirectionalcoupon, which can occur due to either specimenpreparation or testing problems or both, can re-duce strength as much as 30% due to an initial1� misalignment. Furthermore, bonded end tabsintended to minimize load-introduction prob-lems in high-strength unidirectional materialscan actually cause premature coupon failure(even in nonunidirectional coupons) if not ap-plied and used properly. Because of these andsimilar issues, tensile testing is subject to a greatdeal of “art” in order to obtain legitimate data.Alternatives to problematic tests, such as theunidirectional tensile test, are often available,and careful attention must be paid to the testspecification for recommendations. Reference 1is also an excellent resource for test optimizationsuggestions.

In-Plane Tensile Test Methods

Straight-sided coupon tensile tests include:

● ASTM D 3039/D 3039M, “Standard TestMethod for Tensile Properties of Polymer-Matrix Composites”

● ISO 527, “Plastics—Determination of Ten-sile Properties”

● SACMA SRM 4, “Tensile Properties of Ori-ented Fiber-Resin Composites”

● SACMA SRM 9, “Tensile Properties of Ori-ented Cross-Plied Fiber-Resin Composites”

ASTM D 3039/D 3039M, originally releasedin 1971 and updated several times since then, isthe original standard test method for straight-sided rectangular coupons (Fig. 3). It is still themost commonly used in-plane tension method.ISO 527 parts 4 and 5 and the two SACMAtensile test methods, SRM 4 and SRM 9, aresubstantially based on ASTM D 3039 and as aresult, are quite similar. Care should be taken,however, not to substitute one method for an-other, because subtle differences between themdo exist. In general, the ASTM standard offers

better control of testing details that may causevariability, as discussed subsequently. For thisreason, it is the preferred method.

In each of the previous test methods, a tensilestress is applied to the specimen through a me-chanical shear interface at the ends of the cou-pon, normally by either wedge or hydraulicgrips. The material response is measured in thegage section of the coupon by either strain gagesor extensometers, subsequently determining theelastic material properties.

If used, end tabs are intended to distribute theload from the grips into the specimen with aminimum of stress concentration. A schematicexample of an appropriate failure mode of amultidirectional laminate using a tabbed tensilecoupon is shown in Fig. 4. Because the straight-sided specimen provides no geometric stress-concentrated region, such as would be found ina specimen with a reduced-width gage section,failure often occurs at or near the ends of thetabs or grips. While this failure mode is not nec-essarily invalid, care must be taken when eval-uating the data to guard against unrealisticallylow strengths resulting from poorly performingtabs or overly aggressive gripping.

Design of end tabs remains somewhat of anart, and an improperly designed tab interfacewill produce low coupon strengths. For this rea-son, a standard tab design has not been man-dated by ASTM, although unbeveled 90� tabsare preferred. Recent comparisons confirm thatthe success of a tab design is more dependent onthe use of a sufficiently ductile adhesive than onthe tab angle. An unbeveled tab applied with aductile adhesive will outperform a tapered tabthat has been applied with an insufficiently duc-tile adhesive. Therefore, adhesive selection ismost critical to bonded tab use. Furthermore, theuse of a softer tab material is usually preferredwhen testing high-modulus materials (such asfiber-glass tabs on a graphite-reinforced speci-men).

The simplest way to avoid bonded tab prob-lems is to not use them. Many laminates (mostly


Fig. 4 Typical tension failure of multidirectional laminate using a tabbed coupon

nonunidirectional) can be successfully testedwithout tabs, or with friction rather than bondedtabs. Flame-sprayed unserrated grips have alsobeen successfully used in tensile testing withouttabs.

Other important factors that affect tensiontesting results include control of specimen prep-aration, specimen design tolerances, control ofconditioning and moisture content variability,control of test machine-induced misalignmentand bending, consistent measurement of thick-ness, appropriate selection of transducers andcalibration of instrumentation, documentationand description of failure modes, definition ofelastic property calculation details, and data re-porting guidelines. These factors are describedin detail by ASTM D 3039/D 3039M.

Limitations of the straight-sided coupontensile methods are described subsequently.

Bonded Tabs. The stress field near the termi-nation of a bonded tab is significantly three-di-mensional, and critical stresses tend to peak atthis location. Much research has been done onminimizing peak stresses, but it is impossible tomake general recommendations that are appro-priate for all materials and configurations. Fur-thermore, improperly designed tabs can signifi-cantly degrade results. As a result, tabless ortabbed configurations that use unbonded tabs arebecoming more popular, when the resulting fail-ure mode is appropriate.

Specimen Design. There are, particularlywithin ASTM D 3039, a number of coupon de-sign options included in the standard, which areneeded to cover the wide range of materials sys-tems and lay-up configurations within the scopeof the test method. Great care should be takento ensure that an appropriate geometry is chosenfor the material being tested.

Specimen Preparation. Specimen preparationplays a crucial role in test results. While this istrue for most composite mechanical tests, it isparticularly important for unidirectional tests,and unidirectional tensile tests are no exception.Fiber alignment, control of coupon taper, andspecimen machining (while maintaining align-ment) are the most critical steps of specimenpreparation. For very low strain-to-failure ma-

terials systems or test configurations, like the 90�unidirectional test, flatness is also particularlyimportant. Edge machining techniques (avoid-ing machining-induced damage) and edge sur-face finishes are also particularly critical tostrength results from the 90� unidirectional test.

Unidirectional Testing. All the elements thatmake tensile testing subject to error are exacer-bated in the unidirectional case, particularly inthe 0� direction. This has led to the increased useof a much less sensitive [90/0]ns-type laminatecoupon (also known as the “crossply” coupon)from which unidirectional properties can be eas-ily derived (Ref 4). Properly tested crossply cou-pons often produce results equivalent to the bestattainable unidirectional data. While unidirec-tional testing is still performed, and in certaincases may be preferred or required, a straight-sided, tabless, [90/0]ns-type coupon is now gen-erally believed to be the lowest cost, most reli-able configuration for lamina tensile testing ofunidirectional materials. This straight-sided tab-less configuration also works equally well fornonunidirectional material forms and for othergeneral laminates. Another advantage is that,unlike with 0� unidirectional specimens, [90/0]ns-type coupon failures do not usually maskindicators of improper testing/specimen prepa-ration practices.

Width tapered coupon tensile tests arestandardized in ASTM D 638, “Standard TestMethod for Tensile Properties of Plastics.” Thetest, developed for and limited to use with plas-tics, uses a flat, width-tapered tensile couponwith a straight-sided gage section. Several ge-ometries are allowed, depending on the materialbeing tested. Figure 5 shows a schematic of onegeneral configuration. Despite its heritage, thiscoupon has also been evaluated and applied tocomposite materials. The coupon taper is ac-complished by a large cylindrical radius betweenthe wide gripping area at each end and the nar-rower gage section, resulting in a shape that jus-tifies the nickname of the “dogbone” coupon.The taper makes the specimen particularly un-suited for testing of 0� unidirectional materials,because only about half of the gripped fibers arecontinuous throughout the gage section. This


Fig. 6 Stress concentration adjacent to a hole in a compositelaminate subjected to uniaxial loading

Fig. 5 Schematic of typical ASTM D 638 test specimen geometry. W, width; Wc, width at center; WO, width overall; T, thickness;R, radius at fillet; RO, outer radius; G, gage length; L, length; LO, length overall; D, distance between grips

usually results in failure by splitting at the ra-dius, due to inability of the matrix to shear theload from terminated fibers into the gage sec-tion.

While the ASTM D 638 coupon configurationhas been successfully used for fabric-reinforcedcomposites and with general nonunidirectionallaminates, some materials systems remain sen-sitive to the stress concentration at the radius.For its intended use with plastics, the coupon ismolded to shape. Likewise, discontinuous fibercomposites can be molded to the required ge-ometry. To ensure valid results, care must betaken that the molding flow does not create pref-erentially oriented fibers. For laminated materi-als the coupon must be machined, ground, orrouted to shape. The coupon also has the draw-back of having a relatively small gage volumeand is poorly suited for characterization ofcoarse weaves with repeating units larger thanthe gage width of 6.4 to 13 mm (0.25 to 0.50in.). The standardized procedure, due to the in-tended scope, does not adequately cover the test-ing parameters required for advanced compos-ites.

Limitations of the ASTM D 638 method aredescribed in the following paragraphs.

Standardization. While the ASTM D 638 testis standardized, it was not developed for ad-vanced composites and is primarily applicableto relatively low-modulus, unreinforced materi-


als, or low-reinforcement volume materials in-corporating randomly oriented fibers.

Specimen Preparation. Special care is re-quired to machine the taper into a laminated cou-pon.

Stress State. The radius transition region candominate the failure mode and result in reducedstrength results. The width-tapered coupon is notsuitable for unidirectional laminates, and is lim-ited to fabrics or nonunidirectional laminateswhen gage section failures can be attained.

Limited Gage Section Volume. The limitedgage width makes it unsuitable for coarse fab-rics.

The sandwich beam test is standardized asASTM C 393, “Standard Test Method for Flex-ural Properties of Flat Sandwich Constructions.”While primarily intended as a flexural test forsandwich core shear evaluation, the scope alsoallows use for determination of facing tensilestrength. While this use is not well documentedwithin the test method, it has been used for ten-sile testing of composite materials, particularlyfor 90� properties of unidirectional materials, orfor fiber-dominated testing in extreme nonam-bient environments. This test specimen isclaimed by some to be less susceptible to han-dling and specimen preparation damage than D3039-type 90� specimens, resulting in higherstrengths and less test-induced variation.

In order to assure failure in the tensile face-sheet, the compression facesheet is often man-ufactured from the same material, but at twicethe thickness as the tensile facesheet.

Limitations of the ASTM C 393 method aredescribed subsequently.

Cost. Specimen fabrication is relatively ex-pensive.

Stress State. The effect on the stress state ofthe sandwich core has not been studied in ten-sion and could be a concern.

Standardization. While this test technically isstandardized, its practical application and limi-tations are not well studied or documented.

Environmental Conditioning. Conditioning isproblematic because of the difficulty of assuringtensile facesheet moisture equilibrium due to themoisture protection offered by the compressionfacesheet and the core. The extended condition-ing times required also often cause adhesivebreakdown prior to testing.

Out-of-Plane Tensile Test Methods

ASTM D 6415, “Standard Test Method forMeasuring the Curved Beam Strength of a Fiber-

Reinforced Polymer-Matrix Composite,” is cur-rently the only published standard for out-of-plane tensile testing specifically relating tocomposites, though modifications to ASTM C297, C 633 and D 2095 are also often employed.These methods are not discussed here, and thereader is referred to Ref 3 and the test standardsfor more information.

Open Hole Tensile Test

Cutouts and holes are requirements in manystructural applications. The effect of cutouts incomposite laminates is greater than the effectcaused by the reduction in load-carrying areaalone. Stress concentrations are produced in thelaminate adjacent to cutout boundaries that sub-stantially reduce load-carrying capacity. Stressconcentrations are a function of laminate aniso-tropy and cutout geometry. Sharp notches pro-duce higher stress concentration factors than cir-cular cutouts. However, the notch sensitivity oflaminates is significantly influenced by laminatestacking sequence and a host of microstructuralmaterials characteristics like matrix toughness,matrix stiffness, and fiber to matrix adhesion.High stress concentrations produce complexdamage zones, which in turn redistribute thestress and increase the energy required to pro-duce failure significantly above that predictedfrom the stress concentration factor alone. It hasbeen shown that larger notches produce lowerstrengths, because the stress concentrations in-volve a larger volume, increasing the probabilityof failure due to a critical flaw (Ref 5). The stressdistribution illustrated in Fig. 6 is the basis forthe point stress criterion for notched strengthprediction (Ref 6), which states that failure oc-curs when the stress at some characteristic dis-tance d0 reaches the unnotched tensile strengthof the composite.

The test method for open hole tension uses acircular cutout in a test specimen (Fig. 7). Themethod is now standardized as test methodASTM D 5766 “Standard Test Method for OpenHole Tensile Strength of Polymer Matrix Com-posite Laminates.” It employs a 305 mm longby 38 mm wide (12 in. by 1.5 in.) specimencontaining a 6.35 mm (0.25 in.) hole. Quasi-iso-tropic laminate configurations are specified to be(�45/0/�45/90�)2s for tape or (�45/(0/90�))2sfor fabric prepregs. While other laminate config-urations and geometries are possible, it is rec-ommended that the width-to-hole diameter ratioof 6 be maintained.


Fig. 7 Open hole tensile test specimen geometry. All dimen-sions are in millimeters.

The specimen should be machined to thespecification shown in Fig. 7. Tolerance on thehole location relative to the specimen centerlineis critical, since eccentricity can significantly de-crease strengths. Specimens can be tabbed or un-tabbed, although untabbed specimens reducecost. If ultimate strain and modulus are desired,specimens may be instrumented with a straingage located on the specimen centerline 25 mm(1 in.) from the hole center ASTM D 5766, how-ever, covers only notched strength and does notcontain provisions for strain measurement.

The test is performed as a uniaxial tensile testfollowing ASTM D 3039. The specimen isloaded until tension failure occurs through thenotch. If failure occurs outside the notch, the testresult should be discarded, since the failure wascaused by a flaw in the material. If failures con-sistently fall outside the notch area, the naturallyoccurring flaws in the material are larger thanthe notch (this is possible with some sheet mold-ing compounds). Then, the specimen designmust be scaled to reflect the material inhomo-geneity level. At least five specimens should betested per test condition.

The notched strength rN is calculated as thetensile strength of the laminate based on the far-field stress:

r � P/bd (Eq 4)N

where P is the maximum load, b is the specimenwidth, and d is the specimen thickness. If thespecimen is instrumented, the modulus is deter-mined as:

P � P3 1E � (Eq 5)x 0.002 bd

where P1 and P3 are the loads at 1000 and 3000microstrain, respectively. The strain at failure isdetermined from the stress-strain curve.

Notched strength data is typically used formaterials screening and for determining designallowables. For design, it is necessary to gen-erate empirical data based on the material, thelaminate configuration, and the hole sizes re-quired. In lieu of generating empirical data forevery conceivable material, laminate, and holesize combination, it is possible to use the pointstress criterion (PSC) analysis to interpolatenotched strength over a range of hole diametersby testing a series of three different notch sizesfor the material and laminate construction of in-terest (Ref 7, 8).

Tensile Testing of Metal-Matrix Composites

Tensile testing of metal-matrix composites isbased on ASTM Standard D 3552 (Ref 9). Inaddition to a straight-sided coupon similar to theASTM D 3039 specimen for polymeric-matrixcomposites, two tapered specimen configura-tions, flat and round, are available in conjunctionwith this test method. Flat panels are producedby such techniques as diffusion bonding,whereas composites fabricated by various liquidinfiltration and other methods used for produc-ing massive materials are better suited tocircular-cross-section shapes. The flat specimenconfiguration is shown in Fig. 8. The circular-cross-section specimen is of limited use and willnot be discussed here. A complete description ofthis specimen can be found in ASTM D 3552.

For 0� flat specimens, tabs are bonded to thegrip section to cushion the end region from fil-ament damage. Straight-sided coupons have agage length of 50.8 mm (2 in.) or 76.2 mm (3in.) and a width of 9.525 mm (0.375 in.) or 12.7mm (0.5 in.), respectively. The recommendedtab length, LT, is 25.4 mm (1 in.). Tapered spec-imens have a gage length, LG, of 25.4 mm (1 in.)


Fig. 8 Metal-matrix composite tensile specimen

and a gage-section width, WG, of either 6.35 mm(0.25 in.) or 9.525 mm (0.375 in.). The shoulderand tab lengths, L1 and LT, respectively, shouldbe 25.4 mm (1 in.). The radius of curvature ofthe shoulder, R, should be a minimum of 25.4mm (1 in.). For tensile testing of materials inlimited supply, a 25.4 mm (1 in.) gage sectionmay be utilized in conjunction with a 6.35 mm(0.25 in.) gage width. The tab region may bereduced to 19.05 mm (0.75 in.) and the radiusof the shoulder reduced to 12.7 mm (0.5 in.). Itshould be noted that with 0� tapered specimens,failure may tend to initiate at or near the filletradius. If this occurs, a straight-sided specimenshould be substituted.

Because 90� unidirectional composites tend tohave low strength, larger widths are necessaryto obtained reproducible data. In this case, astraight-sided coupon with a gage length of 25.4mm (1 in.) and a width of 12.7 mm (0.5 in.) isrecommended. The tab length remains at 25.4mm (1 in.). If availability of material dictates asmaller specimen, the gage section may be re-duced to 12.7 mm (0.5 in.).

As in the case of polymeric-matrix specimens,strain measurements can be obtained by utilizingan extensometer or strain gages. If Poisson’s ra-tio is to be determined, strain must be measuredin both the longitudinal and transverse direc-tions. Gages should not measure less than 3 mm(0.1181 in.) in the longitudinal direction and notless than 1.5 mm (0.0591 in.) in the transversedirection. For specimens with short (12.7 mm,or 0.5 in.) gage sections, extensometers are notrecommended.

Self-aligning wedge-type or lateral-pressure-type grips with serrated or knurled surfaces arerequired by ASTM Standard D 3552. Grippingpressure should be sufficient to prevent speci-men slippage without damaging the end tabs.

Emery cloth or a similar material can be used todistribute the pressure more uniformly if the ser-rations are too coarse.

Mechanical properties of metal-matrix com-posites are very sensitive to specimen prepara-tion. Special care should be taken in machiningor trimming. For some types of metal-matrixcomposites, conventional machining methodsare appropriate. In other cases, grinding or elec-trical discharge machining (EDM) should beused. Damaging vibrations must be minimizedduring machining, and in the EDM method thespecimen must be mounted in such a manner asto ensure good electrical contact and thus pre-vent extraneous arcing and resulting specimendamage.

Data Reduction

Calculations of strength, Young’s modulus,and Poisson’s ratio are the same for both poly-meric-matrix and metal-matrix composites. Ten-sile strength in the load direction is determinedby dividing the maximum load by the cross-sec-tional area of the gage section:

PS � (Eq 6)L hWG

where SL is ultimate tensile strength in the loaddirection in megapascals or pounds per squareinch; P is maximum load, in newtons or pounds(force); h is specimen thickness, in millimetersor inches; and WG is the gage-section width ofthe specimen, in millimeters or inches.

Young’s modulus in the load direction is de-termined from the slope of the load-strain curvein the linear region:


(DP/De )LE � (Eq 7)L hWG

where EL is Young’s modulus in the load direc-tion, in megapascals or pounds per square inch;and DP/DeL is the slope of the load-strain curvein the linear portion of the curve, where eL de-notes the strain parallel to the load.

Poisson’s ratio can be calculated from the re-lationship

DeTm � � (Eq 8)LT DeL

where �LT is Poisson’s ratio relative to the loaddirection; and DeT/DeL is the slope of the strain-strain curve, where eT denotes the strain trans-verse to the load direction.

Application of Tensile Tests to Design

It is often desired to use coupon-level data fordesign purposes. Thus, it is appropriate to con-sider the merits, for design purposes, of tensile-test data generated in accordance with ASTMStandard D 3039 for polymeric-matrix compos-ites and Standard D 3552 for metal-matrix com-posites. Because both of these test methods in-volve straight-sided specimens, one must becareful that failures do not consistently occurnear the end tabs. Even for the tapered metal-matrix specimens, consistent failure near the fil-lets are of concern.

In addition to these obvious pitfalls, one hasto be concerned with the over-all failure pro-cesses that occur in laminates. In particular casesfor which the initial failure mode is delaminationdue to free edges, one must carefully assesswhether such a failure process represents howthe material will behave in the structure orwhether the data is an artifact of the test method.In fact, failure modes produced at the couponlevel should always be evaluated as to their ap-plicability to behavior in a structure. This is par-ticularly true for multidirectional fiber-re-inforced composites.

Other considerations include the influence of“first ply failure” on design. In particular, matrixcracking (first ply failure) may occur far belowultimate failure in a multidirectional laminate.The effect of first ply failure on the usefulnessof the laminate in the structure is an important

design consideration that is not of concern to theexperimentalist performing tensile tests. It maybe important, however, for the experimentalistto determine first ply failure. This is usuallydone by observing a plateau in the stress-straincurve. For fiber-dominated laminates, such as[0�/90�]s, observance of a plateau may requiremonitoring of the transverse stress-strain curve,because matrix failure in the 90� plies will nothave an influence on the longitudinal stress-strain curve.

ACKNOWLEDGMENTS


● J.M. Whitney, Tensile Testing of Fiber-Re-inforced Composites, Tensile Testing, 1st ed.,P. Han, Ed., ASM International, 1992, p183–200

● D. Wilson and L.A. Carlsson, MechanicalTesting of Fiber-Reinforced Composites,Mechanical Testing and Evaluation, Vol 8,ASM Handbook, ASM International, 2000, p905–932

● S. Bugaj, Constituent Materials Testing,Composites, Vol 21, ASM Handbook, ASMInternational, 2001, p 749–758

● J. Moylan, Lamina and Laminate Mechani-cal Testing, Composites, Vol 21, ASM Hand-book, ASM International, 2001, p 766–777

REFERENCES

1. “Standard Test Method for Tensile Strengthand Young’s Modulus for High-ModulusSingle-Filament Materials,” D 3379, AnnualBook of ASTM Standards, ASTM Interna-tional

2. “Standard Test Methods for Properties ofContinuous Filament Carbon and GraphiteFiber Tows,” D 4018, Annual Book of ASTMStandards, ASTM International Testing andMaterials

3. Composite Materials, Vol 1, Chapter 6, MIL-HDBK-17-1E, Department of Defense Hand-book

4. Use of Crossply Laminate Testing to DeriveLamina Strengths in the Fiber Direction,Composite Materials, Vol 1, Chapter 6, MIL-HDBK-17-1E, Department of Defense Hand-book

5. J.M. Ogonowski, Analytical Study of Finite


Geometry Plates with Stress Concentrations,AIAA Paper 80-0778, American Institute ofAeronautics and Astronautics, New York,1980, p 694

6. J.M. Whitney and R.J. Nuismer, Stress Frac-ture Criteria for Laminated Composites Con-taining Stress Concentrations, J. Compos.Mater., Vol 8, 1974, p 253

7. L.A. Carlsson and R.B. Pipes, ExperimentalCharacterization of Advanced Composite

Materials, 2nd ed., Technomic, Lancaster,1987

8. R.B. Pipes, R.C. Wetherhold, and J.W. Gil-lespie, Jr., Notched Strength of CompositeMaterials, J. Compos. Mater., Vol 13, 1979,p 148

9. “Test Method for Tensile Properties of FiberReinforced Metal Matrix Composites,” D3552, Annual Book of ASTM Standards,ASTM International

CHAPTER 12

Tensile Testing of Components

THE MECHANICAL EVALUATION ofcomponents requires an engineer to use manysources of information. It requires an under-standing of service conditions, design, andmanufacturing variables. While there are manytypes of component tests for a multitude of prod-ucts, this chapter focuses on three examples ofengineering components that undergo signifi-cant loading in tension: threaded fasteners andbolted joints; adhesive joints; and welded joints.For some components, tensile loading is not theprimary concern. For example, rolling contactfatigue is the most important consideration forrolling-element bearings. Gears, in addition torolling contact fatigue tests, are tested for resis-tance to wear, bending fatigue, and impact. Pres-sure vessels, piping, and tubing are tested fortheir creep and fracture resistance.

An overview of mechanical properties forcomponent design can be found in Ref 1. Prop-erties and design for static (tensile and com-pressive) loads, dynamic (impact and fracturetoughness) loads, and cyclic (fatigue) loads areaddressed.

Testing of ThreadedFasteners and Bolted Joints

Fastener engineering and the mechanical test-ing of threaded fasteners and bolted joints is animportant specialty within the field of mechan-ical engineering. With the wide variety of fas-teners and bolted joints available for use, no oneset of tests can be specified to cover all appli-cations. Fasteners are routinely tested for hard-ness, tensile strength, and torsional strength, aswell as corrosion and hydrogen embrittlement.Before describing the standardized tensile testfor externally threaded fasteners, some briefbackground information is provided to help the

reader understand the relationships betweentorque, angle-of-turn, tension, and friction.

Torque, Angle, Tension, and Friction

A proper amount of tension, or clampingforce, must be developed to ensure that a boltedassembly will function in a safe and reliablemanner. The most common attempt to indirectlyestimate fastener tension is to take torque mea-surements either dynamically as the fastener istightened or with a breakaway audit after thefact. The torque that is required to produce thedesired tension in a fastener is dependent on sev-eral factors, with frictional characteristics beingthe most important. Angle-of-turn measure-ments combined with torque measurements canhelp overcome the unknown friction-inducedvariability in the torque-tension relationship.

Tension. The tension that is created in athreaded fastener when it is tightened representsthe clamping force that holds the assembly to-gether. Once the assembly is brought together,the fastener responds like a tension spring, andthe assembly acts like a compression spring. Theinteraction between the fastener and the assem-bly is illustrated in Fig. 1. As the fastener isturned and load is applied, the fastener isstretched, and the parts are compressed. Thiscompression results in an elastic joint in whichthe fastener is normally the more flexible mem-ber, and the assembly is the more rigid member.

The amount of clamping force that the fastenermust provide to hold the assembly together mustbe sufficient to both maintain preloading and pre-vent slipping of the parts or opening of the jointwhen the service loads are applied. The factorsthat primarily establish the preload requirementare the stiffness of the materials in the joint andthe loads that are placed on the assembly.

Fastener tension can be measured using dif-ferent devices, such as strain-gaged bolts or fas-




Fig. 2 Typical distribution of energy from torque applied to abolted assemblyFig. 1 Spring effect of fastener and assembly under load

tener force washers, or by using special tech-niques, such as ultrasonic bolt measurement.Although these devices and methods are usefulin research and engineering efforts, they are of-ten impractical or costly for evaluating fastenertension in production quality-control efforts.

Torque. The most common way to estimateclamping force is to observe the amount oftorque applied to the fastener, either as the fas-tener is tightened or with a breakaway audit ofthe tightened fastener. This procedure assumesthat the relationship between torque and tensionis known, such that, for example, the nut factor,or K, from the simple equation T � KDF (whereT is torque, D is diameter, and F is clampingforce) is established and known to have accept-able variability. The truth of the matter is that iftorque alone is measured, it can never be knownwith certainty whether the desired tension hasbeen achieved. Thus, unfortunately, it must beconcluded that torque is a highly unreliable, to-tally inaccurate measurement for evaluation ofthe preload on a threaded fastener. However, formany noncritical fasteners, where safety or thefunctional performance of an assembly is notcompromised, it may be acceptable to specifyand monitor torque alone. The most commonmeasurement tools are hand torque wrenchesthat are used for installation and torque auditmeasurements and rotary torque sensors that areused to measure installation torque dynamically.

In order for tension to be developed, thetorque applied to a fastener must overcome fric-

tion under the head of the fastener and in thethreads, and the fastener or nut must turn. Be-cause the friction may absorb as much as 90 to95% of the energy applied to the fastener, aslittle as 5 to 10% of the energy is left for gen-erating fastener tension as shown in Fig. 2. If theamount of friction varies greatly, wide variationsin clamping force are produced, which can meanloose or broken bolts leading to assembly fail-ures. To ensure proper assembly of critical fas-teners, more than torque must be measured.

Angle. The amount of fastener tension can becorrelated to fastener rotation once the parts ofan assembly are drawn firmly together. Theclamping force that is developed in this zone ofthe assembly process, called the elastic tighten-ing region, has been proven to be proportionalto the angle-of-turn. This proportional relation-ship is based on the helix of the threads and isnot influenced by the frictional characteristics ofthe joint once sufficient clamping force has beenproduced to firmly align the components suchthat a linear torque-angle signature slope is at-tained. More detailed information on the rela-tionship between torque and angle-of-turn canbe obtained by torque-angle signature analysisdescribed in Ref 2.

Friction Measurements. Whereas fastenerengineering analysis of threaded fasteners mustconsider material strength, surface finishes, plat-ing, and coatings to ensure reliable performance,for predictable and repeatable assemblies it isalso necessary to understand, measure, and con-trol the frictional characteristics in both thethread and underhead regions. This is particu-

Tensile Testing of Components / 197

Fig. 3 Torque-tension research head, 800 kN capacity

larly true when developing fastener-locking de-vices such as locknuts, serrated underheads, spe-cial thread forms, and thread-locking adhesivesand friction patches. Achieving a specific clampforce during installation is always the desiredresult, and the roles of thread friction and un-derhead friction must be analyzed and under-stood to ensure joint integrity.

To determine both thread friction and under-head friction, measurements are taken using atorque-tension research head, as shown in Fig.3. This device is a special load cell designed tosimultaneously measure both thread torque and

clamp load. When used with torque sensors thatmeasure the input torque, it is possible to deter-mine the underhead friction torque and thethread friction torque. With this measurementequipment, the fastener can then be tested to es-tablish and maintain standards for friction per-formance.

For example, in the test plot illustrated in Fig.4, a locknut is initially driven onto a bolt. Thethread friction torque is equal to the input torqueuntil contact with the underhead-bearing surfaceis made. Once contact is made with the under-head area, the underhead friction torque is mea-sured as the difference between the total inputtorque and the thread torque. As clamp force isdeveloped, the pitch torque is calculated andsubtracted from the thread torque to compute thethread-friction torque. Note that for prevailingtorque locknuts, the elastic origin is located atthe prevailing torque level as shown in Fig. 4,not at the zero torque level used for fastenerswithout prevailing torque characteristics.

Considerations in Testing. There are a num-ber of factors that can affect the tension createdin a bolt when torque is applied. Depending onthe fastener and joint configuration, direct mea-surement of tension is not always practical oreven possible by any means. Fortunately, torqueand angle measurements can be taken for mostbolted joints and then analyzed to assist in de-termination of important characteristics andproperties related to strength and reliability.

Fig. 4 Determining friction forces for prevailing torque locknut


When tightening a threaded fastener, it is al-most always important to know both how muchtorque is applied and how far the fastener isturned. Similarly, it is always important to fullyunderstand how friction affects the relationshipof torque, angle, and tension.

To ensure that critical joints are tightenedproperly, it must be kept in mind that it is thecontrol of tension that is most important, not thecontrol of torque. This fact must always be con-sidered when choosing and setting up tools,when monitoring production, and when per-forming quality control audits. The fastener-tightening process is dependent upon the energytransfer from the tightening tool into the fastenerand bolted joint. The integrated area under thetorque-angle signature curve is a measure of theenergy absorbed by the assembly.

Standard Test Methods for DeterminingMaterials Properties of Fasteners

The materials properties of the fastener mustbe known before a more detailed analysis of thebolted joint is possible. Many standards exist forthe testing of fasteners. ASTM F 606M (Ref 3),a specification developed through the proce-dures of ASTM for metric fasteners, is consid-ered to be one of the most complete. The cor-responding standard for English threadedfasteners is ASTM F 606. More complete de-scriptions of the methods can be found in thestandard. The text following in this section is asummary of the basic test methods according toASTM F 606M.

The test methods described in ASTM F 606Mestablish procedures for conducting mechanicaltests to determine the materials properties of ex-ternally and internally threaded fasteners. Forexternally threaded fasteners, the following testmethods are described:

● Product hardness● Proof load by length measurement, yield

strength, or uniform hardness● Axial tension testing of full-sized products● Wedge tension testing of full-sized products● Tension testing of machined test specimens● Total extension at fracture testing

Product Hardness

The hardness of fasteners and studs can bedetermined on the ends, wrench flats, or un-threaded shanks after removal of any oxide, de-carburization, plating, or other coating material.

Rockwell or Vickers hardness standards may beused at the option of the manufacturer. Hardnessis determined at midradius of a transverse sec-tion of the product taken at a distance of onediameter from the point end of the product. Thereported hardness is the average of four hardnessreadings located at 90� to one another. Accept-able alternative methods of determining hard-ness for bolts are either at midradius, one di-ameter from the end, or on the side of the headof a hex-head or square-head product of all prop-erty classes after adequate preparation to removeany decarburization. As explained subsequently,uniform hardness measurement is one methodfor determining the proof load.

Tensile Tests

Fasteners and studs should be tested at full-size and to a minimum ultimate load in kilonew-tons (kN) or stress in megapascals (MPa). Suchtesting includes proof-load tests (by length mea-surement, yield strength, or uniform hardness),axial tensile tests, wedge tensile tests, and totalextension-at-fracture tests.

Proof-Load Tests. The basic proof-load testconsists of stressing the product with a specifiedload that the product must withstand without anymeasurable permanent set and evaluating thefastener in terms of any change in length. Alter-native tests to determine the ability of a fastenerto pass the proof-load test are the yield-strengthtest and the uniform hardness test. Although anyof the alternative test methods described may beused, the proof-load test is the arbitrationmethod used in case of any dispute.

Method 1, Length Measurement. The overalllength of the specimen is measured at its truecenterline with an instrument capable of mea-suring changes in length of 0.0025 mm with anaccuracy of 0.0025 mm in any 0.025 mm range.Measuring the length between conical centers onthe centerline of the fastener or stud with matingcenters on the measuring anvils is preferred. Thehead or body of the fastener or stud should bemarked so that it can be placed in the same po-sition for all measurements.

The product is assembled in the fixture of thetension-testing machine so that six completethreads are exposed between the grips. Tests forheavy hex structural bolts are based on fourthreads. This is obtained by freely running thenut or fixture to the thread runout of the speci-men and then unscrewing the specimen six fullturns. For continuous threaded fasteners, at least


Table 1 Required minimum length of fastenersfor tensile testing

Nominal product diam (D), mm Min length, mm

5 126 148 2010 2512 3014 3516 4020 45Over 20 3D

Source: Ref 3Fig. 5 Tensile testing of full-size fastener (typical set-up).

Source: Ref 3

six full threads should be exposed. The fastenershould be loaded axially to the proof load spec-ified in the product specification. The speed oftesting, as determined with a free-running crosshead, should not exceed 3 mm/min, and theproof load should be maintained for a period of10 s before releasing the load. Upon release ofthis load, the length of the fastener or studshould be measured again to determine perma-nent elongation. A tolerance (for measurementerror only) of �0.013 mm is allowed betweenthe measurements made before loading and thatmade after loading.

Variables, such as straightness, thread align-ment, or measurement error, could result in ap-parent elongation of the product when the spec-ified proof load is initially applied. In such cases,the product may be retested using a 3% greaterload and is considered acceptable if there is nodifference in the length measurement after thisloading within a 0.013 mm measurement toler-ance as outlined.

Method 2, Yield Strength. The product is as-sembled in the testing equipment as describedfor method 1. As the load is applied, the totalelongation of the product or any part of it thatincludes the exposed threads should be mea-sured and recorded to produce a load-elongationdiagram. The load or stress at an offset equal to0.2% of the length of fastener occupied by sixfull threads is determined, as shown in Fig. 5.

Method 2A, Yield Strength for AusteniticStainless Steel and Nonferrous Materials. Theproduct is assembled in the testing equipment asdescribed in method 1. As the load is applied,the total elongation of the product should bemeasured and recorded in order to produce aload-elongation diagram. The load or stress atan offset equal to 0.2% strain should be deter-mined based on the length of the bolt betweenthe holders as shown in Fig. 5, which will besubject to elongation under load by using theyield-strength method described in the section“Tensile Testing of Machined Test Specimens.”

Method 3, Uniform Hardness. The fastenersare tested for hardness as described previously,and in addition, the hardness is determined inthe core. The difference between the midradiusand core hardness should be not more than threepoints on a Rockwell C scale, and both readingsmust be within product specification.

Short Fasteners and Studs. Fasteners withlengths less than those shown in Table 1, or thatdo not have sufficient threads for proper en-gagement, are deemed too short for tensile test-ing. Acceptance is then based on a hardness test.If tests other than product hardness are required,their requirements are referenced in the productspecification.

Axial Tensile Testing of Full-Sized Prod-ucts. Fasteners are tested in a holder with a loadaxially applied between the head and a nut or ina suitable fixture as shown in Fig. 5. Sufficientthread engagement must exist to develop the fullstrength of the product. The nut or fixture shouldbe assembled on the product, leaving six com-plete fastener threads exposed between the grips.Studs are tested by assembling one end of thethreaded fixture to the thread runout. If the studhas unlike threads, the end with the finer pitchthread, or with the larger minor diameter, isused. The other end of the stud is assembled inthe threaded fixture, leaving six complete


Table 3 Requirements for wedge-holeclearance and radius for tensile testing offasteners

Nominal productdiam, mm

Nominal clearancein hole, mm

Nominal radius oncorners of hole, mm

To 6 0.50 0.70Over 6–12 0.80 0.80Over 12–20 1.60 1.30Over 20–36 3.20 1.60Over 36 3.20 3.20

Source: Ref 3

Table 2 Wedge angles for tensile testing offasteners

Degrees

Nominal productdiam, mm Fasteners(a)

Studs and flangefasteners

5–24 10 6Over 24 6 4

(a) For heat-treated fasteners that are threaded one diam or closer to the undersideof the head, a wedge angle of 6� for sizes 5 to 24 mm and 4� for sizes over 24mm should be used. Source: Ref 3

Fig. 6 Wedge-test details for fasteners. D, diameter of bolt; C,clearance of wedge hole; R, radius; T, thickness of

wedge at short side hole; W, wedge angle

threads exposed between the grips. For contin-uous studs, at least six complete threads are ex-posed between the fixture ends.

The maximum speed of the free-running crosshead should not exceed 25 mm/min. When re-porting the tensile strength of the product, thethread stress area is calculated as follows:

2A � 0.7854(D � 0.9382P) (Eq 1)s

where As is the thread stress area, mm2; D is thenominal diameter of the fasteners or stud, mm;and P is thread pitch, mm.

The product should support a load prior tofracture not less than the minimum tensilestrength specified in the product specification forits size, property class, and thread series. In ad-dition, failure should occur in the body or in thethreaded section with no fracture at the junctureof the body and head.

Wedge Tensile Testing. The wedge tensilestrength of a hex- or square-head fastener,socket-head cap screw, or stud is the tensile loadthat the product is capable of sustaining whenstressed with a wedge under the head. The pur-pose of this test is to obtain the tensile strength

and to demonstrate the head quality and ductilityof the product.

Wedge Tensile Testing of Fasteners. The ulti-mate load of the fastener is determined as de-scribed previously under “Axial Tensile Testingof Full-Sized Products,” except to place a wedgeunder the fastener head. When both wedge andproof-load testing are required by the productspecification, the proof-load-tested fastener forwedge testing should be used. The wedge musthave a minimum hardness of 45 HRC for fas-teners having an ultimate tensile strength of1035 MPa or less, and a minimum of 55 HRCfor fasteners having a tensile strength in excessof 1035 MPa. Additionally, the wedge shouldhave the following:

● A thickness of one-half the nominal fastenerdiameter (measured at the thin side of thehole as shown in Fig. 6)

● A minimum outside dimension such that atno time during the test will any corner load-ing of the head of the product occur adjacentto the wedge

● An included angle as shown in Table 2 forthe product type being tested

The hole in the wedge should have a clearanceover the nominal size of the fastener and haveits edges top and bottom rounded as specified inTable 3.

The fastener is then tensile tested to failure.The fastener must support a load prior to fracture


Fig. 8 Tensile-test specimen with turned-down shank. Source:Ref 3

Fig. 7 Wedge-test details for studs. D, diameter of stud; C,clearance of wedge hole; R, radius; T, thickness of

wedge at short side hole; W, wedge angle

not less than the minimum tensile strength spec-ified in the product specification for the appli-cable size, property class, and thread series. Inaddition, the fracture should occur in the bodyor threaded portion with no fractures at the junc-tion of the head and the shank.

Wedge-Tensile Testing of Studs. When bothwedge-tension and proof-load testing are re-quired, one end of the same stud previously usedfor proof-load testing is assembled in a threadedfixture to the thread runout. For studs havingunlike threads, the end with the finer-pitchthread or with the larger minor diameter is used.The other end of the stud should be assembledin a threaded wedge to the runout and then un-screwed six full turns, leaving six completethreads exposed between the grips as shown inFig. 7. For continuous threaded studs, at leastsix full threads are exposed between the fixtureends. The angle of the wedge for the stud sizeand property class is as specified in Table 2.

The stud should be assembled in the testingmachine and tensile tested to failure, as de-scribed previously under “Axial Tensile Testingof Full-Sized Products.” The minimum hardnessof the threaded wedge is 45 HRC for productshaving an ultimate tensile strength of less than1035 MPa and 55 HRC for product lines havingan ultimate tensile strength in excess of 1035MPa. The length of the threaded section of thewedge must be equal to at least the diameter ofthe stud. To facilitate removal of the brokenstud, the wedge can be counterbored. The thick-ness of the wedge at the thin side of the hole is

equal to the diameter of the stud plus the depthof the counterbore. The thread in the wedgeshould have class 4H6H tolerance, except whentesting studs having an interference fit thread, inwhich case the wedge will have to be threadedto provide a finger-free fit. The supporting fix-ture should have a hole clearance over the nom-inal size of the stud, and the top and bottomedges should be rounded or chamfered to thesame limits specified for the hardened wedge inTable 3.

The stud must support a load prior to fractureof not less than the minimum tensile strengthspecified in the product specification for its size,property class, and thread series.

Tensile Testing of Machined Test Speci-mens. Where fasteners and studs cannot betested at full-size, tests are conducted using testspecimens machined from the fastener or stud.Fasteners and studs should have their shanksmachined to the dimensions shown in Fig. 8.The reduction of the shank diameter of heat-treated fasteners and studs with nominal diam-eters larger than 16 mm should not exceed 25%of the original diameter of the product. Alter-natively, fasteners 16 mm in diameter or largermay have their shanks machined to a test spec-imen with the axis of the specimen located mid-way between the axis and outside surface of thefastener as shown in Fig. 9. In either case, ma-chined test specimens should exhibit tensilestrength, yield strength (or yield point), elon-gation, and reduction of area equal to or greaterthan the values of these properties specified forthe product size in the applicable product spec-ification when tested in accordance with this sec-tion.

Tensile Properties: Yield Point. Yield point isthe first stress in a material, less than the maxi-mum obtainable stress, at which an increase instrain occurs without an increase in stress. Yield


Fig. 10 Stress-strain diagram for determination of yieldstrength by the offset method. o-m is the specified

offset. To determine offset yield strength, draw line m-n parallelto the line o-A. From the intersection point r, draw a horizontalline to determine the offset yield strength, R.

Fig. 9 Location of standard tensile-test specimen when turnedfrom large sized fastener. Source: Ref 3

Fig. 11 Stress-strain diagram showing yield point corre-sponding with top of knee. o-m, offset to yield point.

Source: Ref 3

point is intended for application only for mate-rials that may exhibit the unique characteristicof showing an increase in strain without an in-crease in stress. A sharp knee or discontinuitycharacterizes the stress-strain diagram. The yieldpoint can be determined by one of the followingmethods:

● Drop-of-the-beam or halt-of-the-pointermethod: In this method, an increasing loadis applied to the specimen at a uniform rate.When a lever and poise machine is used, thebeam is kept in balance by running out thepoise at an approximately steady rate. Whenthe yield point of the material is reached, theincrease of the load will stop, but the poiseshould be run a small amount beyond thebalance position, and the beam of the ma-chine will drop for a brief interval of time.When a machine equipped with a load-in-dicating dial is used, there is a halt or hesi-tation of the load-indicating pointer, whichcorresponds to the drop of the beam. Theload is recorded at the drop of the beam orthe halt of the pointer. This point is the yieldpoint of the fastener or stud.

● Autographic diagram method: When asharp-kneed stress-strain diagram is obtainedby an autographic device, the yield point istaken as either the stress corresponding to thetop of the knee, as shown in Fig. 10, or asthe stress at which the curve drops, as shownin Fig. 11.

● Total extension-under-load method: Whentesting material for yield point, the test spec-

imens may not exhibit the well-defined dis-proportionate deformation that characterizesa yield point as measured by the previousmethods. In these cases, the followingmethod can be used to determine a valueequivalent to the yield point in its practical


Fig. 12 Stress-strain diagram showing yield point or yieldstrength by extension-under-load method. o-m, spec-

ified extension under load. Line m-n is vertical, and the intersec-tion point, r, determines yield strength value, R. Source: Ref 3

significance that may be recorded as theyield point. A class C or better extensometeris attached to the specimen. When the loadproducing a specified extension is reached,the stress corresponding to the load as theyield point is recorded and the extensometerremoved (Fig. 12).

Yield Strength. Yield strength is the stress atwhich a material exhibits a specified limitingdeviation from the proportionality of stress tostrain. The deviation is expressed in terms ofstrain, percentage of offset, total extension un-der load, and so on. Yield strength may be de-termined by the offset method or the extension-under-load method.

To determine the yield strength by the offsetmethod, it is necessary to secure data (auto-graphic or numerical) from which a stress-straindiagram may be drawn. Then, on the stress-strain diagram layoff, o-m, as shown in Fig. 10,equal to the specified value of the offset, m-nshould be drawn parallel to o-A and thus locater. The yield-strength load, R, is the load corre-sponding to the highest point of the stress-straincurve before or at the intersection of m-n andr. In reporting values of yield strength obtainedby this method, the specified value of the offsetused should be stated in parenthesis after theterm yield strength, thus:

Yield strength (0.2% offset) � 360 MPa

In using this method, a minimum extensometermagnification of 250 to 1� is required. A classB1 extensometer meets this requirement. (Ex-tensometer system classification is discussed inChapter 4, “Testing Equipment and Strain Sen-sors.”)

The extension-under-load method is used todetermine the acceptance or rejection of mate-rials whose stress-strain characteristics are wellknown from previous tests of similar materialsin which stress-strain diagrams are plotted. Forthese tests, the total strain corresponding to thestress at which the specified offset occursshould be known as within satisfactory limits.The stress on the specimen, when total strengthis reached, is the value of the yield strength.The total strain can be obtained satisfactorilyby the use of a class B1 extensometer. The ex-tension under load (mm/mm of gage length)can be determined as follows:

YS/E � r (Eq 2)

where YS is the specified yield strength, MPa;E is the modulus of elasticity, MPa; and r isthe limiting plastic strain, mm/mm.

Tensile strength is calculated by dividing themaximum load the specimen sustains during atensile test by the original cross-sectional areaof the specimen.

Elongation. The ends of the fractured speci-men are fitted together carefully and the dis-tance between the gage marks measured to thenearest 0.25 mm for gage lengths of 50 mm orunder, and to the nearest 0.5 mm of the gagelength for gage lengths over 50 mm. A per-centage scale reading to 0.5% of the gagelength may be used. The elongation is the in-crease in length of the gage length, expressedas a percentage of the original gage length. Inreporting elongation values, both the percentageincrease and the original gage length should begiven.

If any part of the fracture takes place outsidethe middle half of the gage length or in apunched or scribed mark with the reduced sec-tion, the elongation value obtained may not berepresentative of the material. If the elongationso measured meets the minimum requirementsspecified, no further testing is indicated, but ifthe elongation is less than the minimum re-quirements, the test should be discarded andperformed again.


Fig. 13 Determination of total extension at fracture (AL) for a screw product. Source: Ref 3

Reduction of Area. The ends of the fracturedspecimen are fitted together and the mean di-ameter or the width and thickness at the small-est cross section measured to the same accuracyas the original dimensions. The difference be-tween the area thus found and the area of theoriginal cross section expressed as a percentageof the original area is the reduction in area.

Total Extension at Fracture Test. The testto determine extension at fracture, AL, is carriedout on stainless steel and nonferrous productsin the finished condition with the length equalto or in excess of those minimums listed in Ta-ble 1. The products to be tested are measuredfor total length, L1, described as follows andshown in Fig. 13.

Both ends of the fastener or stud are markedusing a permanent marking substance, such asbluing, so that the measuring reference pointsfor determining total lengths, L1 and L2, are es-tablished. An open-end caliper and steel rule orother device capable of measuring to within0.25 mm are used to determine the total lengthof the product (Fig. 13).

The product under test is screwed into thethreaded adapter to a depth of one diameter(Fig. 5) and load applied axially until the prod-uct fractures. The maximum speed of the free-running cross head should not exceed 25 mm/min.

After the product has been fractured, the twobroken pieces are fitted closely together, and theoverall length, L2, is measured. The total exten-sion at fracture, AL, is then calculated as fol-lows:

A � L � L (Eq 3)L 2 1

The value obtained should equal or exceed theminimum values shown in the applicable spec-ification for the product and material type.

Testing of Adhesive Joints

Adhesive bonding is a materials joining pro-cess in which an adhesive (usually a thermoset-ting or thermoplastic resin) is placed betweenthe faying surfaces of the parts or bodies calledadherends. The adhesive then solidifies or hard-ens by physical or chemical property changes toproduce a bonded joint with useful strength be-tween the adherends. The strength of the adhe-sive joint is determined by the following tests(Ref 4):

● Peel tests● Lap shear tests● Tensile tests● Fracture mechanics tests

Tensile Tests. Most adhesive joints are de-signed to avoid (or at least reduce) direct tensileforces across the bond line. However, for manyjoints where the primary loading is shear, failuremay be initiated by the induced secondary ten-sile stresses and the adhesive joint’s tensilestrength is of interest. Accordingly, the thirdmost common type of adhesive joint strengthtest is the tensile test (the lap shear test geometryis the most popular followed by the peel test).

The geometries of several tensile tests forwhich there are specific ASTM test proceduresare shown in Fig. 14 (Ref 5). Some of these testgeometries seem relatively simple; however, ithas been demonstrated that the stresses along thebond line have a rather complex dependence ongeometric factors and adhesive and adherentproperties (adhesive thickness and its variationacross the bonded surface, modulus, Poisson’sratio, and so on) (Ref 6).

It is almost always difficult to load tensile ad-hesion specimens in an axisymmetric manner,even if the sample itself is axisymmetric. Non-


Fig. 15 Specimen for testing the cleavage strength of metal-to-metal adhesive bonds. Source: ASTM D 1062

Fig. 14 Typical specimen geometries for testing the tensile strength of adhesive joints. Source: Ref 5

axisymmetric loads have been shown to reducethe bond failure load capability and to causelarge scatter in the resulting failure data. Super-ficially, the geometry for standard tensile adhe-sion tests is deceptively simple. The result of thetensile adhesion test, as normally reported by ex-perimentalists, is simply the failure load dividedby the cross-sectional area of the adhesive (Ref7). Such average stress at failure can be verymisleading. Because of the differences in me-chanical properties of the adhesive and adher-end, the stresses may become singular at thebond edges when analyzed using linear elasticanalysis (Ref 6, 8). Even if the edge singularityis neglected, the stress field in the adhesive isvery complex and nonuniform, with maximumvalues differing markedly from the averagevalue (Ref 6, 8).

Some sense of the complex nature of thestresses can be obtained by visualizing a buttjoint of a low modulus polymer (e.g., a rubber)between two steel cylinders. As these are pulledapart, the rubber elongates much more readilythan the steel. Poisson’s effect will cause a ten-dency for the rubber to contract laterally. How-ever, if it is tightly bound to the metal, it is re-strained from contracting, and shear stresses areinduced at the bond line. Reference 9 providesthe results of a finite element analysis that dem-onstrates how these stresses vary across the sam-

ple. As noted, for an elastic analysis, both theshear and tensile stresses are singular (tendingto infinity) at the outer periphery.

For the tensile specimen configurations con-sidered to this point, the applied loading is in-tended to be axisymmetric. There is anotherclass of specimen in which the dominant stressis deliberately tensile but in which the loadingis obviously “off center.” At least four ASTMstandards describe so-called cleavage specimensand tests. The reader familiar with cohesive frac-ture mechanics will see a similarity between thetest specimen in ASTM D 1062 (“Standard TestMethod for Cleavage Strength of Metal-to-Metal Adhesive Bonds”) as shown in Fig. 15,and the compact tensile specimen commonlyused in fracture mechanics testing. ASTM D1062 specifies reporting the test results as force


Fig. 17 Boeing wedge test (ASTM D 3762). (a) Test specimen.(b) Typical crack propagation behavior at 49 �C (120

�F) and 100% relative humidity. a, distance from load point toinitial crack tip; Da, growth during exposure. Source: Ref 4

Fig. 16 Specimen for testing cleavage peel (by tension load-ing). Source: ASTM D 3807

required, per unit width, to initiate failure in thespecimen, while in fracture mechanics, the re-sults are given as Gc with units of J/m2, whichmight be interpreted as the energy required tocreate a unit surface. A knowledgeable and en-terprising reader may want to adapt the D 1062specimen for obtaining fracture mechanics pa-rameters. ASTM D 3807, “Standard TestMethod for Strength Properties of Adhesives inCleavage Peel by Tension Loading,” uses a dif-ferent geometry to measure the cleavagestrength. In this case, two 25.4 mm (1 in.) wideby 6.35 mm (0.25 in.) thick plastic strips 177mm (7 in.) long are bonded over a length of 76mm (3 in.) on one end, leaving the other endsfree and separated by the thickness of the ad-hesive. Approximately 25 mm (1 in.) from theend of each of these free segments, a “grippingwire” is attached as shown in Fig. 16. Duringtesting, these wires are clamped in the jaws of auniversal testing machine and the sample pulledto failure. The results are reported as load perunit width (kg/m or lb/in.).

ASTM D 5041 (“Standard Test Method forFracture Strength in Cleavage of Adhesives inBonded Joints”) also makes use of a samplecomposed of two thin sheets bonded togetherover part of their length. In this case, forcing awedge (45� angle) between the unbonded por-tion of the sheets facilitates the separation. Theresults are typically given as “failure initiationenergy” or “failure propagation energy” (i.e., ar-eas under the load deformation curve).

This latter test is similar to another test, for-malized as ASTM D 3762 (“Standard TestMethod for Adhesive-Bonded Surface Durabil-ity of Aluminum—Wedge Test”) that has beenfound very useful for studying time-environ-mental effects on adhesive bonds. This test iscalled by various names, but is commonly re-ferred to as the “Boeing Wedge Test” (Ref 10,11). The test has been used by personnel at thisand other aerospace companies to screen variousadhesives, surface treatment, and so on for long-term loading at high temperatures and humidi-

ties. For testing, two long, slender strips of can-didate structural materials are first treated withthe prescribed surface treatment(s) and bondedover part of their length with a candidate adhe-sive (Fig. 17). As in the test described in theprevious paragraph, the free ends are forcedapart by a wedge. The amount of separation bythe wedge (determined by wedge thickness anddepth of insertion) determines the value of thestresses in the adhesive. These stresses can, ofcourse, be adjusted and the values calculatedfrom mechanics of material concepts. When thewedge is in place, the sample is placed in anenvironmental chamber. At periodic time inter-vals, the length of the crack is measured, and aplot of crack length versus time is constructed.The more satisfactory adhesives and/or surfacetreatments are those for which the crack is ar-rested or grows very slowly. While the environ-mental chamber typically contains hot, humidair, there is no reason why other environmentalagents cannot be studied by the same method,including immersion in liquids.

Testing of Welded Joints

Testing for mechanical properties of strengthand ductility for welded joints is somewhat more


complicated than it is for base metal, becausethese properties vary across the weld metal, theadjacent heat-affected zone (HAZ), and the basemetal. Several different tests may be used orcombined to assess the strength of the overallwelded joints. Tensile testing is widely used tomeasure the strength and ductility of the weldmetal alone. Tensile testing of welds in place,with weld metal, HAZ, and base metal, allowsan overall strength to be determined but usuallycannot provide the strengths of the individualparts of the weldment.

Tensile tests of welds can also measure elasticmodulus. However, except in rare cases of dis-similar metal joining, the elastic modulus is notsensitive to the differences between weld, HAZ,and base metal. So, measurement during weldtensile tests is not usually required. Also, mosttensile testing procedures for weld joints cannotbe relied upon to provide accurate values of elas-tic modulus. The specific procedures for testingof elastic modulus distributed by ASTM shouldbe used if required (Ref 12).

Testing of Weld Material. Deposited weldmetal can be tested for the mechanical propertiesof strength and ductility using the same testmethods used for base metals (Ref 13, 14). How-ever, a sufficient volume of deposited weldmetal is required to remove a test specimenmade entirely of weld metal. Often, arc weldsare long only in one direction (the longitudinaldirection), while the through-thickness andcross-weld directions are much smaller. This en-courages all-weld-metal tensile test specimensto be removed with the long direction of thespecimen corresponding to the longitudinal di-rection of the weld. Such longitudinal tensile testspecimens are standard for all-weld-metal tests.

All-weld-metal tests are most commonly doneon specimens with round cross section. The di-ameter of the specimen may need to be reducedfrom that used for base metal so that the speci-men can be taken entirely from weld metal. Rec-tangular cross-section specimens also are usedoccasionally.

Ultimate tensile strength, yield strength (usu-ally based either on yield point or a specifiedoffset), elongation, and reduction of area are allcommonly recorded.

While the specimen surface should besmooth, without deep machining marks, imper-fections within the gage length due to weldingshould not be removed. This requirement mayincrease the variability of results within a groupof similar specimens.

If the data required are for a class of weldmaterial such as an electrode lot, the materialcan be taken from specimens that reduce thepossibility of dilution of base metal into theweld, such as a built-up weld pad. If the datarequired are for a particular weldment, the ge-ometry as well as the welding process and pro-cedure should model those of the weldment asclosely as possible. Some modifications of theweldment may be allowed, such as increasingthe root opening by 6 mm (1⁄4 in.) or butteringthe groove faces with the weld metal to betested. The surface of the tested section, in thegage length, is recommended to be 3 mm (1⁄8 in.)or more from the fusion line.

Testing of Welds in Place. When the weldmetal extends over only part of the tested gagelength, tensile tests can be performed similar tothose performed on the round and rectangularspecimen tests of weld metal. The nonuniform-ity of deformation or stresses of the weld, HAZ,and base metal combination limits the informa-tion normally recorded.

For transverse tests, ultimate strength and thelocation of fracture are the only commonly re-corded parameters, because strength, elongation,and reduction in area will all be affected by theconstraint of the adjacent differing materials. Ifthe weld is undermatched, the yield strengthtends to be higher than it is for an all-weld-metalspecimen, while the elongation over the gagelength and reduction in area are smaller. If theweld yield strength exceeds that of the base ma-terial, that is, it is overmatched, the failure tendsto occur not in the adjacent HAZ, but in the basematerial closer to the end of the gage length,because of the constraint provided by the high-strength weld metal.

Local strain measurements, such as thosemade by strain gages, can add useful informa-tion to the results of transverse testing. The localstrain information can be correlated to the loadand displacement information to allow localstrengths to be determined.

For longitudinal tests, the strain will be nearlyuniform across the weld metal, HAZ, and basemetal. Differences in response to the appliedstrain may result in stresses varying across thecross section. Only ultimate strength is com-monly measured.

Testing standards may need to be varied forsome specific geometries. For instance, girthwelded tubes of less than 75 mm (3 in.) diameterare commonly tested in the form of tubes withcentral plugs at the grips. The weld is placed at


the center of the gage length between the grips.The additional constraint induced by the hoopdirection continuity tends to increase the mea-sured strengths and decrease the measured duc-tilities for tube welds tested in this manner com-pared to a similar joint between flat sheets.

ACKNOWLEDGMENTS


● R.S. Shoberg, Mechanical Testing ofThreaded Fasteners and Bolted Joints, Me-chanical Testing and Evaluation, Vol 8, ASMHandbook, ASM International, 2000, p 811–835

● K.L. Devries and P. Borgmeier, Testing ofAdhesive Joints, Mechanical Testing andEvaluation, Vol 8, ASM Handbook, ASM In-ternational, 2000, p 836–844

● W. Mohr, Mechanical Testing of WeldedJoints, Mechanical Testing and Evaluation,Vol 8, ASM Handbook, ASM International,2000, p 845–852

REFERENCES

1. H.E. Fairman, Overview of MechanicalProperties for Component Design, Mechan-ical Testing and Evaluation, Vol 8, ASMHandbook, ASM International, 2000, p789–797

2. R.S. Shoberg, Mechanical Testing ofThreaded Fasteners and Bolted Joints, Me-chanical Testing and Evaluation, Vol 8,ASM Handbook, ASM International, 2000,p 811–835

3. “Standard Test Method for Determining theMechanical Properties of Externally and In-ternally Threaded Fasteners, Washers, andRivets (Metric),” ASTM F 606M, AnnualBook of ASTM Standards, ASTM

4. K.L. Devries and P. Borgmeier, Testing ofAdhesive Joints, Mechanical Testing andEvaluation, Vol 8, ASM Handbook, ASMInternational, 2000, p 836–844

5. Adhesives, Annual Book of ASTM Stan-dards, Vol 15.06, ASTM (updated annually)

6. G.P. Anderson and K.L. DeVries, Analysisof Standard Bond-Strength Tests, Treatiseon Adhesion and Adhesives, Vol 6, R.L. Pat-rick, K.L. DeVries, and G.P. Andersen, Ed.,Marcel Dekker, 1989

7. J.K. Strozier, K.J. Ninow, K.L. DeVries, andG.P. Anderson, Adhes. Sci. Rev., Vol 1,1987, p 121

8. G.P. Anderson, D.H. Brinton, K.J. Ninow,and K.L. DeVries, A Fracture MechanicsApproach to Predicting Bond Strength, Ad-vances in Adhesively Bonded Joints, Pro-ceedings of a Conference at the Winter An-nual Meeting of ASME, 27 Nov–2 Dec 1988(Chicago), S. Mall, K.M. Liechti, and J.K.Vinson, Eds., ASME, 1988, p 98–101

9. G.P. Anderson and K.L. DeVries, PredictingStrength of Adhesive Joints from Test Re-sults, Int. J. Fract., Vol 39, 1989, p 191–200

10. V.L. Hein and F. Erodogan, Stress Singu-larities in a Two-Material Wedge, Int. J.Fract., Vol 7, 1971, p 317

11. J.A. Marceau, Y. Moji, and J.C. McMillan,A Wedge Test for Evaluating AdhesiveBonded Surface Durability, 21st SAMPESymposium, Vol 21, 6–8 April 1976

12. “Standard Test Method for Young’s Modu-lus, Tangent Modulus, and Chord Modu-lus,” E 111, Annual Book of ASTM Stan-dards, Vol 3.01, ASTM, 1999

13. “Standard Methods of Tension Testing ofMetallic Materials,” E 8, Annual Book ofASTM Standards, Vol 3.01, ASTM, 1999

14. “Standard Methods of Tension TestingWrought and Cast Aluminum, and Magne-sium Alloy Products,” B 557, Annual Bookof ASTM Standards, Vol 3.01, ASTM, 1999

CHAPTER 13

Hot Tensile Testing

HIGH-TEMPERATURE MECHANICALPROPERTIES of metals are determined by threebasic methods:

● Short-term tests at elevated temperatures● Long-term tests of creep deformation at el-

evated temperatures● Short-term and long-term tests following

long-term exposure to elevated temperatures

This chapter focuses on short-term tensile test-ing at high temperatures. Such tests are com-monly referred to as hot tensile, or hot tension,tests. The basic methods and specimens for thesetests are similar to room-temperature testing, al-though the specimen heating, test setup, and ma-terial behavior at higher temperatures do intro-duce some additional complexities and specialissues for hot tensile testing.

Emphasis in this chapter has been put on oneof the most important reasons for conducting hottensile tests—the determination of the hot work-ing characteristics of metallic materials. Theproper hot-working temperature and deforma-tion rate must be established to produce high-quality wrought products of complicated ge-ometries. It is also important that product yieldlosses (from either grinding to remove surfacecracks or excessive cropping to remove endsplits) be held to a minimum, while avoiding theformation of internal cavities (pores). Severecracking is ordinarily the result of high surfacetensile stresses introduced when hot working isconducted either above or below the temperaturerange of satisfactory ductility. Similarly, cavi-tation is associated with internal tensile stresses,which, for a given material, depend on the tem-perature, the deformation rate, and workpiece/die geometry.

The first and most important step in specify-ing appropriate hot-working practice is to deter-mine suitable hot-working conditions. In partic-ular, the tensile ductility (e.g., fracture strain),

the flow stress, and cavity formation conditionsshould be established as a function of tempera-ture and strain rate. A curve of ductility versustemperature or strain rate shows what degree ofdeformation the material can tolerate withoutfailure. On the other hand, a plot of the flowstress versus temperature, along with workpiecesize and strain rate, indicates the force levels re-quired of the hot-working equipment. Last, acurve of cavity volume fraction versus strain,strain rate, and temperature shows what pro-cessing parameters should be selected in orderto produce high-quality products.

Although commercial metalworking opera-tions cannot be analyzed in terms of a simplestress state, workpiece failures are caused by lo-calized tensile stresses in most instances (Ref 1–4). In rolling of plate, for example, edge crack-ing is caused by tensile stresses that form atbulged (unrestrained) edges (Ref 1, 3, 4). Thegeometry of these unrestrained surfaces affectsthe magnitude of tensile stresses at these loca-tions. Moreover, tensile stresses are also createdon the unrestrained surface of a round billet be-ing deformed with open dies. Therefore, to ob-tain a practical understanding of how well a ma-terial will hot work during primary processing,it is essential to know how it will respond totensile loading at the strain rates to be imposedby the specific hot-working operation.

The ideal hot-workability test is one in whichthe metal is deformed uniformly, without insta-bility, at constant true strain rate under well-con-trolled temperature conditions with continuousmeasurement of stress, strain, and temperatureduring deformation followed by instantaneousquenching to room temperature. Two types ofhot tensile tests are discussed in this chapter: theGleeble test and the conventional isothermalhot-tensile test. The major advantage of the hottensile test is that its stress/strain state simulatesthe conditions that promote cracking in most in-




Fig. 1 Gleeble test unit used for hot-tension and hot-compression testing. (a) Specimen in grips showing attached thermocouplewires and linear variable differential transformer (LVDT) for measuring strain. (b) Close-up of a test specimen. Courtesy of

Duffers Scientific, Inc.

dustrial metalworking operations. However,even though the tensile test is simple in nature,it may provide misleading information if notproperly designed. Specifically, parameters suchas the specimen geometry, tension machinecharacteristics, and strain rate and temperaturecontrol all influence the results of the tensiontest. Therefore, the tensile test should be de-signed and conducted carefully, and testing pro-cedures should be well documented when dataare reported.

Equipment and Testing Procedures

The apparatus used to conduct hot tensile testscomprises a mechanical loading system andequipment for sample heating. A variety ofequipment types are used for applying forces(loads) to test specimens. These types rangefrom very simple devices to complex systemsthat are controlled by a digital computer. Themost common test configurations utilize univer-sal testing machines, which have the capabilityto test material in tension, compression, or bend-ing. The word universal refers to the variety ofstress states that can be applied by the machine,in contrast to other conventional test machinesthat may be limited to either tensile loading orcompressive loading, but not both. Universaltest machines or tension-only test frames mayapply loads by a gear (screw)-driven mechanismor hydraulic mechanisms, as discussed in moredetail in the section “Frame-Furnace Tensile-Testing Equipment” in this chapter.

The heating method used for hot tensile test-ing varies with the application. The most com-

mon heating techniques are direct-resistanceheating (in the case of Gleeble systems) and in-direct-resistance or induction heating with con-ventional load frames. In some cases, universaltest machines may include a special chamber fortesting in either vacuum or controlled atmo-sphere. Specimen (testpiece) temperatures typi-cally are monitored and controlled by thermo-couples, which may be attached on the specimensurface or located very close to the specimen. Insome cases, temperature is measured by opticalor infrared pyrometers. Accurate measurementand control is very critical for obtaining reliabledata. To this end, the use of closed-loop tem-perature controllers is indispensable.

The occurrence of deformation heating mayalso be an important consideration, especially athigh strain rates, because it can significantlyraise the specimen temperature.

Gleeble Testing Equipment

The Gleeble system (Ref 5) has been usedsince the 1950s to investigate the hot tensile be-havior of materials and thus to generate impor-tant information for the selection of hot-workingparameters. A Gleeble unit is a high-strain-rate,high-temperature testing machine where a solid,buttonhead specimen is held horizontally by wa-ter-cooled grips, through which electric power isintroduced to resistance heat the test specimen(Fig. 1). Specimen temperature is monitored bya thermocouple welded to the specimen surfaceat the middle of its length. The thermocouple,with a function generator, controls the heat fedinto the specimen according to a programmedcycle. Therefore, a specimen can be tested under

Hot Tensile Testing / 211

Fig. 2 Typical specimen used for Gleeble testing

time and temperature conditions that simulatehot-working sequences.

Contemporary Gleeble systems (e.g., seewww.gleeble.com) are fully integrated servohy-draulic setups that are capable of applying asmuch as 90 kN (10 tons) of force in tension atdisplacement rates up to 2000 mm/s (80 in./s).Different load cells allow static-load measure-ment to be tailored to the specific application.Control modes that are available include dis-placement, force, true stress, true strain, engi-neering stress, and engineering strain.

The direct-resistance heating system of theGleeble machine can heat specimens at rates ofup to 10,000 �C/s (18,000 �F/s). Grips with highthermal conductivity (e.g., copper) hold thespecimen, thus making the system capable ofhigh cooling rates as well. Thermocouples or py-rometers provide signals for accurate feedbackcontrol of specimen temperature. Because of theunique high-speed heating method, Gleeble sys-tems typically can run hot-tension tests severaltimes faster than conventional systems based onindirect-resistance (furnace) heating methods.

A digital-control system provides all the sig-nals necessary to control thermal and mechani-cal test variables simultaneously through thedigital closed-loop thermal and mechanicalservo systems. The Gleeble machine can be op-erated totally by computer, by manual control,or by any combination of computer and manualcontrol needed to provide maximum versatilityin materials testing.

Sample Design. A typical specimen config-uration used in Gleeble testing is shown in Fig.2. This solid buttonhead specimen, with an over-all length of 88.9 mm (3.5 in.), has an unreducedtest-specimen diameter of 6.35 mm (0.25 in.).The length of the sample between the grips atthe beginning of the test is also an importantconsideration. Generally, this length is 25.4 mm(1 in.). Shorter lengths produce a narrow hotzone and restrict hot deformation to a smaller,constrained region; consequently, the apparentreduction of area is diminished. On the otherhand, a long sample length generally produceshigher apparent ductility/elongation values. Forexample, Smith, et al. (Ref 6) have shown thata grip separation of 36.8 mm (1.45 in.) producesa hot zone about 12.7 mm (0.5 in.) long. Whenspecimen diameter is increased, as is necessaryin testing of extremely coarse-grain materials,the grip separation should also be increased pro-portionately to maintain a constant ratio of hot-zone length to specimen diameter.

Test Procedures. It is essential that hot ten-sile tests be conducted at accurately controlledtemperatures because of the usually strong de-pendence of tensile ductility on this process vari-able. To this end, temperature is monitored by athermocouple percussion welded to the speci-men surface. Using a function generator, heatinput to the specimen is controlled according toa predetermined programmed cycle chosen bythe investigator. However, the temperature mea-sured from this thermocouple junction does notcoincide exactly with the specimen temperaturebecause (a) heat is conducted away from thejunction by the thermocouple wires, and (b) thejunction resides above the specimen surface andradiates heat at a rate higher than that of thespecimen itself. Consequently, the thermocouplejunction is slightly colder than the test specimen.Furthermore, specimen temperature is highestmidway between the grips and decreases towardthe grips. In general, the specimen will fracturein the hottest plane perpendicular to the speci-men axis. Therefore, it is important to place thethermocouple junction midway between thegrips in order that the hottest zone of the spec-imen, which will be the zone of fracture, ismonitored. The longitudinal thermal gradientdoes not present a serious problem because thespecimen deforms in the localized region wherethe temperature is monitored. Consequently, themeasured values of reduction of area and ulti-mate tensile strength represent the zone wherethe thermocouple is attached.

Strain rate is another important variable in thehot tensile test. However, strain rate varies dur-ing hot tensile testing under constant-crosshead-speed conditions and must be taken into accountwhen interpreting test data. An analysis of thestrain-rate variation during the hot-tension testand how it correlates to the strain rates in actualmetalworking operations is presented later inthis chapter.

The load may be applied at any desired timein the thermal cycle. Temperature, load, and


Fig. 3 Hypothetical “on-heating” Gleeble curve of specimen reduction of area as a function of test temperature

crosshead displacement are measured versustime and captured by the data acquisition sys-tem. From these measurements, standard me-chanical properties such as yield and ultimatetensile strength can be determined. The reduc-tion of area at failure is also readily establishedfrom tested samples.

If hot-working practices are to be determinedfor an alloy for which little or no hot-workinginformation is available, the preliminary testprocedure usually comprises the measurementof data “on heating.” In such tests, samples areheated directly to the test temperature, held for1 to 10 min, and then pulled to fracture at a strainrate approximating the rate calculated for themetalworking operation of interest. The reduc-tion of area for each specimen is plotted as afunction of test temperature; the resulting “on-heating” curve will indicate the most suitabletemperature range to be evaluated to determinethe optimal preheat* temperature. This tempera-ture, as indicated from the plot in Fig. 3, liesbetween the peak-ductility (PDT) and zero-duc-tility (ZDT) temperatures.

To confirm the appropriate selection of pre-heat temperature, specimen blanks should be

*In the context of this chapter, preheat temperature is thetemperature at which the test specimen or workpiece is heldprior to deformation at lower temperatures. In actual met-alworking operations, preheat temperature usually refers tothe actual furnace temperature.

heat treated at the proposed preheat temperaturefor a time period equal to that of a furnace soakcommensurate with the intended workpiece sizeand hot-working operation. These specimensshould be water quenched to eliminate any struc-tural changes that could result from slow cool-ing. Subsequently, the specimens should betested by heating to the proposed furnace tem-perature, holding at this preheat temperature fora moderate period of time (1 to 10 min) to re-dissolve any phases that may have precipitated,cooling to various temperatures at intervals of25 or 50 �C (45 or 90 �F) below the preheattemperature, holding for a few seconds at thedesired test temperature, and finally pulling intension to fracture at the calculated strain rate.These “on-cooling” data demonstrate how thematerial will behave after being preheated at ahigher temperature. Testing “on cooling” is nec-essary because the relatively short hold timesduring testing “on heating” may not develop agrain size representative of that hold temperatureand may be insufficient to dissolve or precipitatea phase that may occur during an actual furnacesoak prior to hot working. Also, most industrialhot metalworking operations are conducted asworkpiece temperature is decreasing. The “on-cooling” data will indicate how closely the ZDTcan be approached before hot ductility is seri-ously or permanently impaired. In addition, ifdeformation heating (Ref 7) during “onheating”tests has resulted in a marked underestimation


of the maximum preheat temperature, this willbe revealed and can be rectified by examinationof “on-cooling” data.

Frame-Furnace Tensile-Testing Equipment

Universal testing machines and tensile-testframes can be used for hot tensile tests by at-taching a heating system to the machine frame.The frame may impart loading by either a screw-driven mechanism or servohydraulic actuator.Screw-driven (or gear-driven) machines are typ-ically electromechanical devices that use a largeactuator screw threaded through a moving cross-head. The screws can turn in either direction,and their rotation moves a crosshead that appliesa load to the specimen. A simple balance systemis used to measure the magnitude of the forceapplied.

Loads may also be applied using the pressureof oil pumped into a hydraulic piston. In thiscase, the oil pressure provides a simple meansof measuring the force applied. Closed-loopservohydraulic testing machines form the basisfor the most advanced test systems in use today.Integrated electronic circuitry has increased thesophistication of these systems. Also, digitalcomputer control and monitoring of such testsystems have steadily developed since their in-troduction around 1965. Servohydraulic test ma-chines offer a wider range of crosshead speedsof force ranges with the ability to provide eco-nomically forces of 4450 kN (106 lbf ) or more.Screw-driven machines are limited in their abil-ity to provide high forces due to problems as-sociated with low machine stiffness and largeand expensive loading screws, which become in-creasingly more difficult to produce as the forcerating goes up.

For either a screw-driven or servohydraulicmachine, the hot tensile test system is a loadframe with a heating system attached. A typicalservohydraulic universal testing machine with ahigh-temperature chamber is shown in Fig. 4.The system is the same as that used at roomtemperature, except for the high-temperature ca-pabilities, including the furnace, cooling system,grips, and extensometer. In this system, the gripsare inside the chamber but partly protected byrefractory from heating elements. Heating ele-ments are positioned around a tensile specimen.Thermocouple and extensometer edges touchthe specimen. The grip design and the specimengeometry depend on the specific features of theframe and the heating unit as well as the testing

conditions. Temperature is measured by ther-mocouples attached on or located very near tothe specimen. In some cases, a pyrometer canalso be used.

The most common methods of heating in-clude induction heating and indirect-resistanceheating in chamber. Typical examples are shownin Fig. 5. Induction heating (Fig. 5a) usually al-lows faster heating rates than indirect heatingdoes, but accurate temperature control requiresextra care. Induction-heating systems can reachtesting temperatures within seconds. Inductionheating heats up the outer layer of the specimenfirst. Furnaces with a lower frequency have bet-ter penetration capability. Coupling the heatingcoil and the specimen also plays an importantrole in heating efficiency. The interior of thespecimen is heated through conduction. With therapid heating rate, the temperature is often over-shot and nonuniform heating often occurs.

Indirect-resistance heating may provide bettertemperature control/monitoring than inductionheating can. Indirect-resistance heating can becombined readily with specially designed cham-bers for testing either in vacuum or in a con-trolled atmosphere (e.g., argon, nitrogen, etc.).Vacuum furnaces are expensive and have highmaintenance costs. The furnace has to bemounted on the machine permanently, making itinconvenient if another type of heating device isto be used. The heating element is expensive andoxidizes easily. The furnace can only be openedat relatively lower temperatures to avoid oxida-tion. Quenching has to be performed with aninert gas, such as helium.

Environmental chambers (Fig. 5b), which areless expensive than vacuum chambers, have acirculation system to maintain uniform tempera-ture inside the furnace. Inert gas can flowthrough the chamber to keep the specimen fromoxidizing. Temperature inside the chamber canbe kept to close tolerance (e.g., about �1 �C, or�2 �F). However, the maximum temperature ofan environmental chamber is usually 550 �C(1000 �F), while that of a vacuum furnace canbe as high as 2500 �C (4500 �F). The chambercan either be mounted on the machine or rolledin and out on a cart. Split-furnace designs (Fig.5c) are also cost effective and easy to use. Whennot in use, it can be swung to the side. The splitfurnace shown in Fig. 5(c) has only one heatingzone. More sophisticated split furnaces havethree heating zones for better temperature con-trol. Heating rate is also programmable. Whenfurnace heating is used, it is a common practice


Fig. 4 Typical servohydraulic universal testing machine with a chamber and instrumentation for high-temperature testing

to use a low heating rate. In addition, the spec-imen is typically “soaked” at the test tempera-ture for about 10 to 30 min prior to the appli-cation of the load.

The mechanical and thermal control systemsare similar to those described in the previoussection on the Gleeble testing apparatus. Themain advantage of hot tensile test machines isthat the test specimen is heated uniformly alongits entire gage length, and hence other useful ma-terials properties such as total tensile elongation,plastic anisotropy parameter, cavity formation,and so forth can be determined in addition toyield/ultimate tensile strength and reduction ofarea. On the other hand, the overall time neededto conduct a single test may be longer than inthe Gleeble test method.

Specimen Geometry. In tensile testing, elon-gation values are influenced by gage length. Itis thus necessary to state the gage length overwhich elongation values are measured. Whenthe ductilities of different materials (or of a sin-gle material tested under different conditions)are compared in terms of total elongation, thespecimen gage length also should be adjusted inproportion to the cross-sectional area. This is ofgreat importance in the case of small elonga-tions, because the neck strain contributes a sig-nificant portion to the total strain. On the otherhand, the neck strain represents only a small por-tion of the elongation in the case of superplasticdeformation. Unwin’s equation (Ref 8) alsoshows the rationale for a fixed ratio of gagelength with cross-sectional area, expressed as a


Fig. 6 Initial specimen geometry and deformed specimen for cases in which (a) shoulder deformation occurred (Ref 9) or (b) theshoulder remained undeformed (Ref 10)

fixed ratio of gage length to diameter (for roundbars) or gage length to the square root of thecross-sectional area (sheet specimens). This re-inforces the importance of stating the gagelength used in measuring elongation values.Usually, the length-to-diameter ratio is between4 and 6.

In addition to the gage length, the specimenshoulder geometry and hence the gripping sys-tem are also important design considerations. Itis desirable that specimen deformation takesplace only within its gage length; the shouldershould remain undeformed. This is not alwaysthe case, as can be seen from Fig. 6. The mac-rographs of Fig. 6(a) (Ref 9) show the initial anddeformed condition of a specimen in whichmeasurable deformation has occurred within thegrip area. On the other hand, the specimen witha different shoulder geometry (Fig. 6b) de-formed essentially only along its gage length(Ref 10). The shoulder-deformation problem is

not insurmountable. In this regard, analyses andtechniques, such as those developed by Fried-man and Ghosh (Ref 9), should be applied inorder to eliminate the effect of shoulder defor-mation from measured hot-tensile data.

Hot Ductility andStrength Data from the Gleeble Test

The reduction of area (RA) and strength arethe key parameters measured in hot tensile testsconducted with a Gleeble machine (Ref 1, 11,12). Because RA is a very structure-sensitiveproperty, it can be used to detect small ductilityvariations in materials of low to moderate duc-tility, such as specialty steels and superalloys.However, it should be recognized that RA willnot effectively reveal small variations in mate-rials of extremely high ductility (Ref 2). Yield

Fig. 5 Typical examples of heating methods for load-frame tensile testing. (a) Induction heating. (b) Environmental chamber. (c) Split-furnace setup


Table 1 Qualitative hot-workability ratings for specialty steels and superalloys

Hot-tension reductionof area(a), %

Expected alloy behavior under normalhot reductions in open die Remarks regarding alloy hot-working practice

�30 Poor hot workability. Abundant cracks Preferably not rolled or open-die forged. Extrusion may befeasible. Rolling or forging should be attempted only withlight reductions, low strain rates, and an insulating coating.

30–40 Marginal hot workability. Numerous cracks This ductility range usually signals the minimum hot-workingtemperature. Rolled or press forged with light reductions andlower-than-usual strain rates.

40–50 Acceptable hot workability. Few cracks Rolled or press forged with moderate reductions and strainrates

50–60 Good hot workability. Very few cracks Rolled or press forged with normal reductions and strain rates60–70 Excellent hot workability. Occasional cracks Rolled or press forged with heavier reductions and strain rates�70 Superior hot workability. Rare cracks. Ductile

ruptures can occur if strength is too low.Rolled or press forged with heavier reductions and higher

strain rates than normal provided that alloy strength issufficiently high to prevent ductile ruptures.

(a) Ratings apply for Gleeble tensile testing of 6.25 mm (0.250 in.) diam specimens with 25.4 mm (1 in.) head separation.

and tensile strength can be used to select re-quired load capacity of production processingequipment.

Ductility Ratings

Experience has indicated that the qualitativeratings given in Table 1 for hot ductility as afunction of Gleeble reduction-of-area data canbe used to predict hot workability, select hot-working temperature ranges, and establish hot-reduction parameters. “Normal reductions”*may be taken on superalloys when the reductionof area exceeds 50%, but lighter reductions arenecessary when ductility falls below this level.Thus, in this rating system, the minimum hot-working temperature is designated by the tem-perature at which the reduction of area falls be-low approximately 30 to 40%. The maximumhot-working temperature is determined from“on-cooling” data. The objective is to determinewhich preheat temperature provides the highestductility over the broadest temperature rangewithout risking permanent structural damage byoverheating.

An alloy with hot-tensile ductility rated asmarginal or poor may be hot worked, but smallerreductions and fewer passes per heating are re-quired, perhaps in combination with insulatingcoatings and/or coverings. In extreme instances,it may be necessary to minimize development oftensile strains by employing special dies for de-forming under a strain state that more nearly ap-proaches hydrostatic compression (e.g., extru-sion).

*“Normal reductions” as used in this chapter depend on boththe alloy system being hot worked and the equipment beingused. For example, normal reductions for low-carbon steelswould be much greater than those for superalloy systems.

It should be emphasized that the hot tensiletest reflects the inherent hot ductility of a ma-terial, that is, its natural ability to deform underdeformation conditions. If a workpiece pos-sesses defects or flaws, it may crack due to lo-calized stress concentration in spite of good in-herent hot ductility.

Figure 3 illustrates how hot tensile data areused to select a hot-working temperature. Thesafe, maximum hot-working temperature liesbetween the PDT and the ZDT. In this hypo-thetical curve of “on-heating” data, the PDT is1095 �C (2000 �F) and the ZDT is 1200 �C (2200�F). “On-cooling” data should be determined us-ing preheat temperatures between the PDT andthe ZDT. For example, 1095, 1150, 1175, and1200 �C (2000, 2100, 2150, and 2200 �F) wouldbe good preheat temperatures for “on-cooling”studies. Typical “on-cooling” results are de-picted in Fig. 7. A 1200 �C (2200 �F) preheattemperature results in marginal or poor hotworkability over the possible working range,whereas an 1175 �C (2150 �F) preheat tempera-ture results in acceptable hot workability over arelatively narrow temperature range. Both 1150and 1095 �C (2100 and 2000 �F) preheats resultin good hot ductility over a relatively narrowtemperature range. The 1150 �C preheat tem-perature is preferred over the 1095 �C preheattemperature because it provides good hot duc-tility over a broader temperature range.

Hot workability usually is enhanced bygreater amounts of prior hot deformation. Thisoccurs because second phases and segregation-prone elements are distributed more uniformlyand the grain structure is refined. Deformationat high and intermediate temperatures duringcommercial hot-working operations often re-fines the grain structure by dynamic (or static)


Fig. 7 Typical “on-cooling” Gleeble curves of specimen reduction of area as a function of test and preheat temperatures with typicalhot-workability ratings indicated

recrystallization, thereby augmenting subse-quent hot ductility at lower temperatures. Be-cause a specimen tested “on cooling” to the low-temperature end of the hot-working range hasnot been deformed at a temperature where grainsdynamically recrystallize, the grain structure isunrefined. Thus, ductility values will tend to besomewhat lower than those experienced in anactual metalworking operation in which defor-mation at higher temperatures has refined thestructure. The fact that the low-temperature endof the “on-cooling” ductility range is lower thanthe values that would result in plant metalwork-ing operations is not sufficient to alter the prac-tical translation of the results. This feature servesas a safety factor for establishing the minimumhot-working temperature.

Although some alloys will recover hot ductil-ity when cooled from temperatures in the vicin-ity of the ZDT, it is nonetheless wise to avoidhot-working preheat temperatures approachingthe ZDT in plant practice because interior re-gions of the workpiece may not cool sufficientlyto allow recovery of ductility, thereby causingcenter bursting. Because industrial furnaces donot control closer than approximately �14 �C(�25 �F), the recommended furnace tempera-ture ordinarily should be at least 14 �C (25 �F)lower than the maximum temperature indicatedby testing “on cooling.”

Strength Data

In the hot-working temperature range,strength generally decreases with increasingtemperature. However, the strength data plottedin Fig. 8 demonstrate that deformation resistancedoes not vary with preheat temperature to thesame degree as does ductility. Furthermore,strength measured “on heating” is usuallygreater than that measured “on cooling.”

To calculate the force required to deform ametal in an industrial hot-working operation, ac-curate measurement of flow stress is desirable.Ultimate tensile stress measured in the hot ten-sile test is only slightly greater than flow stressat the high-temperature end of the hot-workingrange because work hardening is negligible.However, the difference between ultimate ten-sile stress and flow stress increases as tempera-ture decreases because restoration processescease. Furthermore, the Gleeble tensile test doesnot accurately determine flow stress because thestrain rate is not constant. Nonetheless, the teststill provides useful, comparative informationconcerning how the strength of an alloy variesas a function of temperature within a givenstrain-rate range. For example, by analyzingstrength values for common alloys in relation tothe load-bearing capacity of a given mill, it maybe possible to use test data for a new or unfa-


Fig. 8 Typical “on-heating” deformation-resistance data obtained in Gleeble testing

miliar alloy in judging whether the equipment iscapable of forming the new or unfamiliar alloy.

Hot Tensile Data for Commercial Alloys

For illustrative and comparative purposes,Gleeble hot ductility and strength curves forsome commercial alloys are presented in Fig. 9.The nominal compositions of these materials aregiven in the table accompanying Fig. 9.

The hot tensile strengths for the cobalt- andnickel-base superalloys over the hot-workingtemperature range are substantially higher thanthose for the high-speed tool steel and the high-strength alloy, which are iron-base materials.Furthermore, the ductility data reveal that Rene41 has the narrowest hot-working temperaturerange (DT) of 140 �C (250 �F) of the three su-peralloys. Hot working of this alloy below 1010�C (1850 �F) will lead to severe cracking. Thischaracteristic, coupled with its high deformationresistance, makes this alloy relatively difficult tohot work. On the other hand, HS 188 has highdeformation resistance, but it has high ductilityover a broad hot-working temperature rangefrom 1190 �C (2175 �F) to below 900 �C (1650�F). Therefore, the permissible reduction perdraft may be relatively small if the hot-workingequipment is not capable of high loads, but HS188 can be hot worked over a broader tempera-ture range than Rene 41. However, if the equip-ment has high load capacity, then heavier reduc-tions can be taken on HS 188 than on Rene 41.From the hot-working curves established for theiron-base, high-strength alloy AF 1410, the low

deformation resistance coupled with high duc-tility over a broad temperature range indicatethat this material has extremely good hot work-ability. Mill experience has verified this. Thecurves shown for M42, the high-speed tool steel,reveal that it is intermediate in hot workabilitybetween the superalloys and AF 1410; this con-clusion has also been verified by mill experi-ence.

Figures 10 and 11 illustrate the variation ofhot tensile ductility values at various tempera-tures. These results were correlated to the frac-ture surfaces and structures of the test speci-mens. For the high-strength iron-base alloy AF1410, the “on-heating” curve in Fig. 10 showsthat the ZDT is never reached at practical upper-limit hot-working temperatures. At the highesttemperature tested (1230 �C, or 2250 �F) and atthe PDT (1120 �C, or 2050 �F), where hot-tensileductility is extremely high, the fracture appear-ance is ductile and dynamic recrystallization oc-curs, leading to an equiaxed grain structure. Atthe higher temperature, a coarser grain structureresults from grain growth, which accounts forthe drop in ductility. At the opposite end of thehot-working temperature range (842 �C, or 1548�F), the elongated grain structure reveals that dy-namic recrystallization does not occur, and thefracture surfaces indicate a less ductile fracturemode. The correlation among fracture appear-ance, microstructure, and hot tensile ductilitywas even more evident for a developmentalsolid-solution-strengthened cobalt-base super-alloy (Fig. 11). At the PDT (1150 �C, or 2100�F), dynamic recrystallization occurs, fracture


Fig. 9 Typical “on-cooling” Gleeble curves of strength and ductility as functions of test temperature for several commercial alloys.

was primarily transgranular, and the fracture ap-pearance was ductile. At the ZDT (1200 �C, or2200 �F), both static recrystallization and graingrowth were obvious, but incipient melting was

not evident in the microstructure. Microstruc-tural evidence of incipient melting at the ZDTis observed for some alloys, but not for others(Ref 13).


Fig. 10 Typical Gleeble curve of reduction of area versus test temperature for an aircraft structural steel (AF 1410). At the PDT,dynamic recrystallization occurs leading to an equiaxed grain structure. Fracture appearance is ductile.

An example of the sensitivity of the hot ten-sile Gleeble test is shown in Fig. 12 for iron/nickel-base superalloy Alloy 901 (Ref 14). Asmall amount of lanthanum added to one heat(top curve) was sufficient to reduce the analyzedsulfur content to the 1 to 5 ppm range. This re-sulted in a small improvement in the hot tensileductility according to Gleeble hot-tensile data.

Isothermal Hot Tensile Test Data

From the isothermal hot tensile test, infor-mation can be obtained about a number of ma-

terial parameters that are important with regardto metalworking process design. These includeplastic-flow (stress-strain) behavior, plasticanisotropy, tensile ductility, and their variationwith the test temperature and the strain rate.


Engineering stress-strain curves from isother-mal hot tensile tests are constructed from load-elongation measurements. The engineering, ornominal, stress is equal to the average axialstress and is obtained by dividing the instanta-neous load by the original cross-sectional area

Fig. 11 Typical Gleeble curve of reduction area versus test temperature for a cobalt-base superalloy.


Fig. 12 Gleeble ductility curves for lanthanum-bearing and standard Alloy 901 tested on cooling from 1120 �C (2050 �F). Note thatthe lanthanum-bearing heat displays slightly higher ductility. Specimens represent transverse orientation on a nominal 25

cm square billet. Specimen blanks were heat treated at 1095 �C (2005 �F) for 2 h and then water quenched prior to machining.Specimenswere heated to 1120 �C (2050 �F), held for 5 min, cooled to test temperature and held for 10 s before being tested at a nominal strainrate of 20 s�1 (crosshead speed 5 cm/s; jaw spacing, 2.5 cm). Source: Ref 14

of the specimen. Similarly, the engineering, ornominal, strain represents the average axialstrain and is obtained by dividing the elongationof the gage length of the specimen by its originallength. Hence, the form of the engineeringstress-strain curve is exactly the same as that ofthe load-elongation curve. Examples of engi-neering stress-strain curves obtained from hot-tension testing of an orthorhombic titanium al-uminide alloy (Ref 15) at 980 �C (1800 �F) anda range of nominal (initial) strain rates areshown in Fig. 13. The curves exhibit a stressmaximum at strains less than 10%, a regime ofquasi-stable flow during which a diffuse neckdevelops and the load drops gradually, and,lastly, a period of rapid load drop during whichthe flow is highly localized (usually in the centerof the specimen gage length) and failure occurs.The engineering stress-strain curve does notgive a true indication of the deformation char-acteristics of a metal because it is based entirelyon the original dimensions of the specimen.These dimensions change continuously duringthe test. Such changes are very significant whentesting is performed at elevated temperatures.

The true stress and true strain are based onactual (instantaneous) cross-sectional area andlength measurements at any instant of defor-mation. The true-stress/true-strain curve is alsoknown as the flow curve since it represents thebasic plastic-flow characteristic of the materialunder the particular (temperature-strain rate)

testing conditions. Any point on the flow curvecan be considered the yield stress for a metalstrained in tension by the amount shown on thecurve. An example of the variation of the truestress versus true strain for Al-8090 alloy de-formed under superplastic conditions (T � 520�C, � 7.8 � 10�4 s�1) is shown in Fig. 14e(Ref 16). Under these conditions, it is apparentthat the flow stress is almost independent ofstrain. For ideal superplastic materials, the flowstress is independent of strain. A nearly constant,or steady-state, flow stress is also frequently ob-served at hot-working temperatures in materialsthat undergo dynamic recovery. In these cases,steady-state flow is achieved at strains of the or-der of 0.2, at which the rate of strain hardening

Fig. 13 Engineering stress-strain curves for an orthorhombictitanium alloy (Ti-21Al-22Nb) tested at 980 �C (1795

�F) and a range of initial strain rates (s�1). Source: Ref 15


Fig. 14 True-stress/true-strain data for an Al-8090 alloy de-formed in tension at 520 �C (970 �F) and a true strain

rate of 7.8 � 10�4 s�1. Source: Ref 16

Fig. 15 True-stress/true-strain curves obtained from tensiletesting of submicrocrystalline TiAl samples. Source:

Ref 17

due to dislocation multiplication is exactly bal-anced by the rate of dislocation annihilation bydynamic recovery.

The variation of true stress with true strain canalso give insight into microstructural changesthat occur during hot deformation. For example,for superplastic materials, an increase in the flowstress with strain is normally indicative of strain-enhanced grain growth. A decrease in flowstress, particularly at high strains, can often im-ply the development of cavitation damage (seethe section “Cavitation During Hot Tensile Test-ing” in this chapter) or the occurrence ofdynamic recrystallization. As an example, true-stress/true-strain curves for a c-TiAl submicro-crystalline alloy deformed at temperatures be-tween 600 and 900 �C (1110 and 1650 �F) anda nominal (initial) strain rate of 8.3 � 10�4 s�1

are shown in Fig. 15 (Ref 17). These curves re-veal that deformation at low temperatures, atwhich nonsuperplastic conditions prevail, ischaracterized by an increase of flow stress withstrain due to the strain hardening. At higher tem-peratures, the effect of strain on the flow stressdecreases until it becomes negligible at the high-est test temperature, thus indicating the occur-rence of superplastic flow.

Material Coefficients fromIsothermal Hot Tensile Tests

A number of material coefficients can be ob-tained from isothermal hot tensile tests. These

include measures of strain and strain-rate hard-ening and plastic anisotropy. The strain-hard-ening exponent (usually denoted by the symboln) describes the change of flow stress (with aneffective stress, ) with respect to the effectiverstrain, such that:e,

� ln rn � (Eq 1a)

� ln e

For a uniaxial tensile test, and prior to the de-velopment of a neck, the distinction of effectivestress and strain is not necessary because theyare equal to the axial stress r and strain e, sothat the expression is simply:

� ln rn � (Eq 1b)

� ln e

The strain-hardening exponent may have val-ues from n � 0 for a perfectly plastic solid to n� 1 for an elastic solid; negative values of nmay also be found for materials that undergoflow softening due to changes in microstructureor crystallographic texture during deformation.According to Eq 1, if the constitutive equationfor stress-strain behavior is of the form r� Ken,then a logarithmic plot of true stress versus truestrain results in a straight line with a slope equal


Fig. 16 Tensile elongation as a function of the strain-rate sensitivity. Source: Ref 18

to n. However, this is not always found to be thecase and reflects the fact that this relationship isonly an empirical approximation. Thus, whenthe plot of ln(r) versus ln(e) [or the plot oflog(r) versus log(e)] results in a nonlinear valueof n, then the strain-hardening exponent is oftendefined at a particular strain value. In general, nincreases with decreasing strength level and de-creasing ease of dislocation cross slip in a poly-crystalline material.

The strain-rate sensitivity exponent (usuallydenoted by the symbol m) describes the variationof the flow stress with the strain rate. In termsof effective stress and effective strain rate(r)

it is determined from the following relation-˙(e),ship:

� ln rm � (Eq 2a)˙� ln e

which is simplified for the condition of pure uni-axial tension as:

� ln rm � (Eq 2b)

� ln e

Deformation tends to be stabilized in a ma-terial with a high m value. In particular, the pres-

ence of a neck in a material subject to tensilestraining leads to a locally higher strain rate andthus to an increase in the flow stress in thenecked region due to strain-rate hardening.Such strain-rate hardening inhibits further de-velopment of the strain concentration in theneck. Thus, a high strain-rate sensitivity impartsa high resistance to necking and leads to hightensile elongation or superplasticity. Materialswith values of m equal to or greater than ap-proximately 0.3 exhibit superplasticity, assum-ing cavitation and fracture do not intercede. Anempirical relation between tensile elongationand the m value is revealed in the data collectedby Woodford (Ref 18) shown in Fig. 16. In ad-dition, a number of theoretical analyses havebeen conducted to relate m and tensile failurestrain, ef (Ref 19–21). For example, Ghosh (Ref19) derived:

1/me � �m ln(1 � f ) (Eq 3)f

in which f denotes the size of the initial geo-metric (area) defect at which flow localizationoccurs.

The plastic anisotropy parameter r (or R)characterizes the resistance to thinning of a sheetmaterial during tensile testing and is defined as


Fig. 18 Anisotropy parameter r versus the local axial truestrain for various nominal strain rates. Data corre-

spond to a Ti-21Al-22Nb alloy. Source: Ref 10

Fig. 17 Width versus thickness strain (ew versus et) for an or-thorhombic titanium aluminide specimen deformed

at 980 �C (1795 �F) and a nominal strain rate of 1.67 � 10�4

s�1. Source: Ref 10

the slope of a plot of width strain, ew, versusthickness strain, et, (Ref 22), that is:

dewr � (Eq 4)det

A material that possesses a high r value has ahigh resistance to thinning and hence goodformability, especially during deep-drawingoperations. Materials with values of r greaterthan unity have higher strength in the thicknessdirection than in the plane of the sheet.

The plastic anisotropy parameter can be read-ily measured using specimens deformed in uni-axial tension. However, caution should be ex-ercised when making such measurements toensure that the stress state along the gage lengthis uniaxial. Therefore, measurements in regionsnear the sample shoulder and the failure site(where a stress state of hydrostatic tension maydevelop during necking) should be avoided. Fig-ure 17 shows an example of such data from aTi-21Al-22Nb sample pulled to failure in uni-axial tension at a nominal strain rate of 1.67 �10�4 s�1 and at a temperature of 980 �C (1800�F). Within experimental scatter, the r value isconstant for the majority of deformation. Ap-parently, lower values of r at low strains (nearthe specimen shoulder) or very high strains (atthe fracture tip) are invalid due to constraint orflow-localization effects, respectively, and henceconditions that are not uniaxial.

The r value of a sheet material may be sen-sitive to the testing conditions and in particularto the strain rate and temperature. This is a resultof variation of the mechanism that controls de-formation (e.g., slip, grain-boundary sliding,etc.) with test conditions. For the orthorhombic

titanium aluminide material discussed previ-ously (Ti-21Al-22Nb), the normal plastic aniso-tropy parameter shows a very weak dependenceon strain, but a noticeable variation with strainrate (Fig. 18). This trend can be attributed to thepresence of mechanical and crystallographictexture and the effect of strain rate on the oper-ative deformation mechanism.

Effect of Test Conditions on Flow Behavior

When considering the effect of test conditionson flow behavior, it must be understood that test-ing for the modeling of deformation processesis very different from testing for static mechan-ical properties at very low (quasi-static) loadingrates. Testing conditions for deformation pro-cesses must cover a range of strain rates and mayrequire high strain rates of 1000 s�1 or more.For tensile testing, conventional test frames areapplicable for strain of rates less than 0.1 s�1,while special servohydraulic frames have arange from 0.1 to 100 s�1 (see Chapter 15,“High Strain Rate Tensile Testing”). For strainrates from 100 to 1000 s�1, the Hopkinson(Kolsky)-bar method is used. This chapter andthe following discussions only consider isother-mal conditions and strain rates below 0.1 s�1,where inertial effects can be neglected.

Effect of Strain Rate and Temperature onFlow Stress. At hot-working temperatures, mostmetals exhibit a noticeable dependence of flowstress on strain rate and temperature. For in-stance, the variation of flow stress with strainrate for Ti-6Al-4V (with a fine equiaxed micro-structure) deformed at 927 �C is shown in Fig.19 (Ref 23). For the strain-rate range shown inFig. 19, a sigmoidal variation of the flow stresswith strain rate is observed. From these data, the


Fig. 20 Strain-rate sensitivity (m) versus strain rate for the(e)data corresponding to Fig. 19. Source: Ref 23

Fig. 19 Flow stress as a function of strain rate and grain sizefor a Ti-6Al-4V alloy deformed at 927 �C (1700 �F).

The strain level was about 0.24. Source: Ref 23

strain-rate sensitivity (m value) can be readilycalculated. The result of these calculations (Fig.20) shows that m is low at low strain rates andthen increases and passes through a maximumafter which it decreases again. This behavior istypical of many metals with fine-grain micro-structures and reveals that superplasticity is notmanifested in either the low-stress, low-strain-rate region I or the high-stress, high-strain-rateregion III (refer to Fig. 20). Rather, superplas-ticity is found only in region II in which thestress increases rapidly with increasing strainrate. The superplastic region II is displaced tohigher strain rates as temperature is increasedand/or grain size is decreased. Moreover, themaximum observed values of m increase withsimilar changes in these parameters.

The stress-strain curve and the flow and frac-ture properties derived from the hot-tension testare also strongly dependent on the temperatureat which the test is conducted. In both single-crystal and polycrystalline materials, thestrength decreases with temperature because thecritical resolved shear stress decreases sharplywith an increase in temperature. On the otherhand, the tensile ductility increases with tem-perature because of the increasing ease of re-covery and recrystallization during deformation.However, the increase in temperature may alsocause microstructural changes such as precipi-tation, strain aging, or grain growth that mayaffect this general behavior.

The flow stress dependence on temperatureand strain rate is generally given by a functionalform that incorporates the Zener-Hollomon pa-

rameter, Z � exp (Q/RT) (Ref 24) in which Q˙eis the apparent activation energy for plastic flow,R the universal gas constant, and T is the abso-lute temperature.

Effect of Crosshead Speed Control on HotTensile Data. The selection of constant-strain-rate versus constant-crosshead-speed control inconducting isothermal, hot tensile tests is an im-portant consideration, especially for materialsthat are superplastic. When experiments are con-ducted under constant-crosshead-speed condi-tions, the specimen experiences a decreasingstrain rate during the test, thus making the in-terpretation of results difficult, especially in thesuperplastic regime. A method to correct for thestrain-rate variation involves continuouslychanging the crosshead speed during the tensiontest to achieve nearly constant strain rate. Thisapproach assumes uniform deformation alongthe gage length and no end effects and leads tothe following relation between crosshead speed

desired strain rate the initial gage length lo,d, e,and time t:

d � e l exp(�et) (Eq 5)o

The crosshead-speed schedule embodied inEq 5 has been used successfully for a test of Ti-6Al-4V (Ref 25). Verma et al. (Ref 26) have alsoshown the efficacy of this approach by conduct-ing tensile tests at constant crosshead speed aswell as constant strain rate on superplastic 5083-Al specimens. Figure 21 compares stress-straincharacteristics determined under constant-cross-


Fig. 21 Comparison of stress versus strain for constant nom-inal strain rate (constant crosshead speed, CHS) and

constant true strain rate for Al-5083 at 550 �C (1020 �F).(e)Source: Ref 26

head-speed conditions with those from constant-strain-rate tests for two different initial strainrates. Constant-crosshead-speed tests showedconsistently lower strain hardening (lower flowstresses) and larger strain to failure (higher ten-sile elongations) than the corresponding con-stant-strain-rate tests did. The above findinghighlights the importance of the test controlmode; in addition, this mode should be clearlystated when elongation and/or flow stress dataare reported.

Effect of Gage Length on Strain Distribu-tion. Under superplastic deformation condi-tions, specimen geometry (especially shoulderdesign) plays an important role in the determi-nation of hot tensile characteristics. In the sec-tion “Frame-Furnace Tensile-Testing Equip-ment,” two different specimen designs arediscussed (Fig. 6). For one of these designs, de-formation was limited essentially to the gagesection, while the other had experienced defor-mation in the shoulder section. For the specimengeometry in Fig. 6(a), tensile tests indicated thatsignificant straining can occur in the grip regionsand that large strain gradients exist within thegage section of the specimen. The strain gradient(variation) along the gage length and the defor-mation of the grip section depend on the gagelength and tensile strain rate. As can be seen inFig. 22, the strain gradient of the smaller gagelength (12.7 mm, or 0.5 in.) specimen geometryis much steeper than that of the larger one (63.5mm, or 2.5 in.). With regard to the smaller gagelength specimen, it is observed that the straingradient becomes steeper as the strain rate in-creases. Furthermore, a reduction of deforma-tion in the shoulder can be achieved by decreas-ing the width of the gage section because of thedecrease in deformation load and hence stress

level generated in the shoulder. However, thereare constraints in gage-width reductions arisingfrom the microstructural characteristics of a par-ticular material; in some cases, there may be aninsufficient number of grains across the speci-men section.

Modeling of theIsothermal Hot Tensile Test

The detailed interpretation of data from theisothermal hot tensile test frequently requiressome form of mathematical analysis. This anal-ysis is based on a description of the local stressstate during tension testing and some form ofnumerical calculation. The approach is de-scribed briefly in this section.

Stress State at the Neck

Prior to necking, the stress state in the tensiontest is uniaxial. However, the onset of neckingis accompanied by the development of a triaxial(hydrostatic*) state of stress in the neck. Be-cause the flow stress of a material is stronglydependent on the state of stress, a correctionmust be introduced to convert the measured av-erage axial stress into the effective uniaxial flowstress; that is:

avr � r/F (Eq 6)l T

in which denotes the average axial stress re-avrl

quired to sustain further deformation, is thereffective (flow) stress, and FT is the stress tri-axiality factor. The magnitude of FT (which es-sentially determines the magnitude of the aver-age hydrostatic stress within the neck) dependson the specimen shape (round bar or sheet) andthe geometry of the neck. Bridgman (Ref 27)conducted a rigorous, theoretical analysis withregard to the stress state at the neck for bothround-bar and for sheet specimen geometries.For a plastically isotropic material, the following

*The term hydrostatic stress is defined as the mean value ofthe normal stresses. The term triaxial stress is often used toimply the presence of a hydrostatic stress. However, the termtriaxial stress is not equivalent to hydrostatic stress, becausethe presence of a triaxial stress state could be a combinationof shear stresses and/or normal stresses or only normalstresses. The term hydrostatic stress is thus preferred andmore precise in describing solely normal stresses in threeorthogonal directions.


Fig. 23 Stress triaxiality factor for sheet and round-bar spec-imens

Fig. 22 Strain distribution for 12.7 mm (a) and 63.5 mm (b) gage length specimens for two different strain rates. Length strains areplotted versus original axial position along the gage length. Source: Ref 9

equations were derived for the stress triaxialityfactor of round-bar and sheet speci-r s(F ) (F )T Tmens in the symmetry plane of the neck:

�1R arF � 1 � 2 ln 1 � (Eq 7)T �� a 2R

1/2R asF � 1 � 2 ln 1 �T �� a R1/2 1/2 �12a 1 a

� 1 � � 1 (Eq 8)� � � � � �R 2 R

in which a represents the specimen half radiusor width, and R is the radius of curvature of theneck. For a/R � 0 (in particular, for �2 � a/R� 0), the stress triaxiality factor for sheet tensilespecimens with a convex curvature is given by:

�1F {[2 Q arctan (1/ Q)] � 1} (Eq 9)� �T

where Q � �(1 � 2R/a).The variation of the stress triaxiality factor for

round-bar and sheet specimens as ar s(F ) (F )T Tfunction of the a/R ratio is shown in Fig. 23. Fora positive a/R value (concave neck profiles), FTis less than unity, thus promoting flow stabili-zation. On the other hand, for negative a/R (con-vex neck profiles), FT � 1; thus, flow tends tobe destabilized.

In a rigorous sense, the closed-form equationsfor FT (Eq 7 and 8) are applicable only for theplane of symmetry at the neck. At other loca-tions, the solution for the exact form of FT is notavailable. However, as has been shown from fi-nite-element method (FEM) analyses (Ref 28,

29), Eq 7 and 8 provide a good estimate for thestress triaxiality factor in regions away from thesymmetry plane provided that the local valuesof a and R are inserted into the relations.

Numerical Modeling of the Hot Tensile Test

Two types of methods have been employed tomodel the tension behavior of materials: theFEM and the somewhat simpler finite-difference(“direct-equilibrium”) method originally pre-sented by G’sell et al. (Ref 30), Ghosh (Ref 31),and Semiatin et al. (Ref 32). Both approachesinvolve solutions that satisfy the axial forceequilibrium equation and the appropriate bound-


Fig. 24 Discretization of the sheet specimen for the simula-tions of the isothermal hot tensile test (Ref 33). The

specimen geometry corresponds to the specimen shown in Fig.6(b) (Ref 10, 15)

ary conditions. These models enable the predic-tion of important parameters such as neck pro-file, failure mode, axial-strain distribution, andductility. A comparison of simulation results(e.g., nominal stress-strain curves, axial-straindistribution, and total elongation) obtained fromFEM analyses to those of the direct-equilibriummethod has shown that the latter approach givesrealistic predictions (Ref 29). To this end, a briefdescription of this simpler method is given inthe following paragraphs.

Model Formulation. The formulation of thedirect-equilibrium method is based on discreti-zation of the sample geometry, description of thematerial flow behavior, and development of theappropriate load-equilibrium equation. Thespecimen geometry (dimensions, cross-sectionshape, geometrical defects, etc.) is first specified.The specimen is divided along the axial direc-tion into horizontal slices/elements (Fig. 24).For the material flow behavior, the simple en-gineering power-law formulation has been usedin most modeling efforts, that is:

n m˙r � Ke e (Eq 10)s s

in which and denote the effective stress,˙r, e , es seffective strain, and effective strain rate, respec-tively, of the material. K, n, and m represent thestrength coefficient, strain-hardening exponent,and the strain-rate-sensitivity index, respec-tively.

At any instant of deformation, the axial loadP should be the same in each element in orderto maintain force equilibrium. The load borneby each slice is equal to the product of its load-bearing cross-sectional area and axial stress; theaxial stress is equal to the flow stress correctedfor stress triaxiality due to necking and evalu-ated at a strain rate corresponding to that whichthe material elements experience. (In case ofcavitating material, the strain rate is that of thematrix-material element, not the matrix-cavitycontinuum.) The load-equilibrium condition isthus described by:

i i j jr A /F � r A /F (Eq 11)i lb T j lb T

or, using Eq 10:

m n i i m n j j˙ ˙e e A /F � e e A /F (Eq 12)s s lb T s s lb Ti i j j

in which the subscripts and/or superscripts i andj denote the corresponding parameters for ele-

ments i and j, respectively, FT represents thestress triaxiality factor, and Alb is the load-bear-ing area.

For the case in which the material cavitatesduring tension testing (see the section “Cavita-tion During Hot-Tensile Testing” in this chap-ter), Eq 11 and 12 must be modified. In partic-ular, the presence of cavities affects the externaldimensions of the specimen (because they leadto a volume increase) and hence the load-bearingarea, the stress triaxiality factor, and the strainrate at which the material deforms.

As discussed by Nicolaou et al. (Ref 33),spherical and uniformly distributed cavities in-crease each of the three dimensions (length,width, and thickness and, for round-bar speci-men geometries, diameter) of the tension spec-imen by the same amount. The relationship be-tween the macroscopic area (i.e., the externalarea of the specimen) Am, the load-bearing areaAlb, and the initial (uncavitated) area is thenspAosimply:

2/3A � A /(1 � C ) (Eq 13)m lb v

where Cv is the cavity volume fraction and Albis given by:

spA � A exp(�e ) (Eq 14)lb o s


Fig. 25 Comparison of the engineering stress-strain curvesfor non-strain-hardening samples without or with a 1

or 2% taper predicted using the direct-equilibrium approach.Source: Ref 29

In addition, the length l, width w, and thicknesst, for a sheet specimen, or radius r of a round-bar specimen increase according to:

dd� � (Eq 15)1/3(1 � C )v

in which d� denotes any of the dimensions (l�,w�, t�, or r�) for the case when cavities are pres-ent in the material, and d represents the respec-tive dimension changes with strain alone.

The matrix strain rate can also be related˙e ,sto the macroscopic sample strain rate Using˙e.power-dissipation arguments, the relation be-tween the two strain rates is found to be (Ref34):

˙ ˙e � (1/�q)e (Eq 16)s

in which q is the relative density of the specimen(q � 1 � Cv) and � is the stress-intensificationfactor, which for spherical and uniformly dis-tributed cavities is (Ref 33):

2/3� � 1/q (Eq 17)

Algorithm. After having specified the speci-men geometry and the material-flow relation, theequations for model formulation can be insertedinto an algorithm to simulate the tensile test. Atany instant of deformation, the axial variation instrain rate is calculated based on the load-equi-librium equation, which provides the ratios ofthe strain rates in the elements, and the boundarycondition (e.g., constant crosshead speed),which provides the specific magnitudes of thestrain rates. The strain rates are then used to up-date the macroscopic (and microscopic) strainand cavity volume fraction (for a cavitating ma-terial) in each element. The simulation steps are:

1. An increment of deformation is imposed, anda/R and FT are calculated for each slice.

2. From the true strain and the cavity-growthrate (see the section “Cavitation During HotTensile Testing”), the cavity volume fractionis determined.

3. The true-strain-rate distribution is calculatedfor each element, using the equilibrium equa-tion and the boundary condition.

4. From the true-strain, cavity volume fraction,and strain-rate distributions, the engineeringstress and strain are calculated.

5. Steps 1 to 4 are repeated until a sharp neckis formed (localization-controlled failure) orthe cavity volume fraction at the central ele-ment reaches a value of 0.3 (fracture/cavita-tion-controlled failure).

Example Applications. Several results illus-trate the types of behavior that can be quantifiedusing the direct-equilibrium modeling approach.The first deals with the effect of specimen taperon tensile elongation. Tensile test specimensusually have a small (�2%) reduction in thecross-sectional area from the end to the centerof the reduced section in order to control thelocation of failure. The predicted effect of re-duced-section taper on the engineering stress-strain curves for non-strain-hardening materialsis shown in Fig. 25 (Ref 29). The effect of theabsence of a taper on increased elongation isquite dramatic, especially as the strain-rate sen-sitivity increases from m � 0.02 to m � 0.15.For materials deformed at cold-working tem-peratures (m � 0.02), tensile flow will still lo-calize in the absence of a taper because the re-duced section itself acts as the defect relative tothe greater cross-sectional area of the shoulder(Ref 31, 32). In contrast to the results for sam-ples with and without a 2% taper, the predictionsfor samples with a 1% versus a 2% taper showmuch less difference.

With appropriate modification, the direct-equilibrium modeling approach may also beused to analyze the uniaxial hot tensile testingof sheet materials that exhibit normal plasticanisotropy (Ref 35). Selected results are shownin Fig. 26. The engineering stress-strain curvesexhibit a load maximum, a regime of quasi-sta-ble flow during which the diffuse neck develops


Fig. 26 Direct-equilibrium simulation predictions of engineering stress-strain curves at hot-working temperatures for various valuesof the strain-rate sensitivity and the normal plastic anisotropy parameter. Source: Ref 35

and the stress decreases gradually, and finally aperiod of rapid load drop during which flow ishighly localized in the center of the gage length.When the m value is low, an increase in r in-creases the amount of quasi-stable flow; that is,it stabilizes the deformation in a manner similarto the effect of strain-rate sensitivity. In addition,the simulation results reveal that the flow-sta-bilizing effect of r decreases as m increases andin fact becomes negligible for conditions thatapproach superplastic flow (i.e., m � 0.3).

Cavitation during Hot Tensile Testing

A large number of metallic materials form mi-croscopic voids (or cavities) when subjected tolarge strains under tensile modes of loading.This formation of microscopic cavities, whichprimarily occurs in the grain boundaries duringhigh-temperature deformation, is referred to ascavitation. In some cases, cavitation may lead topremature failure at levels of deformation farless than those at which flow-localization-con-trolled failure would occur. For a given material,the extent of cavitation depends on the specificdeformation conditions (i.e., strain rate and tem-perature). A wide range of materials exhibit cav-itation; these materials include aluminum alloys(Fig. 27a), conventional titanium alloys (Fig.

27b), titanium aluminides, copper alloys, leadalloys, and iron alloys (Ref 36–38).

An important requirement for cavitation dur-ing flow under either hot-working or superplas-tic conditions is the presence of a tensile stress.On the other hand, under conditions of homo-geneous compression, cavitation is not ob-served; in fact, cavities that may be producedunder tensile flow can be removed during sub-sequent compressive flow. In addition, it has alsobeen demonstrated that the superposition of ahydrostatic pressure can reduce or eliminate cav-itation (Ref 39). Hot isostatic pressing can alsoheal the deformation damage of nucleated cav-ities.

Cavitation is a very important phenomenon inhot working of materials because not only mayit lead to premature failure during forming, butit also may yield inferior properties in the finalpart. Therefore, it has been studied extensively,primarily via the tensile test.

Cavitation Mechanisms/Phenomenology

Cavitation occurs via three often-overlappingstages during tensile deformation: cavity nucle-ation, growth of individual cavities, and cavitycoalescence. Each stage is briefly described inthe following sections, while a more detailed re-view of ductile fracture mechanisms is in thearticle “Mechanisms and Appearances of Duc-


tile and Brittle Fracture in Metals” in FailureAnalysis and Prevention, Volume 11 of the ASMHandbook (2002, p 587–626).

Cavity Nucleation. Several possible cavity-nucleation mechanisms have been establishedincluding (a) intragranular slip intersectionswith nondeformable second-phase particles andgrain boundaries, (b) sliding of grains alonggrain boundaries that is not fully accommodatedby diffusional transport into those regions, and(c) vacancy condensation on grain boundaries(Ref 40). A frequently used cavity-nucleationcriterion based on stress equilibrium at the cav-ity interface is:

r � 2(c � c � c )/r (Eq 18)c p i

in which rc is the critical cavity radius abovewhich a cavity is stable; c, cp, and ci denote theinterfacial energies of the void, the particle, andthe particle-matrix interface, respectively; and ris the applied stress. This criterion requires flowhardening, which is minimal in superplastic ma-terials except in cases of significant graingrowth, in order to nucleate cavities at less fa-vorable sites, such as smaller particles. In addi-tion, such surface-energy considerations requirestresses for initiation and early growth that areunrealistically high. Therefore, the developmentof other (constrained-plasticity) approachesbased on nucleation and growth from inhomo-geneities/regions of high local stress triaxialityhas been undertaken (Ref 41).

The cavity-nucleation rate N is defined as thenumber of cavities nucleated per unit area andunit strain. N may either be constant or decreaseor increase with strain. However, such strain de-pendencies are usually not strong. Measure-

ments have shown than N can be bracketed be-tween 104 and 106 cavities per mm3 per unitincrement of strain (Ref 16, 41, 42).

The constrained plasticity analysis suggeststhat a size distribution of second-phase constit-uents/imperfections may lead to a variety of cav-ity-growth rates at the nano/submicron cavity-size level. From an operational standpoint, thiseffect may thus lead one to conclude that cavitiesnucleate continuously rather than merely be-come microscopically observable continuously.Irrespective of the exact mechanism, it isthought that the assumption of continuous nu-cleation of cavities of a certain size (e.g., 1 lm)still produces the same “mechanical” effect onfailure via cavitation or flow localization as thepostulated actual physical phenomenon.

Cavity-growth mechanisms can be classifiedinto two broad categories: diffusional growthand plasticity-controlled growth (Ref 43). Dif-fusional growth dominates when the cavity sizeis very small. As cavity size increases, diffu-sional growth decreases very quickly, and plasticflow of the surrounding matrix becomes thedominant cavity-growth mechanism. An illus-tration of a cavity-growth-mechanism map (Ref44) is shown in Fig. 28. From an engineeringviewpoint, plasticity controlled growth is ofgreatest interest. In such cases, the growth of anisolated, noninteracting cavity is described forthe case of uniaxial tension deformation by:

V � V exp(ge)o

or

gr � r exp e (Eq 19)o � �3

Fig. 27 Examples of cavitation. (a) In aluminum (Al-7475) alloy. Courtesy of A.K. Ghosh. (b) In titanium (Ti-6Al-4V) alloy. Source:Ref 37


Fig. 28 Variation of the cavity-growth rate for different mech-anisms. rc, critical cavity radius; rosp, cavity radius for

onset of superplastic deformation; rcsp, critical cavity radius forsuperplastic deformation. Source: Ref 44

in which V and r are the cavity volume and ra-dius, respectively, Vo and ro are the volume andradius of the cavity when it becomes stable, edenotes axial true strain, and g is the individualcavity-growth rate.

Several analyses have been conducted to cor-relate the cavity-growth rate g with material pa-rameters and the deformation conditions. For ex-ample, Cocks and Ashby (Ref 45) derived thefollowing relation between g and m for a planararray of spherical, noninteracting, grain-bound-ary cavities under tensile straining conditions:

m � 1 2 (2 � m)g � 1.5 sinh (Eq 20)� � � �m 3 (2 � m)

It should be noted that this theoretical rela-tionship between m and the cavity-growth pa-rameter g for an individual cavity follows thesame general trend as the experimentally deter-mined correlation between the strain-rate sensi-tivity and the apparent cavity-growth rate gAPP.The parameter gAPP, which is readily derivedfrom experimental data (Ref 46), is defined by:

C � C exp(g e) (Eq 21)v v APPo

in which Cv is the cavity volume fraction at atrue strain e, gAPP is the apparent cavity-growthrate, and is the so-called initial cavity vol-Cvo

ume fraction.Cavity coalescence is the interlinkage of

neighboring cavities due to a microscopic flow-localization process within the material ligamentbetween them. Coalescence occurs when thewidth of the material ligament reaches a criticalvalue that depends on initial cavity spacing andthe strain-rate sensitivity. Coalescence can occuralong both the longitudinal and transverse direc-tions with the latter being more important be-cause it eventually leads to failure. According toPilling (Ref 47), cavity coalescence may be re-garded as a process that in effect increases themean cavity-growth rate. In particular, the effectof pairwise coalescence on the average cavity-growth rate dr/de can be estimated from:

dr 8C Ug(0.13r � 0.37(dr/de) de) � (dr/de)v i i�

de 1 � 4C Ugdev

(Eq 22)

in which Cv is the instantaneous volume fractionof cavities, g is defined from Eq 19, de (� de)

is a small increment of strain, (dr/de)i is the rateof growth per unit strain of an isolated cavity(� gr/3 from Eq 19), and U is given by:

2U � (1 � gde/3 � (gde) /27) (Eq 23)

The phenomenon of cavity coalescence wasfurther investigated by Nicolaou and Semiatin(Ref 48, 49), who conducted a numerical anal-ysis of the uniaxial tension test considering: thetemporal and spatial location of the cavities in-side the specimen and the temporal cavity ra-dius. Two cases were considered: a stationarycavity array (similar to the analysis of Pilling)and continuous cavity nucleation. The analysisof the stationary cavity array led to a much sim-pler expression than Eq 22, that is:

dr1� gr( ⁄3 � C ) (Eq 24)vde

This simple equation gives predictions verysimilar to the more complex relation of Eq 22.

With regard to the continuous cavity nuclea-tion case, it was found that the average cavityradius was described by:

dr� gr(0.2 � C ) (Eq 25)vde


Fig. 29 Comparison of measurements and predictions of theevolution of average cavity radius with strain for an

Al-7475 alloy assuming continuous nucleation (Eq 25) or a pre-existing cavity array (Eq 24). Source: Ref 49

Fig. 30 Predicted engineering stress-strain curves for tensiletesting of sheet samples with a 2% taper, assuming

strain-hardening exponent n � 0, initial cavity volume fractionCvo � 10�3, various cavity-growth rates g, and a strain-rate sen-sitivity exponent m equal to (a) 0.1, (b) 0.3, or (c) 0.5. Source:Ref 33

A comparison with experimental cavity sizemeasurements (e.g., Fig. 29) revealed that actualresults are bounded by cavity-growth-and-coa-lescence models that assume either a constant,continuous nucleation rate (lower limit) or a pre-existing cavity array with no nucleation of newcavities (upper limit), that is, Eq 25 and 24, re-spectively.


The work of Nicolaou et al. (Ref 33) also shedlight on the effect of cavitation on stress-strainbehavior. Engineering stress-strain (S-e) curvesfor a range of strain-rate sensitivities (m values)and cavity-growth rates gAPP were predicted us-ing the direct-equilibrium modeling approach(Fig. 30); for all of the cases, the strain-hard-ening exponent n was 0. The cavity volume frac-tion (CV) in the central element at failure is alsoindicated in the plots.

Examination of the engineering stress-straincurves reveals that cavitation causes a noticeablereduction in total elongation; this reduction isquantified and discussed in more detail in thenext section. Figure 30 also shows that thestress-strain curves for cavitating and noncavi-tating samples with the same value of m are veryclose to each other, except at elongations closeto failure. Surprisingly, the engineering stress ata given elongation for a cavitating material ishigher than the corresponding stress (at the sameelongation) for a noncavitating material. This in-tuitively unexpected result was interpreted bythe examination of the effective (load-bearing)area at the same elongation of a cavitating and

a noncavitating specimen. In particular, the anal-ysis of Nicolaou et al. (Ref 33) revealed that fora given elongation the effective area of the cav-itating specimen is larger than the area of a non-cavitating one. Therefore, the load and hence theengineering stress required to sustain deforma-tion is higher in the case of a cavitating material.

As shown in Fig. 30, the difference betweenthe engineering stress-strain curves of cavitating


Fig. 31 Micrographs of titanium aluminide specimens that failed in tension. (a) Orthorhombic titanium aluminide that failed intension by flow localization. Source: Ref 10. (b) Near-c titanium aluminide that failed in tension by fracture (cavitation).

Source: Ref 51

Fig. 32 Failure-mode map developed from simulations of thesheet tensile test. Experimental data points are also

shown on the map.

and noncavitating materials is not very large.Therefore, it can be deduced that Considere’scriterion, if implemented in the usual fashion us-ing data from a tensile test (i.e., a plot of loadversus the elongation of the gage section), canbe used to test whether fracture of a tensile spec-imen occurs due to instability, regardless of thepresence of extensive internal cavities in the ma-terial and whether the volume of the material isconserved (Ref 50).

Failure Modes during Hot Tensile Testing

Cavitating hot tensile specimens may fail byeither localized necking (“flow localization”) orfracture/cavitation. The second mode of failureoccurs without flow localization in the neck andresembles a brittle type of fracture because thefracture tip has a considerable area. Micrographsof these modes of failure are presented in Fig.31. The localization type of failure shown in Fig.31(a) is for an orthorhombic titanium aluminide(Ti-21Al-22Nb) deformed at 980 �C (1795 �F)and a nominal strain rate of 1.6 � 10�3 s�1.On the other hand, Fig. 31(b) displays the frac-ture-controlled failure of a c titanium aluminidealloy (Ref 51) deformed in tension at 1200 �C(2190 �F) and a nominal strain rate of 10�3 s�1.

The particular mode of failure of a materialtested under tension conditions can be predictedby the magnitude of the strain-rate sensitivity mand the apparent cavity-growth rate gAPP. The

corresponding failure-mechanism map for non-strain-hardening materials is plotted in Fig. 32.For deformation under superplastic conditions(m � 0.3) and gAPP � 2, the map shows thatfailure is fracture/cavitation-controlled. On theother hand, flow-localization-controlled failureis seen to predominate only for small values ofthe cavity-growth rate. In Fig. 32, experimentalobservations of the failure mode of c and ortho-rhombic titanium aluminides are also plotted.The solid data points correspond to fracture-con-trolled failures, while the open data points cor-


Fig. 33 Elongation as function of the strain-rate sensitivity and (apparent) cavity-growth rate predicted from direct equilibriumsimulations. The individual data points represent experimental data. Source: Ref 33

respond to localization-controlled failures.Given the assumptions made in deriving suchmaps, it can be concluded that the prediction offailure mode from the magnitudes of m and gAPPprovides good agreement with actual behavior.

Total Tensile Elongations

As shown in Fig. 33, cavitation may lead topremature failure and thus to a significant re-duction in the tensile elongation compared tothat measured by Woodford (Ref 18) for non-cavitating metals. For a fixed value of m, thereduction in elongation for fracture-controlledfailure depends on several factors, such as thecavity-nucleation rate, cavity-growth rate, cavityshape and distribution, and the cavity architec-ture.

Several analyses have been conducted toquantify the effect of cavitation on the tensileductility. These include the two-slice approach*by Lian and Suery (Ref 52), micromechanical

*The two-slice approach assumes that the specimen com-prises two regions, one of them consisting of the centralplane of the specimen that contains an initial geometric orstrength defect. The deformation of each region obeys theflow rule while at any instant of deformation the load is thesame in both regions (slices).

approaches by Zaki (Ref 53), and Nicolaou andSemiatin (Ref 54), as well as approaches basedon the direct-equilibrium approach described inthe section “Numerical Modeling of the HotTensile Test” in this chapter. Several results fromthe direct-equilibrium model serve to illustratethe efficacy of such techniques.

The results shown in Fig. 33 correspond to anon-strain-hardening material (n � 0) with a 2%taper and Cvo � 10�3. The topmost curve in thisplot depicts the total elongation as a function ofm for a noncavitating sample, that is, Wood-ford’s trend line. For such a material, the elon-gation is controlled, of course, by the onset oflocalized necking. The remaining curves in Fig.33 for cavitating samples indicate the decrementin elongation due to the occurrence of fractureprior to localized necking. For low values ofgAPP (�2) and m (�0.3), the decrement is equalto zero because failure is still necking con-trolled. On the other hand, the decrement is larg-est for large values of gAPP and m, for which thecritical volume fraction of cavities for fracture(assumed to be 0.30) is reached much before theelongation at which necking occurs. In fact, forgAPP � 5, the total elongation is almost inde-pendent of m for m � 0.3 because fracture inthese cases intercedes during largely uniform,quasi-stable flow.


Fig. 34 Comparison of experimentally determined total elon-gations with (microscopic) model predictions that in-

corporate the cavity architecture. Source: Ref 54

Table 2 Experimental data from the literature for the deformation and failure of cavitating materials

Data point Material m g Tensile elongation, %

1 c-TiAl (as received) 0.38 2.2 2192 c-TiAl (as received) 0.51 2.3 3503 c-TiAl (as received) 0.62 1.8 446, 5324 c-TiAl (heat treated) 0.18 3.4 93, 1045 c-TiAl (heat treated) 0.15 8.0 516 5083 Al 0.50 5.2 1727 Zn-22Al 0.45 1.5 4008 �/b brass 0.60 2.3 4259 Coronze 638 0.33 4.5 275

In most cases, rigorous comparisons of pre-dicted tensile elongations and experimental data(Fig. 33) cannot be made because the cavity-growth rate and the cavity-size population andshape were not measured, while other importantparameters such as the specimen geometry werenot reported. Therefore, a general comparisonbased only on the value of m can be made. Fromthe results of Fig. 33, it is seen that most of thedata points overlie the predicted curves.

Comparisons of reported tensile elongationsdata (Table 2) to predictions of a microscopicmodel (Ref 54) in which the cavity architecturehas been taken into account through the param-eter G are shown in Fig. 34 (G is a factor thatdescribes the geometry of the ligament betweentwo cavities as a function of the cavity architec-ture within the specimen). With the exception ofone data point (No. 9), the major deviations ofthe predictions tend to be on the high side. Thesedeviations could be a result of the neglect in themicroscopic model of the macroscopic strain

gradient in the diffuse neck of real tension sam-ples. In addition, as mentioned previously, spec-imen geometry and deformation in the shoulderregion of actual tension specimens have an ef-fect on measured ductilities, which is difficult toquantify. Nevertheless, agreement between themeasured and predicted ductilities is reasonablygood.

ACKNOWLEDGMENT

This chapter was adapted from P.D. Nicolaou,R.E. Bailey, and S.L. Semiatin, Chapter 7, Hot-Tension Testing, Handbook of Workability andProcess Design, G.E. Dieter, H.A. Kuhn, andS.L. Semiatin, Ed., ASM International, 2003, p68–85.

REFERENCES

1. Met. Ind., Vol 11, 1963, p 247–2492. M.G. Cockroft and D.J. Latham, Ductility

and the Workability of Metals, J. Inst. Met.,Vol 96, 1968, p 33–39

3. J. Inst. Met., Vol 92, 1964, p 254–2564. G. Cusminsky and F. Ellis, An Investigation

into the Influence of Edge Shape on Crack-ing During Rolling, J. Inst. Met., Vol 95(No. 2), Feb 1967, p 33–37

5. E.F. Nippes, W.F. Savage, B.J. Bastian, andR.M. Curran, An Investigation of the HotDuctility of High-Temperature Alloys,Weld. J., Vol 34, April 1955, p 183s–196s

6. D.F. Smith, R.L. Bieber, and B.L. Lake, “ANew Technique for Determining the HotWorkability of Ni-Base Superalloys,” pre-sented at IMD-TMS-AIME meeting, 22 Oct1974

7. S.I. Oh, S.L. Semiatin, and J.J. Jonas, AnAnalysis of the Isothermal Hot Compres-sion Test, Metall. Trans. A, Vol 23A (No.3), March 1992, p 963–975


8. W.C. Unwin, Proc. Inst. Civil Eng., Vol 155,1903, p 170–185

9. P.A. Friedman and A.K. Ghosh, Microstruc-tural Evolution and Superplastic Deforma-tion Behavior of Fine Grain 5083Al, Metall.Mater. Trans. A, Vol 27A (No. 12), Dec1996, p 3827–3839

10. P.D. Nicolaou and S.L. Semiatin, High-Temperature Deformation and Failure of anOrthorhombic Titanium Aluminide SheetMaterial, Metall. Mater. Trans. A., Vol 27A(No. 11), Nov 1996, p 3675–3681

11. R. Pilkington, C.W. Willoughby, and J. Bar-ford, The High-Temperature Ductility ofSome Low-Alloy Ferritic Steels, Metal Sci.J., Vol 5, Jan 1971, p 1

12. D.J. Latham, J. Iron Steel Inst., Vol 92,1963–1964, p 255

13. R.E. Bailey, Met. Eng. Quart., 1975, p 43–50

14. R.E. Bailey, R.R. Shiring, and R.J. Ander-son, Superalloys Metallurgy and Manufac-ture, Proc. of the Third International Con-ference, Claitor’s Publishing, Sept 1976, p109–118

15. P.D. Nicolaou and S.L. Semiatin, An Inves-tigation of the Effect of Texture on theHigh-Temperature Flow Behavior of an Or-thorhombic Titanium Aluminide Alloy, Me-tall. Mater. Trans. A., Vol 28A (No. 3A),March 1997, p 885–893

16. J. Pilling and N. Ridley, Superplasticity inCrystalline Solids, The Institute of Metals,London, UK, 1989

17. R.M. Imayev and V.M. Imayev, MechanicalBehaviour of TiAl Submicrocrystalline In-termetallic Compound at Elevated Tem-peratures, Scr. Met. Mater., Vol 25 (No. 9),Sept 1991, p 2041–2046

18. D.A. Woodford, Strain-Rate Sensitivity as aMeasure of Ductility, Trans. ASM, vol 62(No. 1), March 1969, p 291–293

19. A.K. Ghosh and R.A. Ayres, On ReportedAnomalies in Relating Strain-Rate Sensitiv-ity (m) to Ductility, Metall. Trans. A, Vol7A, 1976, p 1589–1591

20. J.W. Hutchinson and K.W. Neale, Influenceof Strain-Rate Sensitivity on Necking Un-der Uniaxial Tension, Acta Metall., Vol 25(No. 8), Aug 1977, p 839–846

21. F.A. Nichols, Plastic Instabilities and Uni-axial Tensile Ductilities, Acta Mater., Vol 28(No. 6), June 1980, p 663–673

22. M.A. Meyers and K.K. Chawla, MechanicalMetallurgy Principles and Applications,Prentice Hall, 1984.

23. N.E. Paton and C.H. Hamilton, Microstruc-tural Influences on Superplasticity in Ti-6Al-4V, Metall. Trans. A, Vol 10A, 1979, p241–250

24. G.E. Dieter, Mechanical Metallurgy, 3rded., McGraw-Hill, 1986

25. A.K. Ghosh and C.H. Hamilton, Mechani-cal Behavior and Hardening Characteristicsof a Superplastic Ti-6Al-4V Alloy, Metall.Trans. A, Vol 10A, 1979, p 699–706

26. R. Verma, P.A. Friedman, A.K. Ghosh, S.Kim, and C. Kim, Characterization of Su-perplastic Deformation Behavior of a FineGrain 5083 Al Alloy Sheet, Metall. Mater.Trans. A, Vol 27A (No. 7), July 1996, p1889–1898

27. P.W. Bridgman, Studies in Large PlasticFlow and Fracture, McGraw-Hill, 1952

28. A.S. Argon, J. Im, and A. Needleman, Dis-tribution of Plastic Strain and NegativePressure in Necked Steel and Copper Bars,Metall. Trans. A, Vol 6A, 1975, p 815–824

29. C.M. Lombard, R.L. Goetz, and S.L. Sem-iatin, Numerical Analysis of the Hot Ten-sion Test, Metall. Trans. A, Vol 24A (No.9), Sept 1993, p 2039–2047

30. C. G’sell, N.A. Aly-Helal, and J.J. Jonas, J.Mater. Sci., Vol 18, 1983, p 1731–1742

31. A.K. Ghosh, A Numerical Analysis of theTensile Test for Sheet Metals, Metall. Trans.A, Vol 8A, 1977, p 1221–1232

32. S.L. Semiatin, A.K. Ghosh, and J.J. Jonas,A “Hydrogen Partitioning” Model for Hy-drogen Assisted Crack Growth, Metall.Trans. A, Vol 16A, 1985, p 2039–47

33. P.D. Nicolaou, S.L. Semiatin, and C.M.Lombard, Simulation of the Hot-TensionTest under Cavitating Conditions, Metall.Mater. Trans. A., Vol 27A (No. 10), Oct1996, p 3112–3119

34. S.L. Semiatin, R.E. Dutton, and S. Shama-sundar, Materials Modeling for the HotConsolidation of Metal Powders and Metal-Matrix Composites, Processing and Fabri-cation of Advanced Materials IV, T.S. Sri-vatsan and J.J. Moore, Ed., The Minerals,Metals, and Materials Society, 1996, p 39–52

35. P.D. Nicolaou and S.L. Semiatin, Scr. Ma-ter., Vol 36, 1997, p 83–88

36. M.M.I. Ahmed and T.G. Langdon, Excep-tional Ductility in the Superplastic Pb-62Pct Sn Eutectic, Metall. Trans. A, Vol 8A,1977, p 1832–1833


37. S.L. Semiatin, V. Seetharaman, A.K.Ghosh, E.B. Shell, M.P. Simon, and P.N. Fa-gin, Cavitation During Hot Tension Testingof Ti-6Al-4V, Mater. Sci. Eng. A, Vol A256,1998, p 92–110

38. C.C. Bampton and J.W. Edington, The Ef-fect of Superplastic Deformation on Sub-sequent Service Properties of Fine-Grained7475 Aluminum, J. Eng. Mater. Tech., Vol105 (No. 1), Jan 1983, p 55–60

39. J. Pilling and N. Ridley, Cavitation in Alu-minium Alloys During Superplastic Flow,Superplasticity in Aerospace, H.C. Heikke-nen and T.R. McNelley, The MetallurgicalSociety, 1988, p 183–197

40. G.H. Edward and M.F. Ashby, IntergranularFracture During Powder-Law Creep, ActaMetall., Vol 27, 1979, p 1505–1518

41. A.K. Ghosh, D.-H. Bae, and S.L. Semiatin,Initiation and Early Stages of CavityGrowth During Superplastic and Hot De-formation, Mater. Sci. Forum, Vol 304–306,1999, p 609–616

42. S. Sagat and D.M.R. Taplin, Fracture of aSuperplastic Ternary Brass, Acta Metall.,Vol 24 (No. 4), April 1976, p 307–315

43. A.H. Chokshi, The Development of CavityGrowth Maps for Superplastic Materials, J.Mater. Sci., Vol 21, 1986, p 2073–2082

44. B.P. Kashyap and A.K. Mukherjee, Cavi-tation Behavior During High TemperatureDeformation of Micrograined SuperplasticMaterials—A Review, Res Mech., Vol 17,1986, p 293–355

45. A.C.F. Cocks and M.F. Ashby, Creep Frac-ture by Coupled Power-Law Creep and Dif-fusion Under Multiaxial Stress, Met. Sci.,Vol 16, 1982, p 465–478

46. P.D. Nicolaou, S.L. Semiatin, and A.K.Ghosh, An Analysis of the Effect of Cavity

Nucleation Rate and Cavity Coalescence onthe Tensile Behavior of Superplastic Mate-rials, Metall. Mater. Trans. A, Vol 31A,2000, p 1425–1434

47. J. Pilling, Effect of Coalescence on CavityGrowth During Superplastic Deformation,Mater. Sci. Technol., Vol 1 (No. 6), June1985, p 461–466

48. P.D. Nicolaou and S.L. Semiatin, Modelingof Cavity Coalescence During Tensile De-formation, Acta Mater, Vol 47, 1999, p3679–3686

49. P.D. Nicolaou and S.L. Semiatin, The Influ-ence of Plastic Hardening on Surface De-formation Modes Around Vickers andSpherical Indents, Acta Mater, Vol 48, 2000,p 3441–3450

50. L. Weber, M. Kouzeli, C. San Marchi, andA. Mortensen, On the Use of Considere’sCriterion in Tensile Testing of MaterialsWhich Accumulate Internal Damage, Scr.Mater. Vol 41, 1999, p 549–551

51. C.M. Lombard, “Superplasticity in Near-Gamma Titanium Aluminides,” Ph.D. The-sis, University of Michigan, Ann Arbor, MI,2001

52. J. Lian and M. Suery, Effect of Strain RateSensitivity and Cavity Growth Rate on Fail-ure of Superplastic Material, Mater. Sci.Technol., Vol 2, 1986, p 1093–1098

53. M. Zaki, Micronecking and Fracture inCavitated and Superplastic Materials, Me-tall. Mater. Trans. A, Vol 27A, 1996, p1043–1046

54. P.D. Nicolaou and S.L. Semiatin, A Theo-retical Investigation of the Effect of Mate-rial Properties and Cavity Architecture/Shape on Ductile Failure During the HotTension Test, Metall. Mater. Trans. A., Vol29A, 1998, p 2621–2630

CHAPTER 14

Tensile Testing at Low Temperatures

THE SUCCESSFUL USE of engineering ma-terials at low temperatures requires that knowl-edge of material properties be available. Nu-merous applications exist where the servicetemperature changes or is extreme. Therefore,the engineer must be concerned with materialsproperties at different temperatures. Some of thetypical materials properties of concern arestrength, elastic modulus, ductility, fracturetoughness, thermal conductivity, and thermal ex-pansion. The lack of low temperature engineer-ing data, as well as the use of less common en-gineering materials at low temperatures, resultsin the need for low-temperature testing.

The terms “high temperature” and “low tem-perature” are typically defined in terms of thehomologous temperature (T/TM), (where T is theexposure temperature, and TM is the meltingpoint of a material (both given on the absolutetemperature scale, K). The homologous tem-perature is used to define the range of applica-tion temperatures in terms of the thermally ac-tivated metallurgical processes that influencemechanical behavior.

The term “low temperature” is typically de-fined in terms of boundaries where metallurgicalprocesses change. One general definition of“low-temperature” is T � 0.5 TM. For manystructural metals, another definition of low tem-perature is T � 0.3 TM, where recovery pro-cesses are not possible in metals and where thenumber of slip systems is restricted. For thesedefinitions, room temperature (293 K) is almostalways considered a low temperature for a metalwith a few exceptions, such as metals that havemelting temperatures below 200 �C (indium andmercury). In a structural engineering sense, lowtemperature may be one caused by extreme coldweather. A well-known example of this is thebrittle fracture of ship hulls during WWII thatoccurred in the cold seas of the North Atlantic(Ref 1). For many applications, low temperature

refers to the cryogenic temperatures associatedwith liquid gases. Gas liquefaction, aerospaceapplications, and super-conducting machineryare examples of areas in engineering that requirethe use of materials at very low temperatures.The term cryogenic typically refers to tempera-tures below 150 K. Service conditions in super-conducting magnets that use liquid helium forcooling are in the 1.8 to 10 K range.

The mechanical properties of materials areusually temperature dependent. The most com-mon way to characterize the temperature depen-dence of mechanical properties is to conduct ten-sile tests at low temperatures. Depending on thedata needed, a test program can range from afull characterization of the response of a materialover a temperature range, to a few specific testsat one temperature to verify a material perfor-mance. Many of the rules for conducting lowtemperature tests are the same as for room tem-perature tests. Low-temperature test proceduresand equipment are detailed in this chapter. Therole that temperature plays on the properties oftypical engineering materials is discussed also.Important safety concerns associated with low-temperature testing are reviewed.

Mechanical Properties atLow Temperatures

In general, lowering the temperature of a solidincreases its flow strength and fracture strength.The effect that lowering the temperature of asolid has on the mechanical properties of a ma-terial is summarized below for three principalgroups of engineering materials: metals, ceram-ics, and polymers (including fiber-reinforcedpolymer, or FRP composites). An excellent




Fig. 1 Simplified deformation behavior (Ashby) maps (a) for face-centered cubic metals and (b) for body-centered cubic metals.Source: Ref 2

source for an in-depth coverage of materialproperties at low temperatures is Ref 2.

Metals. Most metals are polycrystalline andhave one of three relatively simple structures:face-centered cubic (fcc), body-centered cubic(bcc), and close-packed hexagonal (hcp). Thetemperature dependence of the mechanical prop-erties of the fcc materials are quite distinct fromthose of the bcc materials. The properties of hcpmaterials are usually somewhere in between fccand bcc materials. The general aspects of tem-perature-dependent mechanical behavior may bediscussed using the deformation behavior mapsshown in Fig. 1(a) and (b). The axes of thesegraphs are normalized for temperature andstress. Temperature is normalized to the meltingtemperature, while stress is normalized to theroom temperature shear modulus, G (Ref 2).

The behavior characteristic of a pure, an-nealed fcc material is shown in Fig. 1(a). Thesmall increase of yield strength that occurs uponcooling is characteristic of the fcc behavior. Theultimate strength, which is shown as the ductilefailure line, increases much more than the yieldstrength on cooling. The large increase in ulti-mate strength coupled with the relatively smallincrease in yield strength in fcc materials resultsfrom ductile, rather than brittle, failure (Ref 2).

Figure 1(b) illustrates the classic bcc behav-ior. The large temperature dependence of theyield strength, the smaller temperature depen-dence of the ultimate strength, and a regionwhere the specimen fails before any significantplastic deformation occurs should be noted(Ref 2).

The previous discussion is for pure annealedmetals. Engineering alloys may behave some-what differently, but the trends are relativelyconsistent. Solid solution strengthening typi-cally increases yield and ultimate strengths ofthe fcc alloys while giving the yield strength anincreased temperature dependence. The tem-perature dependence of the ultimate strength isstill greater than that of the yield strength, allow-ing the alloy to maintain its ductile behavior.The ultimate tensile strengths of the fcc metalshave stronger temperature dependence thanthose of bcc metals. Austenitic stainless steelshave fcc structures and are used extensively atcryogenic temperatures because of their ductil-ity, toughness, and other attractive properties.Some austenitic steels are susceptible to marten-sitic transformation (bcc structure) and low-tem-perature embrittlement. Plain carbon and low al-loy steels having bcc structures are almost neverused at cryogenic temperatures because of theirextreme brittleness. Cases of anomalous strengthbehavior have been reported where a maximumstrength is reached at temperatures above 0 K.These cases are unique and usually involve sin-gle crystal research materials or very soft ma-terials, although yield strengths of commercialbrass alloys are reported to be higher at 20 Kthan at 4 K (Ref 2).

Ceramics. Ceramics are inorganic materialsheld together by strong covalent or ionic bonds.The strong bonds give them the desirable prop-erties of good thermal and electrical resistanceand high strength but also make them very brit-tle. Graphite, glass, and alumina are ceramics

Tensile Testing at Low Temperatures / 241

used at low temperature usually in the form offibers that reinforce polymer-matrix compositematerials. The high temperature (�77 K) super-conducting compounds are ceramics that posechallenging problems with respect to using brit-tle materials at low temperatures.

Polymers and Fiber-Reinforced Polymer(FRP) Composites. Polymers are rather com-plex materials having many classifications and awide range of properties. Two important prop-erties of polymers are the melting temperature,Tm, and the glass transition temperature, Tg, bothof which indicate the occurrence of a phasechange. The glass transition temperature, themost important material characteristic related tothe mechanical properties of polymer, is influ-enced by degree of polymerization. The Tg is thetemperature, upon cooling, at which the amor-phous or crystalline polymer changes phase to aglassy polymer. For most polymers at tempera-tures below Tg, the stress-strain relationship be-comes linear-elastic, and brittle behavior is com-mon. Some ductile or tough polymers exhibitplastic yielding at temperatures below Tg (Ref3). The Tg represents the temperature belowwhich mass molecular motion (such as chainsliding) ceases to exist, and ductility is primarilydue to localized strains. Suppression of Tg helpsto produce tougher polymers. The strong tem-perature dependence of the modulus is a distin-guishing feature of polymers compared to met-als or ceramics.

Fiber-reinforced polymer composites are usedextensively at low temperatures because of theirhigh strength-to-weight ratio and their thermaland electrical insulating characteristics. TheFRPs tend to have excellent tensile strength thatincreases with decreasing temperature. Re-inforcing fibers commonly used in high-perfor-mance composites for low-temperature appli-cations are alumina, aramid, carbon, and glass.Typical product forms are high-pressure moldedlaminates (such as cotton/phenolics and G-10)and filament-wound or pultruded tubes, straps,and structures. Although the FRP compositeshave desirable tensile strength, other mechanicalproperties such as fatigue and interlaminar shearstrength are sometimes questionable. Two goodsources of properties of structural composites atlow temperature are Ref 4 and 5.

Test Selection Factors:Tensile versus Compression Tests

Tensile and compression tests produce engi-neering data but also facilitate study of funda-

mental mechanical-metallurgical behavior of amaterial, such as deformation and fracture pro-cesses. If obtaining engineering data is the ob-jective and the materials application is at lowtemperature, the designer must be sure that me-chanical properties are stable at the desired tem-peratures. One important factor related to low-temperature testing is that the low temperaturemay cause unstable brittle fracture behavior thattensile or compression tests may fail to reveal.The cooling of materials, especially bcc metalsand polymers, can cause the materials to un-dergo a ductile-to-brittle transition. This behav-ior is not unique to steel but has its counterpartin many other materials. Brittle fracture occursin the presence of a triaxial stress state to whicha simple tensile or compression test will not sub-ject the material. Brittle fracture is caused byhigh tensile stress, while ductile behavior is re-lated to shear stress. A metal that flows at lowstress and fractures at high stress will always beductile. If, however, the same material is re-treated so that its yield strength approaches itsfracture strength, its behavior may become al-tered, and brittleness may ensue (Ref 1). If thematerials application is at low temperature, thedesigner must be sure that mechanical propertiesare stable, because the possibility of brittle frac-ture requires modification of the design ap-proach.

If the material in question is a new materialor a material for which little or no low-tempera-ture data exist, screening tests that can assesssusceptibility to brittle fracture are advisable.Two such screening tests are Charpy impact testsand notch tensile tests. Conducting Charpy ornotch tensile tests at various temperatures candetect a ductile-to-brittle transition over a tem-perature range. Ultimately, if the fracture tough-ness of the material is an issue, fracture tough-ness testing should be performed.

The intended service condition for the mate-rial should influence the test temperature and thedecision to perform tensile tests. It is good prac-tice to determine the properties while simulatingthe service conditions. Of course, life is not al-ways this simple, and actual service conditionsmay not be easily achieved with an axial stresstest at a given temperature.

Tensile testing is the most common test of me-chanical properties and is usually easier thanother test methods, such as compression testing,to conduct properly at any temperature. Thecompressive and tensile Young’s moduli of mostmaterials are identical. Fracture of a material is


caused by tensile stress that causes crack prop-agation. Tensile tests lend themselves well tolow-temperature test methods because the use ofenvironmental chambers necessitates longerthan normal load trains. Pin connections andspherical alignment nuts can be used to take ad-vantage of the increased length for self-align-ment purposes. For most homogeneous materi-als, stress-strain curves obtained in tension arealmost identical to those obtained in compres-sion (Ref 6). Exceptions exist where there is dis-agreement between the stress-strain curves intension and compression. This effect, termed“strength differential effect,” is especially no-ticeable in high-strength steels (Ref 7).

There are times when compression testing isrequired such as when the service-conditionstress is compressive or when the strength of anextremely brittle material is required. The sec-ond case is true for almost all polymers at cry-ogenic temperatures as they become extremelybrittle, glassy materials. The fillet radius of areduced-section tensile-test sample can createenough of a stress riser that the material failsprematurely. Stress concentrations, flaws, andsubmicroscopic cracks largely determine thetensile properties of brittle materials. Flaws andcracks do not play such an important role incompression tests because the stress tends toclose the cracks rather than open them. The com-pression tests are probably a better measure ofthe bulk material behavior because they are notas sensitive to factors that influence brittle frac-ture (Ref 3). A brittle material will be nearlylinear-elastic to failure, providing a well-definedultimate compressive strength. The following ta-ble lists competing factors that influence the testmethod choice, many of which are generic whilesome are specific to conditions associated withlow-temperature testing.

Tension Compression

AdvantagesCommonSelf-aligningWell-defined gage sectionGood for modulus, yield,

ultimate, and ductilityparameters

Good for modulus and yieldstrength

No gripsNo stress concentration in

sample designGood for ultimate strength of

brittle materialsEasy sample installationInexpensive sample cost

DisadvantagesSensitive to specimen designDifficult to test brittle materials

and composites wheremachining reduced section isnot plausible

End effects (friction/constraint)Sensitive to alignmentNot always good for ultimate

strengthNeed containment for fractured

material

The temperature at which to run the test canbe a simple determination such as when me-chanical properties data for a material at the pro-posed service temperature are not available.Other cases are not so straightforward, and thetemperature choice should be based on cost andthe ability to provide conservative results.Sometimes, a material is to be used at a coldtemperature, but testing it at room temperaturewill yield conservative data that are sufficient forthe application. For many 4 K applications, con-servative properties can be measured at 77 K ina simpler, more economical test. The degree ofstrengthening that will occur upon cooling from77 to 4 K is much less than that which occursfrom 295 to 77 K. When there is doubt aboutthe applicability of data from tests at a tempera-ture other than the service temperature, testingshould be done at the service temperature. Goodpractice is to test above, below, and at the servicetemperature for a more complete understandingof the material behavior.

The relative costs and difficulty of the testsare important. Tests conducted in liquid mediaare simpler to perform, in general, than inter-mediate temperature tests that require tempera-ture control. Below is a list of testing media andtheir associated temperatures (Ref 2).

Substance Temperature, K Bath type

Ice water 273 SlushIsobutane 263 Liquid at BPCarbon tetrachloride 250 SlushPropane 231 Liquid at BPTrichloroethylene 200 SlushCarbon dioxide 195 SolidMethanol 175 Slushn-pentane 142 SlushIso-pentane 113 SlushMethane 112 Liquid at BPOxygen 90.1 Liquid at BPNitrogen 77.3 Liquid at BPNeon 27.2 Liquid at BPHydrogen 20.4 Liquid at BPHelium (He4) 4.2 Liquid at BPHelium (He3) 3.2 Liquid at BP

All temperatures given at 0.1 MPa (1 atm). BP, boiling point

Some of these substances are more common,cheaper, or easier to handle than others. Themost commonly used substances in mechanicaltests are ice water, CO2/methanol slush, liquid-nitrogen (LN2) cooled methanol, LN2, and liquidhelium (LHe). Obvious hazards are associatedwith the use of oxygen and hydrogen, and theyshould be avoided if possible. Safety issues con-cerning the use of cooled methanol, LN2, andLHe are discussed subsequently in this chapter.


Fig. 2 A 100 kN capacity test machine equipped with cryostatfor low-temperature testing

Cost of the cryogenic medium is also an issue.Since LN2 is common and readily available, itscost is relatively low. LHe, on the other hand, isabout a factor of ten times as expensive as LN2.Liquid neon is sometimes used because it is easyto handle and its liquid boiling point temperatureis relatively close to that of liquid hydrogen, butit can be 20 to 40 times as expensive as LHe.The sublimation temperature of dry ice (CO2) is195 K, and it can be used to cool a methanol orpropanol bath with relative ease. Many of thesebath cooling techniques are tried and true meth-ods that require some practice to perfect but areusually inexpensive and simple ways to controltest sample temperature. Low-temperature con-trol can also be accomplished with electronictemperature control systems that utilize heatersand a cooling medium. Electronic temperaturecontrol systems are described in the followingsection.

Equipment

Low-temperature tensile tests can be per-formed on electromechanical or servohydraulictest machines with capacities of approximately50 to 100 kN. The 100 kN machine is preferablefor high strength materials such as steels or com-posites but of course larger or smaller capacitiescan be used as necessary. Direct tension testsusually require a simple ramp function that ispossible on the more economical electrome-chanical (screw-drive) test machine. Computercontrolled servo-hydraulic test systems are ver-satile and can perform a variety of tasks as wellas direct tension tests.

To facilitate the low-temperature requirement,the test machine must be equipped with a tem-perature-controlled environmental chamber.One consideration for the suitability of the ma-chine for low-temperature tests is the ease withwhich a low-temperature environmental cham-ber can be implemented. The physical charac-teristics of the test machine come into play, suchas the maximum distance between crossheadsand load columns.

A major factor to consider for cryogenic testsis the cryostat. “Cryostat” is a general term foran environmental chamber designed for cryo-genic temperatures and can be as simple as acontainer (dewar) to hold a liquid cryogen. Cry-ostats designed for mechanical testing have theadded requirement of providing structural sup-port to react to tensile forces that are applied to

the test material. Typically, a load frame is de-signed as an insert to a dewar. Since a dewar isa vacuum-insulated bucket to hold liquid, it isnot advisable to have a hole in the bottom forpull-rod penetration because it introduces a leakpotential for liquid, vacuum, and heat. Theclosed-bottom feature of a cryostat necessitatesthat the applied load and reacted load be intro-duced from the top. Cryostats are described fur-ther in the subsequent section “EnvironmentalChambers.”

The simplest method to introduce the loadpath from the top on a servo-hydraulic machineis to use a machine that has the hydraulic actu-ator mounted on top of the upper crosshead. Hy-draulic machines with this configuration areavailable, and the arrangement does not restrictnormal use of the machine. Figure 2 shows aservo-hydraulic test machine equipped with amechanical test cryostat. The screw-drive typetest machine is usually accommodating andshould have a movable lower crosshead with athrough hole for the load train. References 8 and9 give details of the design of cryostats for me-chanical test machines.


Fig. 3 Schematic of simple tensile canister from a standard-configuration machine for low-temperature testing

If the machine is not configured as describedin the preceding paragraphs, the machine is rela-tively incompatible for cryogenic tests. Cryo-genic tests on an incompatible machine requirespecially designed cryostats or an external framesystem both of which are usually expensive andcumbersome alternatives. Figure 3 shows aschematic of a simple test chamber (canister) forimmersion bath tests above liquid nitrogen tem-perature. This fixture provides an inexpensivemethod for conducting tests on conventionalmachines down to approximately 100 K.

Environmental Chambers. For low tempera-ture tests, an environmental chamber is a ther-mal chamber that contains a gaseous or liquidbath media used to control the low temperatureof a test. Sub-room-temperature environmentsare obtained with three basic chamber designs:a conventional refrigeration chamber; a ther-mally insulated box-container, or a cryostat de-signed for cryogenic temperatures with vacuuminsulation; and thermal radiation shielding.

Conventional refrigeration covers the tem-perature range from �10 to �100 �C (�50 to�150 �F) and could be employed for tests in thisrange, much the same as furnaces are used ontest machines to achieve elevated temperatures.Although mechanical refrigeration seems like alogical choice to cool environmental chambers,it is rarely used. This is probably because of thecapital expense and the relative simplicity ofother methods.

Commercial environmental chambers de-signed for use with test machines are availablefor controlling temperatures from approximately800 K down to 80 K. Such chambers use elec-trical heaters for elevated temperatures and coldnitrogen gas cooling for sub-room-temperature.The cold nitrogen gas is supplied from a liquidnitrogen storage dewar. The flow of cold gas de-termines the cooling power and is controlled atthe inlet with a variable flow valve that is reg-ulated by the temperature controller. These sys-tems are versatile in that a wide range of testtemperature is possible with a single system.Some of the disadvantages are bulkiness, whichcan make setup difficult, and that the tests canbe time consuming with respect to attainingequilibrated test temperatures.

As mentioned previously, cryogenic tempera-ture tests are conducted in a cryostat. Reference10 is an excellent historical perspective on low-temperature mechanical tests that details a num-ber of cryostat designs, many of which use con-ventional machines with standard load path

configurations. Pull-rod penetration through thebottom of a cryostat introduces a leak potentialfor liquid, vacuum, and heat and is not recom-mended for liquid bath-cooled tests. Modernmechanical test cryostats are typically a combi-nation of a custom designed structural loadframe fit into a commercial open-mouth bucketdewar. Some of the design details of a tensiletest cryostat are shown in the schematic in Fig.4 and photograph in Fig. 5. The design of thecryostat load frame is driven by engineering de-sign factors such as cost, strength, stiffness, ther-mal efficiency, and ease of use. A good designphilosophy is to produce a versatile fixture thatcan test a variety of specimens over a range oftemperatures. The effect of lowering the tem-perature on the properties of a material can beevaluated by comparing the baseline room tem-perature properties. It is advisable to have thetest apparatus capable of testing the material atboth room temperature and cold temperatures.Construction materials used are austenitic stain-less steels, titanium alloys, maraging steels, andFRP composites. For tensile tests, the cryostatframe reacts to the load in compression. Theframe can be thermally isolated with low-ther-mal conductivity, FRP composite standoffs.


Fig. 5 Tensile test cryostat. The force-reaction posts have fi-ber-reinforced polymer composite stand-offs.Fig. 4 Schematic of a tensile test cryostat

Cryogen Liquid Transfer Equipment. Thesupply and delivery of cryogenic fluids requirespecial equipment. The equipment describedhere pertains to the use of the two most commoncryogen test media, liquid nitrogen and liquidhelium. Both liquid helium and nitrogen can bepurchased from suppliers (usually welding sup-ply distributors) in various quantities that are de-livered in roll-around storage dewars. Liquid ni-trogen can be transferred out of the storagedewar into the test dewar with simple or com-mon tubing materials. Its thermal properties andinexpensive price allow its flow through unin-sulated tubes. For example, butyl rubber hosecan be attached to the storage dewar, and thehose will freeze as the liquid passes through.Liquid helium, on the other hand, is more dif-ficult to handle, and it requires special vacuum-insulated transfer lines. Liquid helium transferlines are usually flexible stainless steel lines withend fittings to match the inlet ports of the testcryostat and the supply cryostat. For both liquid

nitrogen and helium, the storage tank is pres-surized to enable transfer of the liquid.

Instrumentation. The minimum instrumen-tation requirement in any tensile test is that forforce measurement. Typically, forces are mea-sured with the test machine force transducer(load cell) in the same manner as for forces mea-sured in room temperature tests. During low-temperature tests, precautions should be taken toensure the load cell remains at ambient roomtemperature.

Strain measurements may require temperaturedependent calibration. Common strain measure-ment methods used are test machine displace-ment, bondable resistance strain gages, andclip-on extensometers. Also applicable to low-temperature strain measurements but less com-monly used are capacitive transducer methods(Ref 11), noncontact laser extensomers, and lin-ear variable differential transformers (LVDT)with extension rods to transmit displacementsoutside of the environmental chamber to theLVDT-sensing device.

Test machine displacement (stroke or cross-head movement) is a simple, low-accuracymethod of estimating specimen strain. The in-accuracy comes because the displacement in-cludes deflection of the test fixturing plus the testspecimen gage section. Compensating for testfixturing compliance improves accuracy.

Bondable resistance strain gages are for sen-sitive measurements such as modulus and yieldstrength determination. The strain gage manu-facturer supplies strain gage bonding proceduresfor use at cryogenic temperatures. The overallrange of strain gages at cryogenic temperatures


is limited to about 2% strain. Applicable straingages recommended by strain gage manufactur-ers have temperature dependent calibration datadown to 77 K. Interest in their use down to 4 Khas resulted in strain gage research verifyingtheir performance to 4 K (Ref 12). A typicalgage factor (GF) is 2 for NiCr alloy foil gagesand it increases approximately 2 to 3% on cool-ing from 295 to 4 K. Thermal output strain sig-nals are a large source of error that must becompensated for. Compensation is usually ac-complished using the bridge balance of the straincircuit where zero strain can be adjusted to co-incide with zero stress. If this is not possible,other steps must be taken to electrically or math-ematically correct the thermal output strain.

Extensometers applicable to low-temperaturetests utilize strain gages mounted to a bendingbeam element. The temperature sensitivity canbe determined by calibrating with a precisioncalibration fixture that enables calibration atvarious temperatures. Depending on the accu-racy desired, it is possible to use one or twocalibration factors over a large temperaturerange. A typical strain-gage extensometer-cali-bration factor changes about �1% over the tem-perature range from 295 to 4 K.

Temperature measurement is done with an as-sortment of temperature sensors. Reference 2has a section devoted to temperature measure-ment at low temperatures. The most commonmethod of temperature measurement is to use athermocouple. Type E thermocouples (Chromelversus Constantan) and Type K (Chromel versusAlumel) cover a wide range of temperature andcan be used at 4 K when carefully calibrated. Abetter choice of thermocouple, designed to havehigher sensitivity at cryogenic temperatures, isa AuFe alloy versus Chromel thermocouple.Electronic temperature sensors (diodes and re-sistance devices) are available with readoutdevices that have higher precision than ther-mocouples. Silicon diodes, gallium-aluminum-arsenide diode, carbon glass resistor, platinumresistor, and germanium resistor are some of themore commonly used types of sensors.

Cryogenic temperature controllers that workwith the types of temperature sensors namedabove are available. The majority of temperaturecontrollers vary heating power and require thatthe test chamber environment is slightly coolerthan the set-point temperature. The test engineeris responsible for the environmental chamberand cooling medium of the system. The con-trollers use the temperature sensors as the feed-

back sensor to operate a control loop and supplypower for resistive heaters.

Additional Equipment Considerations. Tef-lon-insulated lead wires are advisable at verylow temperatures because the insulation will beless likely to crack and cause problems. Elec-tronic noise reduction can be an issue in low-temperature tests because lead wires tend to belong. Standard methods of noise reduction areshielding and grounding. Self-heating and ther-mocouple effects are important issues at lowtemperatures. Precautions should be taken to en-sure that thermal effects do not mask the testdata. Strain gage excitation voltages should bekept low. Reference 10 gives the parameters interms of power density for calculating excitationvoltage to be used for strain gages at 4 K.

Tensile TestingParameters and Standards

As at room temperature, tensile tests at lowtemperature are for determining engineering de-sign data as well as for studying fundamentalmechanical-metallurgical behaviors of a mate-rial such as deformation and fracture processes.The usual engineering data from tensile tests areyield strength, ultimate tensile strength, elasticmodulus, elongation to failure, and reduction ofarea. The effects of material flaws (inclusions,voids, scratches, etc.) are amplified in low-tem-perature testing, as materials become more brit-tle and sensitive to stress concentrations. Datascatter tends to increase, and the quantity of teststo characterize a material is usually greater thanthat used for room temperature testing. The testengineer must judge when sufficient testing hasbeen done to provide representative data on amaterial.

Test fixture alignment is important at low tem-peratures because of necessarily long load trains.Self-alignment in tensile tests can be accom-plished through the use of universal joints,spherical bearings, and pin connections. Thealignment should meet specifications detailed inASTM E 1012, “Standard Practice for Verifica-tion of Specimen Alignment Under TensileLoading.” Strain measurement should be doneusing an averaging technique that can reduce er-rors associated with misalignment or bendingstress. Strain measurement equipment is detailedabove in the instrumentation section.

Metals. The standard tensile test method formetals, ASTM E 8, covers the temperature range


Fig. 6 Schematics of tensile specimen commonly used at low temperature. (a) Round. (b) Flat. Dimensions are in inches (millimeters).thd, threaded

from 10 to 40 �C (50 to 100 �F) and is used asa guideline for lower temperature tests. The needfor engineering data in the design of supercon-ducting magnets has resulted in the adoption ofthe tensile test standard ASTM E 1450 for testsof structural alloys in liquid helium at 4.2 K.

The strain rate sensitivity of the flow stress inmetals decreases as temperature is reduced. Typ-ical strain rates in standard tensile tests are onthe order of 10�5 s�1 to 10�2 s�1 and do nothave a pronounced effect on the material flowstress. The strain rate becomes important in cry-ogenic temperature tests because of a tendencyfor specimen heating causing discontinuousyielding in displacement control tests. Discon-tinuous yielding is a subject of low-temperatureresearch of alloys, well described in ASTM E1450. The localized strain/heating phenomenontypically initiates after the onset of plastic strainand results in a serrated stress-strain curve.ASTM test standard E 1450 prescribes a maxi-mum strain rate of 10�3 s�1 and notes that lowerrates may be necessary. The strain required toinitiate discontinuous yielding increases withdecreasing strain rate. If discontinuous yieldingstarts before the 0.2% offset yield strength isreached, the associated load drop affects the es-timation of the yield strength. It may be possibleto slow the strain rate to postpone the serratedcurve until after the 0.2% offset yield strengthis reached and then to increase the rate, not toexceed 10�3 s�1. Reference 13 reports researchon the effect of strain rate in tensile tests at 4 K.

Test specimen sizes are preferably small forlow-temperature tests. The common 12.7 mm(0.5 in.) round, ASTM-standard tensile speci-

men is rarely used at low temperature. Tensilespecimens should be small due to size con-straints placed by the environmental test cham-ber, which is designed for thermal efficiency.Standard capacity test machines (100 and 50 kN)favor small specimens due to high tensilestrengths encountered at low temperatures. Asubscale version of the 12.7 mm (0.5 in.) roundthat meets ASTM specifications and works wellat cryogenic temperature is shown in Fig. 6(a).A 100 kN force capacity test machine can gen-erate about 3.5 GPa stress on a 6 mm diametergage section. Figure 6(b) shows a flat, subscaletensile specimen that is also commonly used atcryogenic temperatures.

Polymers and Fiber-Reinforced Polymer(FRP) Composites. Tensile tests of FRP com-posites are governed in test procedure ASTM D3039, while polymers and low modulus (�20GPa) composites are tested using the guidelinesestablished in ASTM D 638. Neither have spe-cific temperature ranges or limitations.

The problem with testing polymers at lowtemperatures is the tendency for polymers to beextremely brittle materials. Test temperaturesbelow room temperature are usually well belowthe glass transition temperature, Tg, of the poly-mer. The test specimen designs in ASTM D 638are susceptible to grip failures once the materialis brittle. Traditional strain measurement tech-niques must be performed carefully. Clip-on ex-tensometers must mechanically attach to the ma-terial, usually producing some sort of stressconcentration that may initiate failure. Straingages locally reinforce low-modulus material,and the associated error and correction method


Table 1 Safety issues associated with the use of liquid cryogens for low-temperature testing

Safety issue Solution

Liquid cryogens can spill or splash onto the body and causefreezing of human tissue.

Personnel should wear appropriate clothing and avoid directcontact with cold parts.

Helium, nitrogen, or carbon dioxide can displace air in a confinedarea.

Cryogens should be used only in well-ventilated areas.

Volumetric expansion is extremely high (typically 700–1000 times)when a liquid cryogen vaporizes. Such expansion is dangerouswhen it occurs in closed containers or fixture components withpotential for trapped gas/liquid volumes.

Cryostats must include safety pressure-relief capabilities;redundancy is necessary because mechanical relief valves mayfreeze or malfunction. Component parts such as tubes orthreaded connections that can trap liquids or gases should beidentified, and solutions (such as weep holes) included in thedesign. If there is potential for liquid to get into a space, provideexit relief rather than trying to seal the liquid out.

Oxygen-rich (flammable) condensation can form on chilledsurfaces (surfaces that are chilled to temperatures below 90 Kand then exposed to air; common on uninsulated liquid nitrogentransfer lines and inside open-mouth dewars containing liquidnitrogen or helium residue).

Inform personnel of potential fire hazard, and take appropriateprecautions.

Low temperatures may cause embrittlement of the material, causingit to fail at lower-than-expected loads.

Test personnel must be aware of the potential and prepare forbrittle fracture of structural components.

is explained in Ref 14. Most tensile tests of poly-mers show an increase in tensile strength uponcooling from 295 to 77 K and a decrease or con-stant level of strength with continued cooling to4 K (Ref 15). One would expect the strength tocontinue to increase with decreasing tempera-ture. This anomalous behavior is probably anartifact of the tensile testing of an extremely brit-tle material.

Tensile tests of FRP composites at low tem-peratures are simpler than tests of neat polymersbecause of the more rugged sample. One chal-lenge is the gripping of high-strength, unidirec-tionally reinforced composites. The convenienceof hydraulic wedge grips is not usually an optionin low-temperature tests. An example of a low-temperature tensile test program to characterizea unidirectionally reinforced epoxy compositefrom 295 to 4 K is described in Ref 16.

Temperature Control

Test temperature is controlled by a bath tem-perature or by controlling the temperature of agaseous environment. The temperature of thetest specimen should be maintained �1 K forthe duration of the test. For bath-cooled tests,the temperature of the bath and the specimenshould be the same. A potential source for erroris the conduction path or heat sink that the loadtrain provides, possibly causing the specimen tobe warmer than the bath. For tests at tempera-tures below 77 K (typically 4 K tests), the testcryostat is precooled with liquid nitrogen as aneconomical time-saving step.

The temperature of the specimen is usuallymonitored for tests using gaseous environmenttemperature control. The temperature should bemeasured at the gage section and at the grippedends to ensure that the temperature across thelength of the specimen is constant. For tempera-tures above 80 K, the cooling can be a staticmethod, such as a pool of liquid nitrogen in thedewar below the test fixturing. Test temperaturesbelow the liquid nitrogen bath temperature arebest accomplished through the use of cold he-lium gas for cooling power. This can be accom-plished with a flow cryostat, where coolingpower is regulated by throttling the flow of thecold gas or liquid. Between the manual regula-tion of the cooling medium and the regulatedheater power, one can obtain constant test tem-peratures between 77 and 4 K. Variations of cry-ogenic temperature control exist such as cryo-genic refrigerators, which can be applied to thetemperature control of mechanical tests. Cryo-coolers and other mechanical refrigerationtechniques are not commonly used in mechani-cal tests, due to the initial capital expense andthe relative simplicity of other cooling methods.

Safety

Safety in a laboratory or industrial setting isalways a concern. Some of the safety issues withrespect to low-temperature testing are commonsense issues, while some others are not so ob-vious. Table 1 describes the most commonsafety issues and appropriate solutions for each.Safety issues associated with the use of liquid


hydrogen or liquid oxygen are not dealt withinthis article and can be found in Ref 10. In ad-dition to the issues listed in Table 1, personnelshould consider general safety issues related totension and compression testing at all tempera-ture ranges.

ACKNOWLEDGMENT

This chapter was adapted from R.P. Walsh,Tension and Compression Testing at Low Tem-peratures, Mechanical Testing and Evaluation,Vol 8, ASM Handbook, ASM International,2000, p 164–171.

REFERENCES

1. E.R. Parker, Brittle Behavior of Engineer-ing Structures, John Wiley & Sons, 1957

2. R.P. Reed and A.F. Clark, Ed., Materials atLow Temperatures, ASM, 1983

3. L.E. Neilsen and R.F. Landel, MechanicalProperties of Polymers and Composites,Marcel Dekker, NY, 1994, p 249–263

4. M.B. Kasen et al., Mechanical, Electrical,and Thermal Characterization of G-10CRand G-11CR Glass-Cloth/Epoxy LaminatesBetween Room Temperature and 4 K, Ad-vances in Cryogenic Engineering, Vol 28,1980, p 235–244

5. R.P. Reed and M. Golda, Cryogenic Prop-erties of Unidirectional Composites, Cryo-genics, Vol 34 (No. 11), 1994, p 909–928

6. E.P. Popov, Mechanics of Materials, 2nded., Prentice-Hall, NJ, 1976

7. J.P. Hirth and M. Cohen, Metalls. Trans.,Vol 1, Jan 1970, p 3

8. G. Hartwig and F. Wuchner, Low Tempera-ture Mechanical Testing Machine, Rev. Sci.Instrum., Vol 46, 1975, p 481–485

9. R.P. Reed, A Cryostat for Tensile Test in theTemperature Range 300 to 4 K, Advancesin Cryogenic Engineering, Vol 7, PlenumPress, NY, 1961, p 448–454

10. J.H. Lieb and R.E. Mowers, Testing ofPolymers at Cryogenic Temperatures,Testing of Polymers, J.V. Schmitz, Ed., Vol2, John Wiley & Sons, 1965, p 84–108

11. R.P. Reed and R.L. Durcholz, Cryostat andStrain Measurement for Tensile Tests to1.5 K, Advances in Cryogenic Engineer-ing, Vol 15, Plenum Press, NY, 1970, p109–116

12. C. Ferrero, Stress Analysis Down to Liq-uid Helium Temperature, Cryogenics, Vol30, March 1990, p 249–254

13. R.P. Reed and R.P. Walsh, Tensile StrainEffects in Liquid Helium, Advances inCryogenic Engineering, Vol 34, PlenumPress, 1988, p 199–208

14. C.C. Perry, Strain Gage Reinforcement Ef-fects on Low Modulus Materials, Manualon Experimental Methods for MechanicalTesting of Composites, R.L. Pendelton andM.E. Tuttle, Ed., Society for ExperimentalMechanics, 1989, p 35–38

15. R.P. Reed and R.P. Walsh, Tensile Prop-erties of Resins at Low Temperatures, Ad-vances in Cryogenic Engineering, Vol 40,Plenum Press, NY, 1994, p 1129–1136

16. R.P. Walsh, J.D. McColskey, and R.P.Reed, Low Temperature Properties of aUnidirectionally Reinforced Epoxy Fibre-glass Composite, Cryogenics, Vol 35 (No.11), 1995, p 723–725

CHAPTER 15

High Strain Rate Tensile Testing

HIGH STRAIN RATE TENSILE TESTINGis necessary to understand the response of ma-terials to dynamic loading. Strain rates rangingfrom 100 s�1 to �104 s�1 occur in many pro-cesses or events of practical importance, such asforeign object damage, explosive forming,earthquakes, blast loading, structural impacts,terminal ballistics, and metalworking. The be-havior of materials under high strain rate tensileloads may differ considerably from that ob-served in conventional tensile tests.

High strain rate sensitivity is primarily man-ifested in variations in yield and failure criteria.Yielding and failure are also affected by stressstate, ratio of mean stress to deviatoric stress,stress amplitude, stress history, and temperature.Tests must be designed to simulate the most rele-vant load characteristics. For example, manyprocesses involving dynamic tensile stress in-clude compressive prestress. Strain rate sensitiv-ity also depends on whether engineering or truestrain formulations are used, because local in-stabilities (such as necking) are often suppressedat high rates.

Measurement of strain is a major problem inhigh strain rate tensile testing. In quasi-statictesting, the diameter of the minimum cross sec-tion in a cylindrical specimen can be measured;such measurements are virtually impossible orhighly impractical in high-rate testing. Further-more, although strains are easily measured overa uniform gage length section in quasi-statictesting, the same measurements are considerablymore difficult to obtain at high strain rates. Me-chanical extensometers are the primary tool usedin quasi-static tests, but they are of little use athigh rates of strain because of the effects of in-ertia.

Therefore, high-rate tests use strain gages, op-tical extensometers, and displacement measure-ments between loading fixtures to determine orinfer the dynamic tensile strains in a test speci-

men. At very high rates of strain, strains may bemeasured in some experimental configurationsonly through wave propagation analysis. Thisprocedure generally requires that assumptionsbe made about the constitutive behavior, thatwave propagation analysis be carried out, andthat predictions and experimental observationsbe compared. Unique solutions cannot be guar-anteed, because some other constitutive modelmay conceivably provide similar results in a par-ticular wave propagation problem.

Conventional Load Frames

Strain rate effects in tension are determinedby performing conventional tensile tests at vary-ing loading rates up to approximately 100 s�1.Conventional test machines are available withincreased ram velocities, as are high-speedpneumatic and hydraulic machines. The speedcapability of a machine may be influenced byseveral factors. Speed may be a function of theload that the ram is attempting to apply, and theno-load speed may be much higher than the full-load speed. The distance traveled may also affectthe speed capability. A long stroke machine mayattain a given speed only after a significantamount of travel. Depending on the specimenlength, considerable specimen strain could occurbefore final maximum velocity is obtained. Fi-nally, the ability to control speed is a functionof the response capability of a servo-controlledmachine working in a closed-loop mode. Open-loop machines provide speeds that may be influ-enced by specimen strength and cannot easilyreproduce predetermined velocities or strainrates on materials with different yield strengthsor strain-hardening behaviors. Additional infor-mation on the operational characteristics of con-ventional tensile testing machines can be found




Fig. 3 Nondimensional strain profile. See text for details andexplanation of symbols.

Fig. 2 Graph of the function f(s). See text for details and ex-planation of symbols.

Fig. 1 Schematic of tensile test configuration. See text for de-tails and explanation of symbols.

in Chapter 4, “Tensile Testing Equipment andStrain Sensors.”

Effects of Inertia and Wave Propagation.A fundamental difference between a high strainrate tension test and a quasi-static tension test isthat inertia and wave propagation effects arepresent at high rates. It must be determined howfast a uniaxial tension test can be run to obtainvalid stress-strain data. To determine this, con-sider a specimen of initial length L subjected toa uniform velocity �0 at time t � 0, as shownin Fig. 1. This hypothesis could represent a testin a constant crosshead velocity testing machine,or a drop-weight type of test in which a largemass impacts one end of the specimen. If (x,t)denotes the displacement of any point in the xdirection and assuming purely uniaxial mo-tion—that is, neglecting radial inertia effects—the equation of motion is:

2 2� u � u2� c (Eq 1)2 2�t �x

where u is displacement and

1/2Ec � (Eq 2)� �qis the longitudinal wave velocity in a bar or rod,where E is Young’s modulus, and q is mass den-sity. Applying the boundary conditions of theleft end fixed and the right end moving with con-

stant velocity �0 and assuming initial conditionsof zero displacement and velocity, the solutionis:

m L x x0u(x,t) � f s � � f s � (Eq 3)� � � � ��2c L L

where s � tc/L is a dimensionless time, and s� 1 represents the time it takes a wave to prop-agate the length of the specimen. The functionf(s) is shown in Fig. 2. Strain can be obtainedfrom e � �u/�x and stress from r � Ee. Byintroducing the dimensionless variables:

xn � (Eq 4a)

L

m0m* � (Eq 4b)c

plots of stress and strain can be constructed as afunction of time. Figure 3 illustrates strain nor-malized with respect to �* against dimensionlesstime s at an arbitrary position n along the bar.The dashed line indicates the average strain inthe bar, which is normally total displacement di-vided by bar length.

The localized strain is measured by a straingage with a gage length that is small comparedto the length of the specimen. Figure 4 illustratesthe normalized stresses at both ends of the bar.The response at the fixed end is recorded by aload cell. Figures 3 and 4 illustrate that stressesand strains accumulate from numerous wavespropagating back and forth in the bar. Note thatthe solution to the mathematical problem has as-sumed an instantaneous jump in velocity at t �0, whereas some finite rise time usually occurs

High Strain Rate Tensile Testing / 253

Fig. 4 Stress history at ends of bar. See text for details andexplanation of symbols.

because of imperfect impact or machine re-sponse.

If many wave transits occur during a test, theuse of average stresses and strains appears jus-tified. However, if the velocity is high, then onlya few wave reflections may occur before thespecimen fails. In this case, individual wavepropagation must be considered; average valuesalone cannot be considered, and the use of thistest to determine dynamic stress-strain responseis precluded. Note that this analysis is based ona material that is linear-elastic and assumes azero rise time in the applied velocity. Stresswaves are propagated at the elastic wave veloc-ity. With material that has deformed into theplastic region, the plastic wave velocity is moreappropriate and generally can be an order ofmagnitude smaller than the elastic wave veloc-ity.

One factor in determining whether or notwave propagation effects limit the validity of atensile test is the sample ring-up time, which isthe time required for a sample to achieve a uni-form state of stress. Generally, measurementsare not valid for times such that L � ct. Thiscorresponds to a situation in which strain e � �/c � Consequently, small strain measure-eL/c.ments are difficult to obtain at very high strainrates. Another concern is that local failure mayoccur at the end to which the load is applied.The magnitude of the stress transient associatedwith the sudden application of velocity �0 is rm

� qc�0.The test must be designed so that rm � Y, the

yield stress. For example, consider a bar 25 mm(1 in.) in length that is accelerated at one end to2.5 m/s (8.2 ft/s). For many engineering mate-rials, including steels, aluminum alloys, and ti-tanium alloys, the elastic wave velocity is about5000 m/s (16,400 ft/s). The maximum stressgenerated at the accelerated end of the bar isqc�. For a steel bar, the first stress pulse is 100MPa (14.5 ksi), and the average strain rate is 100s�1. If a steel with a strength of 1 GPa (145 ksi)is being tested, the maximum allowable drivingvelocity is 25 m/s (82 ft/s). At that velocity, in-stantaneous failure would occur at the drivenend.

Assuming that wave propagation effects maybe neglected in a given test, the second aspectthat must be checked is the response of the loadcell. Load cell ringing is frequently encounteredin high-rate tensile testing. Generally, this timeperiod (reciprocal of the natural frequency inhertz) must be small compared to the total du-

ration of the test. For example, if a load cell hasa natural frequency of 1 kHz, its period of vi-bration is 10�3 s. This load cell could then beused only for experiments that lasted over tentimes that amount, or over 10 ms.

Another condition that must be satisfied is thedistance of the load cell from the end of the spec-imen. If a sufficient distance exists between thespecimen and load cell, the finite elastic wavetransit time may result in load data that are nottime-coincident with strain data. To preventphase lags from obscuring the experimentaldata, the wave transit time from the specimen toload cell should be negligibly small comparedto the test duration. Otherwise, the load datamust be corrected for the delay, and such cor-rections seldom are precise.

Strain Measurement. The final aspect ofhigh-speed tensile testing is determination ofstrain. The most direct, reliable method useselectrical resistance strain gages. The frequencyresponse capability of strain gages is consider-ably greater than the mechanical response of thecombination of load train, specimen, and loadcell.

Another method of measuring strain involvesthe use of optical extensometers, in which dis-placement measurements across the loading fix-tures are divided by an actual or effective gagelength. When using crosshead displacementmeasurements, caution must be exercised to en-sure that these represent only specimen elonga-tion and not machine, ram, or load train elon-gations. The same precautions that apply inquasi-static tests also apply in dynamic tests.

If the above precautions are observed, validstress-strain data can be obtained up to maxi-mum strain rates in the range of 10 to 100 s�1.For higher strain rates, or for cases in which the


above criteria are not met, highly specializedtesting techniques may have to be used. As dis-cussed below, these include:

Applicable strain rate, s�1 Testing technique

104 Expanding ring test�105 Flyer plate test100–103 Split-Hopkinson pressure bar test103–104 Rotating wheel test

Expanding Ring Test

The expanding ring test is a highly sophisti-cated technique for subjecting metals to tensilestrain rates over 104 s�1 (Ref 1, 2). Although thetesting principle is simple, its performance re-quires specialized equipment available in only afew laboratories. The ring test can determine thehigh-rate stress-strain relationships, but a sim-plified, more widely used version can be em-ployed to determine ultimate strain only (Ref3, 4).

This test involves the sudden radial accelera-tion of a ring due to detonation of an explosivecharge or electromagnetic loading. The ring rap-idly becomes a free-flying body, expanding ra-dially, and decelerating due to its own internalcircumferential stresses. A thin ring must beused for the analysis to be valid; the wall thick-ness should be less than one tenth the ring di-ameter, which is typically 25 mm (1 in.). If R isthe radius of the ring, q the density, and r thehoop stress:

2d Rr � �qR (Eq 5)2dt

To obtain stress-strain data, radial displace-ment as a function of time must be calculated.Strain is proportional to change in radius (justas engineering strain in tension is DL/L0); thus:

Re � ln (Eq 6)

R0

where R0 is the initial radius. Stress may be com-puted from Eq 5 by double differentiation of ra-dial displacement data as a function of time.Ring displacement can be obtained through theuse of high-speed photography, streak cameras,displacement interferometers, or other methodsfor measuring radius as a function of time.

It is difficult to determine stress accurately bydouble differentiation of displacement data. Sev-

eral laboratories have used a laser velocity in-terferometer to measure ring velocity directly(Ref 5, 6). Thus, only a single differentiation isnecessary to calculate stress, and precision is im-proved considerably.

Advantages of the Ring Test. The ring testhas two principal advantages. The expandingring test subjects the material to a state of dy-namic uniaxial stress without the wave propa-gation complications that accompany other highstrain rate tests. Also, the maximum strain rateavailable in the ring test is higher than in anyother common tension tests involving large plas-tic strains.

Limitations of the Ring Test. Strain rate inthe expanding ring test is not usually constant.The strain rate is computed from (dR/dt)/R, andboth of these terms vary continually. Strain rateis usually greatest at the start of ring decelera-tion, when strain is smallest. Values in excess of104 s�1 are readily obtained. If the ring does notrupture, the strain rate falls to zero at the end ofthe test.

Ring specimens also experience a compres-sive preload in the radial direction that often ex-ceeds the yield stress during the accelerationphase. Because load history is known to affectthe subsequent stress-strain behavior of manymaterials, data obtained from expanding ringtests do not always agree with results from othertests at slightly lower strain rates.

The difficulties, expense, and limitations ofthe expanding ring test preclude its use as a stan-dard test technique for generating high strainrate stress-strain data in tension. Only a few lab-oratories are capable of performing this test.However, if subjecting a material to high strainrates in tension without determining stress-straindata is of primary interest, the expanding ringtest is much easier to conduct. A number of in-vestigators have used this test to determine strainto failure under dynamic loading (Ref 3, 4).Here, the accurate determination of radial dis-placement versus time is not as critical, becausestresses are not calculated. Less precise dis-placement data provide reasonably accurate de-terminations of strain rate. The ambiguity aris-ing from possible strain rate history effects stillexists when the expanding ring test is used inthis simpler manner.

The expanding cylinder test, a variation ofthe ring test, provides a dynamic stress stateequivalent to that produced in a quasi-static ten-sile test on a wide sheet versus a thin strip ofmaterial. A difficulty encountered in this type of


Fig. 5 Schematic of gas-gun-launched flyer plate impact test setup

test is the need for an impulse to be generatedsimultaneously in time along the axis of the cyl-inder. Because explosive detonation along awire, for example, propagates at a finite wavespeed, uniform deformation along the length ofthe axis cannot be ensured. Dimensions, deto-nation wave speeds, and synchronization ofmultiple detonation all must be considered care-fully to ensure that the cylinder is deformed asuniformly as possible and that axial stress wavesare not generated (Ref 7).

Flyer Plate and ShortDuration Pulse Loading

Traditionally, flat plate impact tests have beenused to obtain high strain rate yield data, shockwave response data, and equation of state datafor materials undergoing uniaxial strain. Uni-axial strain refers to a three-dimensional state ofstress in which deformation or strain occurs inonly one direction—the direction of loading.The uniaxial strain condition persists for only ashort period of time, until stress waves originat-ing at lateral boundaries reach the specimen in-terior. In a typical experiment, this time periodis on the order of several to tens of microsec-onds. Uniaxial strain is defined mathematicallyas:

u � 0, u � u � 0 (Eq 7)x y z

where x is the direction of loading; ux is the dis-placement in that direction; and y and z are or-thogonal directions in a plane normal to x. Thestrains are obtained from the displacement de-rivatives, thus:

e � 0, e � e � 0 (Eq 8)x y z

The flat plate impact test is performed bylaunching a flat flyer plate against a second sta-tionary target plate. Compressed gas guns, pro-pellant guns, magnetic accelerators, and explo-sives have all been used to launch the flyer plate(Ref 8). Extreme precision must be achieved toeliminate relative tilt at the instant of impact. Atypical experimental setup using a gas gun isshown in Fig. 5. The flyer plate is carried in thegas gun in a plastic sabot. Velocity of the flyeris determined from the transit time between theshorting pin in the gun barrel and time-of-arrivalpins in the target. The target is supported by aspall ring that suppresses late-time radial tensilewaves.

The stress waves along the axis normal to theimpact plane are shown in Fig. 6. A flyer plateof thickness d, moving left to right, strikes aninitially stationary target of thickness T; the im-pact occurs at the origin, O, of the (x,t) coordi-nates. Elastic-plastic behavior is assumed in Fig.6. Elastic waves propagate at approximately cL,the longitudinal elastic sound speed. Plasticwaves propagate at approximately (B/q),�where B is the bulk modulus. The arrivals of theelastic and plastic waves at the target rear sur-face are denoted as E and P.

Propagation speeds are always relative to thematerial into which the wave is moving. Strainoccurs only at the wave fronts. The amplitudeof the E wave in Fig. 6 is known as the Hugoniotelastic limit (HEL) and is simply related to theuniaxial yield stress, Y, as:

B � 4l/3r � Y (Eq 9)HEL � �2l


Fig. 6 Lagrangian diagram showing stress waves in flyer plateexperiment. See text for details and explanation of

symbols.

where l is the shear modulus. The final state ofthe shocked material is characterized by a stressand particle velocity. The functional relationshipbetween these two variables depends on the ma-terial and is known as the Hugoniot. The statebehind the P wave in Fig. 6 lies on the Hugoniot(see Ref 9 for a discussion of Hugoniots). If theflyer and target plates are composed of the samematerial, the particle velocity behind the P waveis one half the impact velocity.

Reference 10 discusses determination of par-ticle velocity when the flyer and target are com-posed of different materials. If the Hugoniot ofthe target is known, then the stress can be cal-culated from the particle velocity. Hugoniots formost engineering metals can be found in Ref 11.

Compressive waves reflect from a free surfaceas tensile (rarefaction) waves, which begin toarrive at the target rear surface at point R in Fig.6. The tensile (rarefaction) waves may interactand cause spall failure. This causes material sep-aration in the target, which is indicated at pointSP in Fig. 6. The sudden relaxation of tensilestress generates a shock wave that arrives at thefree surface at point S.

Spall is a form of tensile failure under an ex-tremely high strain rate and a nearly sphericalstress tensor. Spall usually is characterized bythe spall stress, rspall, defined as the highest ten-sile stress that exists in the material prior to rup-ture. When designing spall experiments, theflyer plate diameter, a, must be large enough sothat the phenomena of interest occur within atime a/2cL after the impact.

Flat plate impact tests normally are used tomeasure rHEL and spall strength. For example,consider the characterization of a steel by thistechnique. The value of rHEL for steel is usuallybetween 5 and 15 kilobar (kbar), a useful unitfor analyzing shock experiments; 1 kbar � 0.1GPa. When density is expressed as g/cm3 � 10and velocity is given in km/s (or, equivalently,mm/ls), stress is given in kbar.

To measure the Hugoniot elastic limit, the im-pact velocity must be sufficient for the peakstress to exceed rHEL. Peak stress is given by:

r � qUu (Eq 10)

where U is shock propagation speed, and u isparticle velocity. Peak particle velocity is halfthe impact velocity, u0, for a symmetric im-pact. For steel-on-steel impacts, Eq 10 be-comes approximately r � 200 u0. For r �rHEL � 15 kbar, u0 � 75 m/s (245 ft/s) is

required. This presents no problem when a gasgun is used.

Experiments with u0 � 100 m/s (�330 ft/s)are often difficult because of impact tilt, whichbecomes more critical at low velocities. Also,impact velocity must not be so high that the ve-locity of the P wave (Fig. 6) exceeds cL. Thatlimit for steels usually is greater than 1 km/s (0.6mile/s). The limit for other materials can befound by consulting the tables in Ref 11.

Given an appropriate impact velocity, to de-termine rHEL one of the following measure-ments must be made. The peak particle velocitybehind the E wave can be measured. This canbe accomplished at the free surface with capac-itor gages, sloping mirrors, or a velocity inter-ferometer. The velocity behind the wave is halfthe free surface velocity. The stress is related tothe free surface velocity by Eq 10 with u � cL.

Direct measurement of rHEL can be obtainedby embedded piezoresistive gages. Manganinand carbon gages frequently are used for thispurpose. This technique requires sectioning thetarget or using a backing plate and correcting forpartial transmission of the wave transmittedthrough the interface. Magnetic particle velocitygages can be used for nonconducting targetssuch as plastics and rocks, but they are not suit-able for metals.

Spall stress can be determined by two meth-ods. The simplest, in terms of analysis, interpre-


Fig. 8 Free surface velocity data when spall occurs. See textfor details and explanation of symbols.

Fig. 7 Spall data for low-carbon 1020 steel

tation, and experimental technique, is to varysystematically the flyer plate thickness, d, andimpact velocity, u0, to determine the critical val-ues at which rupture occurs. As the flyer platethickness is increased, the duration of the com-pressive and tensile load increases; the load du-ration is approximately 2d/cL.

Eventually, for flyer plate thicknesses exceed-ing about 5 mm (0.2 in.), the spall stress reachesa load duration limit. In many metals, the lim-iting spall strength is several times the value ofrHEL. Figure 7 illustrates typical spall stress datafor low-carbon steel. The data illustrate that forpulse durations longer than a few microseconds,the greatest tensile stress that the material cansustain without rupture is 25 kbar.

Interpretation of experiments using thinnerflyer plates is more complex, because a com-puter code must be used to calculate the stresshistory on the spall plane. Finite differencecodes (Ref 9) or method of characteristics codes(Ref 12) can be used. Finite difference codes aremore accurate and more widely applicable thanmethod of characteristics codes, but the usermust be specially trained in this subject.

Another approach to spall characterization isto initiate impact above the spall threshold andto deduce the material behavior from the freesurface velocity, D�s, data. Figure 8 illustrates atypical free surface velocity history with spall-ing, E, P, R, and S refer to the same arrivals asexplained in text for Fig. 6. The spall stress isgiven approximately by qcLD�s/2. However, amore exact determination requires code analysis.

The Split-HopkinsonPressure Bar Technique (Ref 13)

The split-Hopkinson pressure bar (SHPB)technique is named for Bertram Hopkinson who,in 1914, used the induced-wave propagation ina long elastic metallic bar to measure the pres-sures produced during dynamic events. Throughthe use of momentum traps of differing lengths,Hopkinson studied the shape and evolution ofstress pulses as they propagated down long me-tallic rods as a function of time. Based on thispioneering work, the experimental apparatus us-ing elastic stress-wave propagation in long rodsto study dynamic processes in materials wasnamed the Hopkinson pressure bar. Later workused two Hopkinson pressure bars in series, withthe sample sandwiched in between, to measurethe dynamic stress-strain response of materials.


Fig. 9 “Top-hat” tensile split-Hopkinson bar sample design. Source: Ref 16

This technique was referred to as the split-Hop-kinson pressure bar. Although the original split-Hopkinson pressure bar apparatus was devel-oped to measure compressive mechanicalbehavior of materials, alternate Hopkinson barschemes were later developed for loading thesamples in uniaxial tension and torsion. Infor-mation on split-Hopkinson pressure bar testingin compression and torsion can be found in Ref13–15.

Tensile Loading Techniques (Ref 13)

The principles and the data analysis for thetensile split-Hopkinson pressure bar are similarto those for the compression SHPB (Ref 13, 14).The primary differences are the methods of gen-erating a tensile-loading pulse, specimen ge-ometry, and the method of attaching the speci-men to the two bars (incident and transmitted).Three separate general types of tension split-Hopkinson pressure bar design have been de-veloped (Ref 13). All three loading techniquesuse measures of the tensile pulses in the inputand transmitter bars, as in the compressiveSHPB, to study the dynamic tensile response ofa material.

Method 1. In the first method, developed byLindholm and Yeakley (Ref 16), the incident baris solid, while the transmitted bar is a hollowtube of the same cross-sectional area as the inputbar. A complex “top-hat” type of sample ge-ometry, as shown in Fig. 9, is machined fromthe material of interest. The specimen essentiallycomprises four parallel tensile bars of equalcross-sectional area. Although specimen ma-chining is somewhat complex in this method, theactual SHPB test is conducted in the identicalmanner because compressive testing and thedata analysis is identical to that outlined previ-ously. The advantage of this tensile loading

method is that, given a suitable hollow trans-mitted bar matched to the incident bar, tensileHopkinson bar tests can be conducted using astandard compressive SHPB loading setup.

Method 2. The second type of tensile split-Hopkinson bar test, and the most commonly im-plemented mode of loading, involves direct ten-sile loading of the incident bar to subject asample in a uniaxial tensile stress state. Thisloading mode can be accomplished using a stan-dard type of axisymmetric circular tension spec-imen threaded directly into the ends of theincident and transmitted pressure bars, a dumb-bell-shaped sample loaded through flanges at-tached to the incident and transmitted bars, or aflat tensile sample loaded using a small com-pression grip assembly designed into the ends ofthe incident and transmitted bars. A tensile pulsein each instance is generated in the incident bareither by loading the end of the incident barthrough direct impact of a mass with a flange onthe end of the incident bar or by releasing a ten-sile pulse stored in the incident bar using aclamping fixture. Figure 10 shows a schematicof a tensile split-Hopkinson bar setup using thehollow-striker-bar loading method. In this load-ing method, a long tensile pulse, similarly stableas in a compressive bar, can be imparted usinga hollow striker tube accelerated along the in-cident bar from a compressed gas breech or froma falling weight in a vertically configured tensilebar. In the second variation, tensile wave loadingin the incident bar is generated through the re-lease of a tensile load that is initially stored in asection of the incident bar.

Method 3. The third type of Hopkinson barloading in tension also uses a circular specimenthreaded into the ends of the two pressure barsbut uses the reflection of the compression pulseat the free end of the transmitted bar to load thesample in tension and a circular collar to protect


Fig. 10 Schematic of a tensile split-Hopkinson pressure bar test setup

the specimen from the initial compressive pulse.After the specimen has been screwed into theincident and transmitted bars, a split shoulder orcollar is placed over the specimen, and it isscrewed in until the pressure bars fit tightlyagainst the shoulder. The shoulder is made ofthe same material as the pressure bars, has thesame outer diameter, and has an inner diameterthat just clears the specimen. The ratio of thecross-sectional area of the shoulder to that of thepressure bars is typically 3 to 4, while the ratioof the area of the shoulder to the net cross-sec-tional area of the specimen is typically 12 to 1.When the striker bar impacts the incident bar, acompressive pulse travels down the incident baruntil it reaches the specimen. The amplitude ofthe pulse, which is a function of the striker ve-locity and length, is twice the elastic wave transittime in the striker bar.

In this loading method, the compression pulsetravels through the composite cross section ofthe loading collar and specimen in an essentiallyundisturbed manner. The relatively loose fit ofthe threaded joint of the specimen into the barsand the large area ratio of the collar to the spec-imen ensure that no compression beyond theelastic limit is transmitted through the specimen.Ideally, the entire compression pulse passesthrough the supporting circular collar as if thespecimen were not present, although in practiceit is operationally difficult to prevent prestrain-ing of the specimen to some degree. The com-pression pulse continues to propagate until itreaches the free end of the transmitted bar whereit reflects and propagates back as a tensile pulse.

Upon reaching the specimen, the tensile pulse ispartially transmitted through the specimen andpartially reflected back into the bar, which isnow acting as the incident bar. Because theshoulder, which carried the entire compressivepulse around the specimen, is not rigidly con-nected to the pressure bars, it will not supportany tensile load. Tight fitting of the collaragainst the two pressure bars is critical in trans-mitting the compression pulse down the barswithout significant wave dispersion or prestrain-ing of the sample. Similarly, the fit of thethreaded tensile specimen against the bars is es-sential to achieve smooth and rapid loading ofthe specimen as the tensile pulse arrives. Failureto remove all play from the threaded joint resultsin uneven loading of the specimen and spuriouswave reflections because of the open gaps in theloading thread area.

Data Analysis (Ref 13)

As mentioned earlier in this section, data anal-ysis for a tensile split-Hopkinson pressure bartest is essentially identical to that of compressionHopkinson bar analysis detailed in Ref 13 and14. The additional complications encountered intensile Hopkinson techniques are related to thefollowing:

● Modification of the pressure bar ends to ac-commodate gripping of complex samples,which alter wave propagation in the sampleand bars

● Potential need for additional diagnostics tocalculate true stress


● Increased need to accurately incorporate in-ertial effects into data reduction to extractquantitative material constitutive behavior

● More complicated stress pulse generationsystems required for tensile and torsion bars

Alteration of the bar ends to accommodatethreaded or clamped samples leads to complexboundary conditions at the bar specimen inter-face and, therefore, introduces uncertainties inthe wave mechanics description of the test.

When complex sample geometries are used,signals measured in the pressure bars record thestructural response of the entire sample, not justthe gage section, where plastic deformation isassumed to be occurring. When plastic strain oc-curs in the sections adjacent to the sample’s uni-form gage area, accurate determination of thestress-strain response of the material is morecomplicated. In these cases, additional diagnos-tics, such as high-speed photography, are man-datory to quantify the loaded section of the de-forming sample. In the tensile bar case, anadditional requirement is that exact quantifica-tion of the deforming sample cross-sectionalarea as a function of strain is necessary toachieve true-stress data. Contrary to a compres-sive SHPB test, in which a right-circular cylin-drical sample is most often utilized, the tensileSHPB test uses a cylindrical specimen with anattached shoulder and additional gripping, in-cluding threads. Because the split-Hopkinsonbar data analysis only provides data on the rela-tive displacement between the ends of the inci-dent and transmitter bars, an effective gagelength generally must be used. This is equivalentto determining strain in a tensile test throughcross-head displacement measurement. The useof strain gages on test samples to determine aneffective gage length is strongly recommended.This calibration is accomplished easily at lowstrain rates, preferably in a conventional test ma-chine in which the cross-head displacement ismonitored separately.

As with any uniaxial tensile test, once local-ized necking occurs, it is no longer possible tosimply convert load-displacement data to stress-strain data. This lack of valid stress-state anal-ysis is related to both the lack of uniform plasticdeformation in the sample and the attendant vol-umetric sample expansion, which damage-evo-lution processes represent. The range of appli-cation of the Hopkinson bar test can be extendedby high-speed photography of necking speci-mens, although an accurate measure of the de-

forming volume of the sample as necking pro-ceeds is difficult at best, given a lack ofknowledge of the damage processes evolvingwithin the sample. An analysis that allows esti-mation of effective stress and strain from theprofile of the necking specimen can be obtained.Using the apparatus described in method 3, pho-tographs can be made with a suitable high-speedcamera system through windows provided in thecollar.

The final complexity inherent to the tensionHopkinson loading configurations has to do withthe increased sample dimensions required. Validdynamic characterization of many materialproduct forms, such as thin sheet materials andsmall-section bar stock, may be significantlycomplicated or completely impractical using ei-ther tensile or torsion Hopkinson bars becauseof an inability to fabricate test samples. Tech-niques have been developed, however, to ad-dress these concerns in the case of testing sheetmaterials in the Hopkinson bar.

Rotating Wheel Test (Ref 14)

Another method for tensile testing at highstrain rates consists of a rotating wheel withclaws or noses that quickly stroke a yoke con-taining test pieces. An early test machine wasdeveloped by Mann in 1936 (Ref 17), and in1944 Fehr et al. (Ref 18) reached strain rates ofnearly 103 s�1 with some bearable ringing. Inthe 1960s, Schopper produced and sold about100 “rotating wheel machines,” which also hada 200 kg (440 lb) wheel with a releasable clawand a specimen within a yoke fixed in front ofthe wheel (Fig. 11). By careful adjustments, ve-locities of about 40 m/s (130 ft/s) were reachedwithout any bending moments. However, theoverall frequency response of the fixture (de-spite the 50 kHz quartz transducer for force-timerecording) was only 2.5 kHz, which is too lowfor high-rate testing.

The essential improvement has been to intro-duce load-measuring gages as close to the gagelength as possible. This is realized by measuringelastic strains and converting to stresses by theelastic modulus. To assure low barriers for re-flections of stress wave propagation, the straingages for load measurement are positioned atcones of 8� on the smallest possible diameter.With this technique, stress-strain records arepossible up to velocities of 30 m/s, which cor-


responds to strain rates of � 2500 s�1 with aegage length of 10.5 mm (0.41 in.) and a diameterof 3.5 mm (0.14 in.) (L/D � 3). Even with highstrain hardening and highly deformable materi-als, there is practically no influence of the testedmaterials on the history of velocity or strain ratelike in a Hopkinson bar setup because the energycontent of the rotating wheel exceeds the frac-

ture energy of the specimen more than 10 times(for striking velocities � � 10 m/s, or 33 ft/s).

A similar setup, but based on a moving massof a few kilograms guided along straight bars,has also been developed by Stelly and Dormevalat CEA, France with good results (Ref 19).Higher strain rates of � 104 s�1, for example,ecan be reached with short gage length. To pro-

Fig. 12 Influence of joining method on stress-time curves for high strain rate tension test specimens

Fig. 11 Principle of high-rate tensile testing with flywheel setup


Fig. 13 Stress-time diagrams from high strain rate tensile testing of carbon steel (0.45% C) between room temperature and 600 �C(1100 �F)

vide easy strain recording for the complete load-ing up to fracture, electro-optical cameras ornoncontact laser interferometers can be used.The advantage of this instrumentation is that thestrain is measured, not calculated under certainassumptions.

In order to avoid more reflections of the stresswave from the upper end of the specimen, thelength beside the gage length is extended to 2s� �c • t (where s is the rod length between gagelength and fixture, �c is the sound velocity, andt is the time to fracture at the used striking ve-locity). In the case of short lengths, a wave trans-mitter bar is connected to the specimen. Thisprocedure requires the evaluation of impedancetransfer between the sample and bar. Figure 12shows stress-time diagrams of screwed, brazed,and welded joints tested under high strain rateconditions at about � 1000 s�1. These resultsereveal that screwing and brazing are insufficientmethods to obtain stress-time diagrams of goodquality. Therefore, in this test setup weldedjoints are most suitable to perform tensile testsat high and very high strain rates.

This procedure was successfully applied forhigh-rate, high-temperature tests (Fig. 13). No-

tice the occurrence of the upper and lower yield-ing and the following nearly undisturbed stress-time records. The wave transmitter bar was usedfor a stress measurement because the straingages at the gage length were unsuitable at testtemperature. Temperatures up to 600 �C (1100�F) are reached with heated air; higher tempera-tures should be possible using small infraredovens (Ref 20, 21) or induction heating.

ACKNOWLEDGMENTS

This chapter was adapted from T. Nicholasand S.J. Bless, High Strain Rate Tension Testing,Mechanical Testing, Vol 8, 9th ed., MetalsHandbook, American Society for Metals, 1985,p 208–214. Information was also taken from Ref13 and 14.

REFERENCES

1. F.I. Niordson, A Unit for Testing Materialsat High Strain Rates, Exp. Mech., Vol 5,1965, p 29–32


2. C.R. Hoggatt and R.F. Recht, Stress-StrainData Obtained at High Strain Rates Usingan Expanding Ring, Exp. Mech., Vol 9,1969, p 441–448

3. D.E. Grady and D.A. Benson, Fragmenta-tion of Metal Rings by ElectromagneticLoading, Exp. Mech., Vol 28, 1983, p 393–400

4. A.M. Rajendran and I.M. Fyfe, Inertia Ef-fects on the Ductile Failure of Thin Rings,J. Appl. Mech., Vol 104, 1982, p 31–36

5. L.M. Barker and R.E. Hollenback, Laser In-terferometer for Measuring High Velocitiesof Any Reflecting Surface. J. Appl. Phys.,Vol 43, 1972, p 4669–4674

6. R.H. Warnes et al., An Improved Techniquefor Determining Dynamic Material Proper-ties Using the Expanding Ring, in ShockWaves and High-Strain-Rate Phenomena inMetals, M.A. Meyers and L.E. Murr, Ed.,Plenum Press, New York, 1981

7. D. Bauer and S.J. Bless, Strain Rate Effectson Ultimate Strain of Copper, in ShockWaves in Condensed Matter, North Holland,Amsterdam, 1983

8. G.R. Fowles, Experimental Technique andInstrumentation, in Dynamic Response ofMaterials to Intense Impulse Loading, P.C.Chou and A.K. Hopkins, Ed., Air Force Ma-terials Laboratory, Wright-Patterson AFB,OH, 1973

9. J.A. Zukas, T. Nicholas, H.F. Swift, L.B.Greszczuk, and D.R. Curran, Impact Dy-namics, John Wiley & Sons, New York,1982

10. R.G. McQueen, S.P. Marsh, J.W. Taylor,J.N. Fritz, and W.J. Carter. The Equation ofState of Solids from Shock Wave Studies,in High Velocity Impact Phenomena, R.Kinslow, Ed., Academic Press, New York,1970

11. S.P. Marsh, LASL Shock Hugoniot Data,University of California Press, Berkeley,1980

12. L.M. Barker and E.G. Young, “SWAP-9:An Improved Stress Wave Analyzing Pro-gram,” Sandia National Laboratories ReportNo. SLA-74-0009. Albuquerque, NM, 1974

13. G.T. Gray III, Classic Split-HopkinsonPressure Bar Testing, Mechanical Testingand Evaluation, Vol 8, ASM Handbook,ASM International, 2000, p 462–476

14. High Strain Rate Tension and CompressionTests, Mechanical Testing and Evaluation,Vol 8, ASM Handbook, ASM International,2000, p 429–446

15. A. Gilat, Torsional Kolsky Bar Testing, Me-chanical Testing and Evaluation, Vol 8,ASM Handbook, ASM International, 2000,p 505–515

16. U.S. Lindholm and L.M. Yeakley, HighStrain Rate Testing: Tension and Compres-sion, Exp. Mech., Vol 8, 1968, p 1–9

17. H.C. Mann, High Velocity Tension ImpactTests, Proc. ASTM, Vol 36 (part 2), 1936, p85–109

18. R.O. Fehr, E. Parker, and D.J. DeMichael,Measurement of Dynamic Stress and Strainin Tensile Test Specimens, J. Appl. Mech.(Trans. ASME), Vol 6A, 1944, p 65–71

19. R. Dormeval and M. Stelly, Influence ofGrain Size and Strain Rate of the Mechan-ical Behavior of High-Purity PolycrystallineCopper, Second Conf. on Mechanical Prop-erties at High Rates of Strain, 1979 (Ox-ford), Institute of Physics, London, SerialNo. 47, p 154–165

20. C.E. Frantz, P.S. Follansbee, and W.E.Wright, New Experimental Techniques withthe Split Hopkinson Pressure Bar, High En-ergy Rate Forming, Berman and Schroeder,Ed., American Society of Mechanical En-gineers, 1984, p 229

21. A.M. Lennon and K.T. Ramesh, A Tech-nique for Measurement of the Dynamic Be-haviour of Materials at High Temperatures,Int. J. Plast., Vol 14 (No. 12), 1998, p 1279–1292

Glossary of Terms

Aaccuracy. (1) The agreement or correspondence

between an experimentally determined valueand an accepted reference value for the ma-terial undergoing testing. The reference valuemay be established by an accepted standard(such as those established by ASTM), or, insome cases, the average value obtained by ap-plying the test method to all the samplingunits in a lot or batch of the material may beused. (2) The extent to which the result of acalculation or the reading of an instrument ap-proaches the true value of the calculated ormeasure quantity. Compare with precision.

alligator skin. See preferred term orange peel.anisotropy. The characteristic of exhibiting dif-

ferent values of a property in different direc-tions with respect to a fixed reference systemin the material. See also planar anisotropy.

average linear strain. See engineering strain.axial strain. See uniaxial strain.

BBauschinger effect. The phenomenon by which

plastic deformation increases yield strength inthe direction of plastic flow and decreases itin other directions.

biaxial stress. See principal stress (normal).breaking load. The maximum load (or force)

applied to a test specimen or structural mem-ber loaded to rupture.

breaking stress. The stress at failure. Alsoknown as rupture stress. See also fracturestress.

brittle fracture. Separation of a solid accom-panied by little or no macroscopic plastic de-formation. Typically, brittle fracture occurs byrapid crack propagation with less expenditureof energy than for ductile fracture.

bulk modulus. See bulk modulus of elasticity.

bulk modulus of elasticity (K). The measure ofresistance to change in volume; the ratio ofhydrostatic stress to the corresponding unitchange in volume. This elastic constant canbe expressed by the equation:

r �p 1mK � � �D D b

where K is bulk modulus of elasticity, rm ishydrostatic or mean stress tensor, p is hydro-static pressure, and b is the coefficient of com-pressibility. Also known as bulk modulus,compression modulus, hydrostatic modulus,and volumetric modulus of elasticity.

Cchord modulus. The slope of the chord drawn

between any two specific points on a stress-strain curve. Compare with secant modulus.See also modulus of elasticity.

coefficient of thermal expansion. (1) Changein unit of length (or volume) accompanying aunit change of temperature, at a specified tem-perature. (2) The linear or volume expansionof a given material per degree rise of tem-perature, expressed at an arbitrary base tem-perature or as a more complicated equationapplicable to a wide range.

conventional strain. See engineering strain.conventional stress. See engineering stress.crack-growth rate. Rate of propagation of a

crack through a material due to statically ordynamically applied load.

crazing. Region of ultrafine cracks, which mayextend in a network on or under the surfaceof a resin or plastic material. May appear asa white band. Often found in a filament-wound pressure vessel or bottle. In many plas-tics, craze growth precedes crack growth, of-




ten generating additional strength becausecrazes are load bearing.

cross linking. With thermosetting and certainthermoplastic polymers, the setting up ofchemical links between the molecular chains.When extensive, as in most thermosetting res-ins, cross linking makes an infusible super-molecule of all the chains. In rubbers, thecross linking is just enough to join all mole-cules into a network.

cup fracture (cup-and-cone fracture). Amixed-mode fracture, often seen in tensile-test specimens of a ductile material, where thecentral portion undergoes plane-strain frac-ture and the surrounding region undergoesplane-stress fracture. One of the mating frac-ture surfaces looks like a miniature cup; it hasa central depressed flat-face region sur-rounded by a shear lip. The other fracture sur-face looks like a miniature truncated cone.

cupping test. A mechanical test used to deter-mine the ductility and drawing properties ofsheet metal. It consists of measuring the max-imum depth of bulge that can be formed be-fore fracture. The test is commonly carriedout by drawing the test piece into a circulardie by means of a punch with a hemisphericalend. See also Erichsen cup test, Olsen cuptest, and Swift cup test.

Ddeformation. A change in the form of a body

due to stress, thermal change, change in mois-ture, or other causes. Measured in units oflength.

dimpled rupture. A fractographic term describ-ing ductile fracture that occurs through theformation and coalescence of microvoidsalong the fracture path. The fracture surfaceof such a ductile fracture appears dimpledwhen observed at high magnification and usu-ally is most clearly resolved when viewed ina scanning electron microscope. See also duc-tile fracture.

discontinuous yielding. The nonuniform plasticflow of a metal exhibiting a yield point inwhich plastic deformation is inhomoge-neously distributed along its length. Undersome circumstances, it may occur in metalsnot exhibiting a distinct yield point, either atthe onset of or during plastic flow.

ductile fracture. Fracture characterized by tear-ing of metal accompanied by appreciablegross plastic deformation and expenditure of

considerable energy. Contrast with brittlefracture.

ductility. The ability of a material to deformplastically before fracturing. Measured byelongation or reduction in area in a tensiletest, by height of cupping in a cupping test,or by the radius or angle of bend in a bendtest.

dynamic modulus. The ratio of stress to strainunder cyclic conditions (calculated from dataobtained from either free or forced vibrationtests, in shear, compression, or tension).

dynamic strain aging. A behavior in metals inwhich solute atoms are sufficiently mobile tomove toward and interact with dislocations.This results in strengthening over a specificrange of elevated temperature and strain rate.

Eeffective yield strength. An assumed value of

uniaxial yield strength that represents the in-fluence of plastic yielding on fracture-test pa-rameters.

elastic calibration device. A device for use inverifying the load readings of a testing ma-chine consisting of an elastic member(s) towhich loads may be applied, combined witha mechanism or device for indicating the mag-nitude (or a quantity proportional to the mag-nitude) of deformation under load.

elastic constants. The factors of proportionalitythat relate elastic displacement of a materialto applied forces. See also modulus of elastic-ity, bulk modulus of elasticity, and Poisson’sratio.

elastic deformation. A change in dimensionsdirectly proportional to and in phase with anincrease or decrease in applied force.

elastic energy. The amount of energy requiredto deform a material within its elastic rangeof behavior, neglecting small heat losses dueto internal friction. The energy absorbed by aspecimen per unit volume of material con-tained within the gage length being tested. Itis determined by measuring the area under thestress-strain curve up to a specified elasticstrain. See also modulus of resilience andstrain energy.

elastic limit. The maximum stress which a ma-terial is capable of sustaining without any per-manent strain (deformation) remaining oncomplete release of the stress. Compare withproportional limit.

elastic recovery. Amount the dimension of astressed elastic material returns to its original

Glossary of Terms / 267

(unstressed) dimension on release of an ap-plied load.

elastic strain. See elastic deformation.elastic strain energy. The energy expended by

the action of external forces in deforming abody elastically. Essentially, all the work per-formed during elastic deformation is stored aselastic energy, and this energy is recoveredupon release of the applied force.

elasticity. The property of a material by virtueof which deformation caused by stress dis-appears on removal of the stress. A perfectlyelastic body completely recovers its originalshape and dimensions after release of stress.

elongation. A term used in mechanical testingto describe the amount of extension of a testpiece when stressed. See also elongation, per-cent.

elongation, percent. The extension of a uniformsection of a specimen expressed as percentageof the original gage length:

L � Lx oElongation, % � � 100Lo

where Lo is original gage length, and Lx isfinal gage length.

engineering strain (e). A term sometimes usedfor average linear strain or conventional strainin order to differentiate it from true strain. Intensile testing it is calculated by dividing thechange in the gage length by the original gagelength.

engineering stress (s). A term sometimes usedfor conventional stress in order to differentiateit from true stress. In tensile testing, it is cal-culated by dividing the breaking load appliedto the specimen by the original cross-sectionalarea of the specimen.

Erichsen cup test. A cupping test used for as-sessing the ductility of sheet metal. Themethod consists of forcing a conical or hem-ispherical-ended plunger into the specimenand measuring the depth of the impression atfracture. Compare with Olsen cup test andSwift cup test.

extensometer. An instrument for measuringchanges in length over a given gage lengthcaused by application or removal of a force.Commonly used in tensile testing of metalspecimens.

Fflexibility. The quality or state of a material that

allows it to be flexed or bent repeatedly with-out undergoing rupture. See also flexure.

flexural modulus. Within the elastic limit, theratio of the applied stress on a test specimenin flexure to the corresponding strain in theoutermost fiber of the specimen. Flexuralmodulus is the measure of relative stiffness.

flexure. A term used in the study of strength ofmaterials to indicate the property of a body,usually a rod or beam, to bend without frac-ture. See also flexibility.

formability. The ease with which a metal canbe shaped through plastic deformation. Theevaluation of the formability of a metal in-volves measurement of strength and ductility,as well as the amount of deformation requiredto cause fracture. Workability is used inter-changeably with formability; however, form-ability refers to the shaping of sheet metal,while workability refers to shaping materialsby bulk deformation (i.e., forging or rolling).

forming limit diagram (FLD). A diagram onwhich the major strains at the onset of neckingin sheet metal are plotted vertically and thecorresponding minor strains are plotted hori-zontally. The onset-of-failure line divides allpossible strain combinations into two zones:the “safe” zone, in which failure during form-ing is not expected, and the “failure” zone, inwhich failure during forming is expected.

fracture stress. The true normal stress on theminimum cross-sectional area at the begin-ning of fracture. This term usually applies totensile tests of unnotched specimens.

Ggage length. The original length of the portion

of a specimen over which strain, change oflength, or other characteristics are deter-mined.

HHall-Petch relationship. A general relationship

for metals that shows that the yield strengthis linearly related to the reciprocal of thesquare root of the grain diameter.

Hartmann lines. See Luders lines.Hooke’s law. Observation that, in the elastic re-

gion of solid material, stress is directly pro-portional to strain and can be expressed as:

Stress r� � constant � E

Strain e

where E is the modulus of elasticity, orYoung’s modulus. The constant relationship


between stress and strain applies only belowthe proportional limit. See also modulus ofelasticity.

hysteresis. The phenomenon of permanently ab-sorbed or lost energy that occurs during anycycle of loading or unloading when a materialis subjected to repeated loading.

Llimiting dome height (LDH) test. A mechani-

cal test, usually performed unlubricated onsheet metal, that simulates the fracture con-ditions in a practical press-forming operation.The results are dependent on the sheet thick-ness.

linear (tensile or compressive) strain. Thechange per unit length due to force in an origi-nal linear dimension. An increase in length isconsidered positive.

load. For testing machines, a force applied to atest piece that is measured in units such aspound-force, newton, or kilogram-force.

longitudinal direction. The principal directionof flow in a worked metal. See also normaldirection and transverse direction.

Luders lines. Elongated surface markings or de-pressions, often visible with the unaided eye,that form along the length of sheet metal or atension specimen at an angle of approxi-mately 45� to the loading axis. Caused by lo-calized plastic deformation, they result fromdiscontinuous (inhomogeneous) yielding.Also known as Luders bands, Hartmann lines,Piobert lines, or stretcher strains.

Mmacrostrain. The mean strain over any finite

gage length of measurement large in compar-ison with interatomic distances. Macrostraincan be measured by several methods, includ-ing electrical-resistance strain gages and me-chanical or optical extensometers. Elasticmacrostrain can be measured by x-ray dif-fraction. Compare with microstrain.

maximum load (Pmax). (1) The load having thehighest algebraic value in the load cycle. Ten-sile loads are considered positive and com-pressive loads negative. (2) Used to determinethe strength of a structural member; the loadthat can be borne before failure is apparent.

maximum stress (Smax). The stress having thehighest algebraic value in the stress cycle, ten-sile stress being considered positive and com-

pressive stress negative. The nominal stress isused most commonly.

mechanical hysteresis. Energy absorbed in acomplete cycle of loading and unloadingwithin the elastic limit and represented by theclosed loop of the stress-strain curves forloading and unloading. Sometimes calledelastic hysteresis.

mechanical metallurgy. The science and tech-nology dealing with the behavior of metalswhen subjected to applied forces.

microstrain. The strain over a gage length com-parable to interatomic distances. These are thestrains being averaged by the macrostrainmeasurement. Microstrain is not measurableby currently existing techniques. Variance ofthe microstrain distribution can, however, bemeasured by x-ray diffraction.

modulus of elasticity (E). The measure of ri-gidity or stiffness of a metal; the ratio ofstress, below the proportional limit, to the cor-responding strain. In terms of the stress-straindiagram, the modulus of elasticity is the slopeof the stress-strain curve in the range of linearproportionality of stress to strain. Also knownas Young’s modulus. For materials that do notconform to Hooke’s law throughout the elasticrange, the slope of either the tangent to thestress-strain curve at the origin or at lowstress, the secant drawn from the origin to anyspecified point on the stress-strain curve, orthe chord connecting any two specific pointson the stress-strain curve is usually taken tobe the modulus of elasticity. In these cases,the modulus is referred to as the tangent mod-ulus, secant modulus, or chord modulus, re-spectively.

modulus of resilience. The amount of energystored in a material when loaded to its elasticlimit. It is determined by measuring the areaunder the stress-strain curve up to the elasticlimit. See also elastic energy, resilience, andstrain energy.

m-value. See strain-rate sensitivity.

Nnecking. (1) Reducing the cross-sectional area

of metal in a localized area by stretching. (2)Reducing the diameter of a portion of thelength of a cylindrical shell or tube.

nominal stress. The stress at a point calculatedon the net cross section by simple elasticitytheory without taking into account the effecton the stress produced by stress raisers suchas holes, grooves, fillets, etc.


normal direction. Direction perpendicular tothe plane of working in a worked metal. Seealso longitudinal direction and transverse di-rection.

normal stress. The stress component perpendic-ular to a plane on which forces act.

notch brittleness. Susceptibility of a material tobrittle fracture at points of stress concentra-tion. For example, in a notch tensile test, thematerial is said to be notch brittle if the notchstrength is less than the tensile strength of anunnotched specimen. Otherwise, it is said tobe notch ductile.

notch depth. The distance from the surface ofa notched test specimen to the bottom of thenotch. In a cylindrical test specimen, the per-centage of the original cross-sectional area re-moved by machining an annular groove.

notch ductility. The percentage reduction inarea after complete separation of the metal ina tensile test of a notched specimen.

notch strength. The maximum load on anotched tensile-test specimen divided by theminimum cross-sectional area (the area at theroot of the notch). Also known as notch ten-sile strength.

n-value. See strain hardening exponent.

O

offset. The distance along the strain coordinatebetween the initial portion of a stress-straincurve and a line parallel to the initial portionthat intersects the stress-strain curve at a valueof stress (commonly 0.2%) that is used as ameasure of the yield strength. Used for ma-terials that have no obvious yield point.

offset modulus. The ratio of the offset yieldstress to the extension at the offset point (plas-tics).

offset yield strength. The stress at which thestrain exceeds by a specified amount (the off-set) an extension of the initial proportionalportion of the stress-strain curve. Expressedin force per unit area.

Olsen cup test. A cupping test in which a pieceof sheet metal, restrained except at the center,is deformed by a standard steel ball until frac-ture occurs. The height of the cup at time offracture is a measure of the ductility. Comparewith Erichsen cup test and Swift cup test.

orange peel. A surface roughening in the formof a pebble-grained pattern where a metal ofunusually coarse grain is stressed beyond its

elastic limit. Also known as pebbles and al-ligator skin.

Ppermanent set. The deformation or strain re-

maining in a previously stressed body afterrelease of load.

Piobert lines. See Luders lines.planar anisotropy. A variation in physical and/

or mechanical properties with respect to di-rection within the plane of material in sheetform. See also plastic strain ratio.

plastic deformation. The permanent (inelastic)distortion of a material under applied stressthat strains the material beyond its elasticlimit.

plastic instability. The stage of deformation ina tensile test where the plastic flow becomesnonuniform and necking begins.

plasticity. The property that enables a materialto undergo permanent deformation withoutrupture.

plastic strain. Dimensional change that does notdisappear when the initiating stress is re-moved. Usually accompanied by some elasticdeformation.

plastic strain ratio (r-value). The ratio of thetrue width strain to the true thickness strain ina tensile test, r � ew/et. Because of the dif-ficulty in making precise measurement ofthickness strain in sheet material, it is moreconvenient to express r in terms of initial andfinal length and width dimensions. It can beshown that

r � (ln W W ) � (ln L W /L W )o f f f o o

where Lo and Wo are initial length and widthof gage section, respectively; and Lf and Wfare final length and width, respectively.

Poisson’s ratio (v). The absolute value of theratio of transverse (lateral) strain to the cor-responding axial strain resulting from uni-formly distributed axial stress below the pro-portional limit of the material.

precision. The closeness of agreement betweenthe results of individual replicated measure-ments or tests. The standard deviation of theerror of measurement may be used as a mea-sure of “imprecision.”

principal stress (normal). The maximum orminimum value of the normal stress at a pointin a plane considered with respect to all pos-sible orientations of the considered plane. Onsuch principal planes the shear stress is zero.


There are three principal stresses on three mu-tually perpendicular planes. The state of stressat a point may be: (1) uniaxial, a state of stressin which two of the three principal stressesare zero; (2) biaxial, a state of stress in whichonly one of the three principal stresses is zero;or (3) triaxial, a state of stress in which noneof the principal stresses is zero. Multiaxialstress refers to either biaxial or triaxial stress.

proof stress. (1) The stress that will cause aspecified small permanent set in a material.(2) A specified stress to be applied to a mem-ber or structure to indicate its ability to with-stand service loads.

proportional limit. The greatest stress a mate-rial is capable of developing without a devi-ation from straight-line proportionality be-tween stress and strain. Compare with elasticlimit. See also Hooke’s law.

Rreduction in area (RA). The difference between

the original cross-sectional area of a tensilespecimen and the smallest area at or after frac-ture as specified for the material undergoingtesting. Also known as reduction of area.

residual stress. Stresses that remain within abody as the result of thermal or mechanicaltreatment or both.

resilience. The ability of a material to absorbenergy when deformed elastically and returnto its original shape on release of load. Seealso modulus of resilience.

rosette. Strain gages arranged to indicate, at asingle position, strain in three different direc-tions.

rupture stress. The stress at failure. Alsoknown as breaking stress. See also fracturestress.

Ssample. (1) One or more units of product (or a

relatively small quantity of a bulk material)that are withdrawn from a lot or processstream and that are tested or inspected to pro-vide information about the properties, dimen-sions, or other quality characteristics of the lotor process stream. Not be confused with spec-imen. (2) A portion of a material intended tobe representative of the whole.

secant modulus. The slope of the secant drawnfrom the origin to any specified point on astress-strain curve. Compare with chord mod-ulus. See also modulus of elasticity.

shear lip. A narrow, slanting ridge along theedge of a fracture surface. The term some-times also denotes a narrow, often crescent-shaped, fibrous region at the edge of a fracturethat is otherwise of the cleavage type, eventhough this fibrous region is in the same planeas the rest of the fracture surface.

specimen. A test object, often of standard di-mensions or configuration, that is used for de-structive or nondestructive testing. One ormore specimens may be cut from each unit ofa sample.

stiffness. (1) The ability of a metal or shape toresist elastic deflection. (2) The rate of stressincrease with respect to the rate of increase instrain induced in the metal or shape; thegreater the stress required to produce a givenstrain, the stiffer the material is said to be.

strain. The unit of change in the size or shapeof a body due to force. Also known as nom-inal strain. See also engineering strain, linearstrain, and true strain.

strain aging. The changes in ductility, hardness,yield point, and tensile strength that occurwhen a metal or alloy that has been coldworked is stored for some time. In steel, strainaging is characterized by a loss of ductilityand a corresponding increase in hardness,yield point, and tensile strength.

strain energy. A measure of the energy absorp-tion characteristics of a material determinedby measuring the area under the stress-straindiagram. Also known as deformation energy.See also elastic energy, resilience, and tough-ness.

strain gage. A device for measuring smallamounts of strain produced during tensile andsimilar tests on metal. A coil of fine wire ismounted on a piece of paper, plastic, or simi-lar carrier matrix (backing material), which isrectangular in shape and usually about 25 mm(1.0 in.) long. This is glued to a portion ofmetal under test. As the coil extends with thespecimen, its electrical resistance increases indirect proportion. This is known as bondedresistance-strain gage. Other types of gagesmeasure the actual deformation. Mechanical,optical, or electronic devices are sometimesused to magnify the strain for easier reading.See also rosette.

strain hardening. An increase in hardness andstrength caused by plastic deformation at tem-peratures below the recrystallization range.Also known as work hardening.

strain-hardening coefficient. See strain-hard-ening exponent.


strain-hardening exponent (n value). Thevalue n in the relationship r � Ken, where ris the true stress, e is the true strain, and K,the strength coefficient, is equal to the truestress at a true strain of 1.0. The strain hard-ening exponent is equal to the slope of the truestress/true strain curve up to maximum load,when plotted on log-log coordinates. The n-value relates to the ability of a sheet of ma-terial to be stretched in metalworking opera-tions. The higher the n-value, the better theformability (stretchability). Also known asthe strain-hardening coefficient.

strain rate. The time rate of straining for theusual tensile test. Strain as measured directlyon the specimen gage length is used for de-termining strain rate. Because strain is dimen-sionless, the units of strain rate are reciprocaltime.

strain-rate sensitivity (m value). The increasein stress (r) needed to cause a certain increasein plastic-strain rate at a given level of(e)plastic strain (e) and a given temperature (T).

D log rStrain-rate sensitivity � m � � �D log e eT

strength. The maximum nominal stress a ma-terial can sustain. Always qualified by thetype of stress (tensile, compressive, or shear).

stress. The intensity of the internally distributedforces or components of forces that resist achange in the volume or shape of a materialthat is or has been subjected to external forces.Stress is expressed in force per unit area andis calculated on the basis of the original di-mensions of the cross section of the specimen.Stress can be either direct (tension or com-pression) or shear. See also engineeringstress, nominal stress, normal stress, residualstress, and true stress.

stress raisers. Changes in contour or disconti-nuities in structure that cause local increasesin stress.

stress ratio (A or R). The algebraic ratio of twospecified stress values in a stress cycle. Twocommonly used stress ratios are the ratio ofthe alternating stress amplitude to the meanstress, A � Sa/Sm, and the ratio of the mini-mum stress to the maximum stress, R � Smin/Smax.

stress-strain curve. See stress-strain diagram.stress-strain diagram. A graph in which cor-

responding values of stress and strain are plot-

ted against each other. Values of stress areusually plotted vertically (ordinates or y-axis)and values of strain horizontally (abscissas orx-axis). Also known as deformation curve andstress-strain curve.

stretcher strains. See Luders lines.Swift cup test. A simulative cupping test in

which circular blanks of various diameters areclamped in a die ring and deep drawn intocups by a flat-bottomed cylindrical punch.Compare with Erichsen cup test and Olsencup test.

Ttangent modulus. The slope of the stress-strain

curve at any specified stress or strain. See alsomodulus of elasticity.

tensile strength. In tensile testing, the ratio ofmaximum load to original cross-sectionalarea. Also known as ultimate strength. Com-pare with yield strength.

tensile stress. A stress that causes two parts ofan elastic body, on either side of a typicalstress plane, to pull apart.

tensile testing. A method of determining the be-havior of materials subjected to uniaxial load-ing, which tends to stretch the metal. A lon-gitudinal specimen of known length anddiameter is gripped at both ends and stretchedat a slow, controlled rate until rupture occurs.Also known as tension testing.

tension. The force or load that produces elon-gation.

tension testing. See tensile testing.testing machine (load-measuring type). A me-

chanical device for applying a load (force) toa specimen.

total elongation. A total amount of permanentextension of a test piece broken in a tensiletest. See also elongation, percent.

total-extension-under-load yield strength. Seeyield strength.

toughness. The ability of a metal to absorb en-ergy and deform plastically before fracturing.

transverse direction. Literally, the “across” di-rection, usually signifying a direction or planeperpendicular to the direction of working. Inrolled plate or sheet, the direction across thewidth is often called long transverse, and thedirection through the thickness, short trans-verse.

triaxial stress. See principal stress (normal).true strain. (1) The ratio of the change in di-

mension, resulting from a given load incre-


ment, to the magnitude of the dimension im-mediately prior to applying the loadincrement. (2) In a body subjected to axialforce, the natural logarithm of the ratio of thegage length at the moment of observation tothe original gage length. Also known as nat-ural strain. Compare with engineering strain.

true stress. The value obtained by dividing theload applied to a member at a given instantby the cross-sectional area over which it acts.Compare with engineering stress.

Uultimate strength. The maximum stress (ten-

sile, compressive, or shear) a material can sus-tain without fracture, determined by dividingmaximum load by the original cross-sectionalarea of the specimen. Also known as nominalstrength or maximum strength.

uniaxial strain. Increase (or decrease) in lengthresulting from a stress acting parallel to thelongitudinal axis of the specimen.

uniaxial stress. See principal stress (normal).uniform elongation. The elongation at maxi-

mum load and immediately preceding the on-set of necking in a tension test.

uniform strain. The strain occurring prior to thebeginning of localization of strain (necking);the strain to maximum load in the tension test.

Vviscoelasticity. A property involving a combi-

nation of elastic and viscous behavior. A ma-terial having this property is considered tocombine the features of a perfectly elasticsolid and a perfect fluid. A phenomenon oftime-dependent, in addition to elastic, defor-mation (or recovery) in response to load.

volumetric modulus of elasticity. See bulkmodulus of elasticity.

Wworkability. See formability.work hardening. See strain hardening.wrinkling. A wavy condition obtained in deep

drawing of sheet metal, in the area of themetal between the edge of the flange and thedraw radius. Wrinkling may also occur inother forming operations when unbalancedcompressive forces are set up.

Yyielding. Evidence of plastic deformation in

structural materials.

yield point. The first stress in a material, usuallyless than the maximum attainable stress, atwhich an increase in strain occurs without anincrease in stress. Only certain metals—thosewhich exhibit a localized, heterogeneous typeof transition from elastic to plastic deforma-tion—produce a yield point. If there is a de-crease in stress after yielding, a distinctionmay be made between upper and lower yieldpoints. The load at which a sudden drop in theflow curve occurs is called the upper yieldpoint. The constant load shown on the flowcurve is the lower yield point.

yield-point elongation. During discontinuousyielding, the amount of strain measured fromthe onset of yielding to the beginning of strainhardening.

yield strength. The stress at which a materialexhibits a specified deviation from propor-tionality of stress and strain. An offset of0.2% is used for many metals. Compare withtensile strength.

yield stress. The stress level of highly ductilematerials, such as structural steels, at whichlarge strains take place without further in-crease in stress.

Young’s modulus. A term used synonymouslywith modulus of elasticity. The ratio of tensileor compressive stresses to the resulting strain.

SELECTED REFERENCES

● Compilation of ASTM Standard Definitions,8th ed., ASTM, 1994

● H.E. Davis, G.E. Troxell, and G.F.W. Hauck,The Testing of Engineering Materials, 4thed., McGraw Hill, 1982

● J.R. Davis, Ed., ASM Materials EngineeringDictionary, ASM International, 1992

● G.E. Dieter, Mechanical Metallurgy, 2nd ed.,McGraw Hill, New York, 1976

● Glossary of Metallurgical Terms and Engi-neering Tables, American Society for Met-als, 1979

● D.N. Lapedes, Ed., Dictionary of Scientificand Technical Terms, 2nd ed., McGraw Hill,1974

● A.D. Merriman, A Dictionary of Metallurgy,Pitman Publishing, London, 1958

● “Metal Test Methods and Analytical Proce-dures,” Annual Book of ASTM Standards,Vol 03.01 and 03.02, ASTM, 1984

● J.G. Tweeddale, Mechanical Properties ofMetals, American Elsevier, 1964

Reference Tables

Table 1 Room-temperature tensile yield strength comparisons of metals and plasticsTensile yield strength

High Low

Material MPa ksi MPa ksi

Cobalt and its alloys 1999 290 179 26Low-alloy hardening steels; wrought, quenched and tempered 1986 288 524 76Stainless steels, standard martensitic grades; wrought, heat treated 1896 275 414 60Rhenium 1862 270 . . . . . .Ultrahigh strength steels; wrought, heat treated 1862 270 1172 170Stainless steels, age hardenable; wrought, aged 1634 237 724 105Nickel and its alloys 1586 230 69 10Stainless steels, specialty grades; wrought, 60% cold worked 1558 226 703 102Tungsten 1517 220 . . . . . .Molybdenum and its alloys 1448 210 565 82Titanium and its alloys 1317 191 186 27Carbon steels, wrought; normalized, quenched and tempered 1296 188 400 58Low-alloy carburizing steels; wrought, quenched and tempered 1227 178 427 62Nickel-base superalloys 1186 172 276 40Alloy steels, cast; quenched and tempered 1172 170 772 112Stainless steels; cast 1138 165 214 31Tantalum and its alloys 1089 168 331 48Steel P/M parts; heat treated 1062 154 517 75Ductile (nodular) irons, cast 1034 150 276 40Copper casting alloys(a) 965 140 62 9Stainless steels, standard austenitic grades; wrought, cold worked 965 140 517 75Niobium and its alloys 931 135 241 35Iron-base superalloys; cast, wrought 924 134 276 40Cobalt-base superalloys, wrought 800 116 241 35Bronzes, wrought(a) 786 114 97 14Heat treated low-alloy constructional steels; wrought, mill heat treated 758 110 621 90High-copper alloys, wrought(a) 758 110 62 9Stainless steels, standard martensitic grades; wrought, annealed 724 105 172 25Cobalt-base superalloys, cast 689 100 517 75Heat treated carbon constructional steels; wrought, mill heat treated 690 100 290 42Hafnium 662 96 221 32Brasses, wrought(a) 638 92.5 69 10Aluminum alloys, 7000 series 627 91 97 14Alloy steels, cast; normalized and tempered 627 91 262 38Copper-nickel-zinc, wrought(a) 620 90 124 18Copper nickels, wrought(a) 586 85 90 13Malleable irons, pearlitic grades; cast 552 80 310 45High-strength low-alloy steels; wrought, as-rolled 552 80 290 42Stainless steels, specialty grades; wrought, annealed 552 80 186 27Stainless steels, standard ferritic grades; wrought, cold worked 552 80 310 45Carbon steels, wrought; carburized, quenched and tempered 531 77 317 46Carbon steel, cast; quenched and tempered 517 75 . . . . . .Stainless steel (410)P/M parts; heat treated 517 75 . . . . . .Steel P/M parts; as-sintered 517 75 207 30Coppers, wrought(a) 496 72 69 10Aluminum alloys, 2000 series 455 66 69 10Ductile (nodular) austenitic irons, cast 448 65 193 28Zinc foundry alloys 441 64 207 30

(continued)

At 0.2% offset for metals, unless otherwise noted; tensile strength at yield for plastics, per ASTM D 638. P/M, powder metallurgy; ABS, acrylonitrile-butadiene-styrene; PVC, polyvinyl chloride. (a) At 0.5% offset. Adapted from Guide to Engineering Materials, Advanced Materials and Processes, Dec 1999




Table 1 (continued)

Tensile yield strength

High Low

Material MPa ksi MPa ksi

Zinc alloys, wrought 421 61 159 23Stainless steels, standard ferritic grades; wrought, annealed 414 60 241 35Aluminum alloys, 5000 series 407 59 41 6Aluminum alloys, 6000 series 379 55 48 7Aluminum casting alloys 379 55 55 8Carbon steels, cast; normalized and tempered 379 55 331 48Stainless steels, standard austenitic grades; wrought, annealed 379 55 207 30Stainless steel P/M parts, as sintered 372 54 276 40Rare earths 365 53 66 9.5Zirconium and its alloys 365 53 103 15Depleted uranium 345 50 241 35Aluminum alloys, 4000 series 317 46 . . . . . .Thorium 310 45 179 26Magnesium alloys, wrought 303 44 90 13Silver 303 44 55 8Carbon steels, cast; normalized 290 42 262 38Beryllium and its alloys 276 40 34 5Aluminum alloys, 3000 series 248 36 41 6Carbon steel, cast; annealed 241 35 . . . . . .Malleable ferritic cast irons 241 35 221 32Palladium 207 30 34 5Gold 207 30 . . . . . .Magnesium alloys, cast 207 30 83 12Polyimides, reinforced 193 28 34 5Platinum 186 27 14 2Iron P/M parts; as-sintered 179 26 76 11Aluminum alloys, 1000 series 165 24 28 4Polyphenylene sulfide, 40% glass reinforced 145 21 . . . . . .Polysulfone, 30–40% glass reinforced 131 19 117 17Acetal, copolymer, 25% glass reinforced 128 18.5 . . . . . .Styrene acrylonitrile, 30% glass reinforced 124 18 . . . . . .Phenylene oxide based resins, 20–30% glass reinforced 117 17 100 14.5Polyamide-imide 117 17 92 13.3Polystyrene, 30% glass reinforced 97 14 . . . . . .Zinc die-casting alloys 96 14 . . . . . .Polyimides, unreinforced 90 13 52 7.5Nylons, general purpose 87 12.6 49 7.1Polyethersulfone 84 12.2 . . . . . .Polyphenylene sulfide, unreinforced 76 11 . . . . . .Polysulfone, unreinforced 70 10.2 . . . . . .Acetal, homopolymer, unreinforced 69 10 . . . . . .Nylon, mineral reinforced 69 10 62 9Polypropylene, glass reinforced 69 10 41 6Polystyrene, general purpose 69 10 34 5.0Phenylene oxide based resins, unreinforced 66 9.6 54 7.8Acetal, copolymer, unreinforced 61 8.8 . . . . . .ABS/polycarbonate 55 8.0 . . . . . .Lead and its alloys 55 8 11 1.6Polyarylsulfone 55 8 . . . . . .ABS/polysulfone (polyarylether) 52 7.5 . . . . . .Acrylic/PVC 48 7.0 45 6.5Tin and its alloys 45 6.6 7 1.3ABS/PVC, rigid 41 6.0 . . . . . .Polystyrene, impact grades 41 6.0 19 2.8Polypropylene, general purpose 36 5.2 33 4.8ABS/polyurethane 31 4.5 26 3.7Polypropylene, high impact 30 4.3 19 2.8

At 0.2% offset for metals, unless otherwise noted; tensile strength at yield for plastics, per ASTM D 638. P/M, powder metallurgy; ABS, acrylonitrile-butadiene-styrene; PVC, polyvinyl chloride. (a) At 0.5% offset. Adapted from Guide to Engineering Materials, Advanced Materials and Processes, Dec 1999

Reference Tables / 275

Table 2 Room-temperature tensile modulus of elasticity comparisons of various materials

Tensile modulus

High Low

Material GPa 106 psi GPa 106 psi

Silicon carbide 655 95 90 13Tungsten carbide-base cermets 650 94.3 425 61.6Tungsten carbide 648 94 448 65Osmium 551 80 . . . . . .Iridium 545 79 . . . . . .Titanium, zirconium, hafnium borides 503 73 490 71Ruthenium 469 68 . . . . . .Rhenium 469 68 . . . . . .Boron carbide 448 65 290 42Boron 441 64 . . . . . .Tungsten 406 59.0 . . . . . .Beryllia 399 58 270 39Titanium carbide-base cermets 393 57 290 42Rhodium 379 55 . . . . . .Titanium carbide 379 55 248 36Molybdenum and its alloys 365 53 317 46Tantalum carbide 365 53 . . . . . .Magnesia 345 50 241 35Alumina ceramic 345 50 207 30Niobium carbide 338 49 . . . . . .Beryllium carbide 317 46 207 30Chromium 289 42 . . . . . .Beryllium and its alloys 289 42.0 186 27.0Graphite-epoxy composites 276 40 134 20Cobalt-base superalloys 248 36.0 199 29.0Zirconia 241 35 158 23Nickel and its alloys 234 34.0 131 19.0Cobalt and its alloys 231 33.6 207 30.0Nickel-base superalloys 231 33.5 126 18.3Iron-base superalloys; cast and wrought 214 31 193 28Silicon nitride 214 31 62 9Alloy steels; cast 207 30 200 29Boron-epoxy composites 207 30 . . . . . .Carbon steels; cast 207 30 . . . . . .Carbon steel, carburizing grades; wrought 207 30 200 29Carbon steels, hardening grades; wrought 207 30 200 29Depleted uranium 207 30 138 20Stainless steels, age hardenable; wrought 207 30 193 28Stainless steels, specialty grades; wrought 207 30 186 27Ultrahigh strength steels; wrought 207 30 186 27Stainless steels; cast 200 29 165 24Stainless steels, standard austenitic grades; wrought 200 29 193 28Stainless steels, standard ferritic grades; wrought 200 29 . . . . . .Stainless steels, standard martensitic grades; wrought 200 29 . . . . . .Boron-aluminum composites 193 28 . . . . . .Malleable irons, pearlitic grades; cast 193 28 179 26Tantalum and its alloys 186 27.0 144 21.0Ductile (nodular) irons; cast 172 25 152 22Malleable ferritic cast irons 172 25 . . . . . .Platinum 172 25 . . . . . .Gray irons; cast 165 24 66 9.6Copper nickels, wrought 151 22.0 124 18.0Mullite 145 21 . . . . . .Zircon 145 21 . . . . . .Ductile (nodular) austenitic irons; cast 138 20 90 13Hafnium 138 20 . . . . . .Copper casting alloys 133 19.3 76 11.0Vanadium 131 19 124 18High-copper alloys, wrought 131 19.0 117 17.0Coppers, wrought 129 18.7 117 17.0Titanium and its alloys 127 18.5 76 11.0Copper-nickel-zinc; wrought 124 18.0 124 18.0Palladium 124 18.0 . . . . . .Brasses; wrought 124 18.0 103 15.0Bronzes; wrought 120 17.5 110 16.0Polycrystalline glass 119 17.3 86 12.5

(continued)

PET, polyethylene terephthalate; ECTFE, ethylene tetrafluoroethylene; ETCFE, ethylene chlorotrifluoroethylene; PVC, polyvinyl chloride; PVF, polyvinyl formal; FEP,fluorinated ethylene propylene; PTFE, polytetrafluoroethylene


Table 2 (continued)

Tensile modulus

High Low


Niobium and its alloys 110 16.0 79 11.5Silicon 107 15.5 . . . . . .Zirconium and its alloys 96 14.0 95 13.8Zinc alloys; wrought 96 14.0 43 6.2Rare earths 84 12.2 15 2.2Gold 82 12.0 . . . . . .Aluminum alloys, 4000 series 79 11.4 . . . . . .Silver 76 11.0 . . . . . .Boron nitride 76 11 48 7Aluminum alloys, 2000 series 74 10.8 70 10.2Silica 72 10.5 . . . . . .Aluminum alloys, 7000 series 72 10.4 71 10.3Aluminum alloys, 5000 series 71 10.3 69 10.0Thorium 71 10.3 . . . . . .Aluminum alloys, 1000 series 69 10.0 69 10.0Aluminum alloys, 3000 series 69 10.0 69 10.0Aluminum alloys, 6000 series 69 10.0 69 10.0Thorium 69 10.0 . . . . . .Tin and its alloys 53 7.7 41 6.0Cordierite 48 7 . . . . . .Magnesium alloys; wrought 45 6.5 41 6.0Magnesium alloys; cast 45 6.5 45 6.5Polyesters, thermoset, pultrusions, general purpose 41 6.0 16 2.3Epoxy, glass laminates 40 5.8 23 3.3Glass fiber-epoxy composites 34 5 . . . . . .Bismuth 32 4.6 . . . . . .Polyimides; glass reinforced 31 4.5 . . . . . .Carbon graphite 28 4.0 4 0.6Graphite, pyrolytic 28 4.0 . . . . . .Phenolics; reinforced 23 3.3 2.4 0.35Alkyds 20 2.9 13 1.9Graphite; recrystallized 19 2.7 5.5 0.8Hickory (shag bark) 15 2.2 . . . . . .Locust (black) 14 2.1 . . . . . .Polyester, thermoplastic, PET; 45 and 30% glass reinforced 14 2.1 9 1.3Birch (yellow) 13 2.0 . . . . . .Douglas fir (coat type) 13 2.0 . . . . . .Lead and its alloys 13 2.0 . . . . . .Pine (long needle, ponderosa) 13 2.0 9 1.3Polyesters, thermoset, reinforced moldings 13 2.0 8.3 1.2Ash (white) 12 1.8 . . . . . .Graphite, general purpose 12 1.8 3.4 0.5Maple (sugar) 12 1.8 . . . . . .Oak (red, white) 12 1.8 . . . . . .Styrene acrylonitrile; 30% glass reinforced 12 1.8 . . . . . .Beech 11 1.7 . . . . . .Carbon and graphite, fibrous reinforced 12 1.8 2 0.3Graphite, premium 11.7 1.7 4.8 0.7Walnut (black) 11.7 1.7 . . . . . .Polycarbonate, 40% glass reinforced 11.7 1.7 5.9 0.86Spruce (sitka) 11.0 1.6 . . . . . .Poplar (yellow) 11.0 1.6 . . . . . .Carbon, petroleum coke base 11.0 1.6 15.8 2.3Indium 10.8 1.57 . . . . . .Basswood 10.3 1.5 . . . . . .Elm (rock) 10.3 1.5 . . . . . .Polysulfone, 30–40% glass reinforced 10.3 1.5 7.6 1.1Cypress (Southern bald) 9.6 1.4 . . . . . .Nylons; 30% glass reinforced 9.7 1.4 6.9 1.0Polyester, thermoplastic, PBT; 40 and 15% glass reinforced 9.7 1.4 5.5 0.8Cedar (Port Orford) 8.9 1.3 . . . . . .Cottonwood (black) 8.9 1.3 . . . . . .Phenylene oxide based resins; 20–30% glass reinforced 9.0 1.3 6.4 0.93Redwood (virgin) 8.9 1.3 . . . . . .Acetal, copolymer; 25% glass reinforced 8.6 1.25 . . . . . .Carbon, anthracite coal base 8.2 1.2 4.1 0.6

(continued)


Reference Tables / 277

Table 2 (continued)

Tensile modulus

High Low


Diallyl phthalates, reinforced 8.3 1.2 4.1 0.6Fir (balsam) 8.3 1.2 . . . . . .Hemlock (Eastern, Western) 8.3 1.2 10.3 1.5Pine (Eastern white) 8.3 1.2 . . . . . .Polybutadienes 8.3 1.2 2.8 0.4Polystyrene, 30% glass reinforced 8.3 1.2 . . . . . .Polyphenylene sulfide, 40% glass reinforced 7.7 1.12 . . . . . .Fluorocarbon, ETFE and ECTFE; glass reinforced 7.6 1.1 . . . . . .Melamines, cellulose electrical 7.6 1.1 6.9 1.0Cedar (Eastern red) 6.2 0.9 . . . . . .Polyimides, unreinforced 4.8 0.70 3.1 0.45Polyesters, thermoset, cast, rigid 4.5 0.65 1.0 0.15Acetal, homopolymer; unreinforced 3.6 0.52 . . . . . .Acrylics, cast, general purpose 3.4 0.50 2.4 0.35Acrylics, moldings 3.4 0.50 1.6 0.23Nylon, mineral reinforced 3.4 0.5 . . . . . .Polystyrene, general purpose 3.4 0.50 3.2 0.46Styrene acrylonitrile; unreinforced 3.4 0.50 2.8 0.40Nylons; general purpose 3.3 0.48 1.9 0.28Polyphenylene sulfide, unreinforced 3.3 0.48 . . . . . .Polystyrene, impact grades 3.2 0.47 1.0 0.15Epoxies, cast 3.1 0.45 0.3 0.05Polycarbonate, unreinforced 3.1 0.45 2.3 0.34ABS 2.9 0.42 2.0 0.29Acetal, copolymer; unreinforced 2.8 0.41 . . . . . .Phenylene oxide based resins; unreinforced 2.6 0.38 2.5 0.36ABS/polycarbonate 2.6 0.37 . . . . . .Acrylic/PVC 2.6 0.37 2.3 0.34Polyaryl sulfone 2.6 0.37 . . . . . .Polysulfone; unreinforced 2.5 0.36 . . . . . .Polyether sulfone 2.4 0.35 . . . . . .ABS/PVC, rigid 2.3 0.33 . . . . . .ABS/polysulfone (polyaryl ether) 2.2 0.32 . . . . . .Allyl diglycol carbonate 2.1 0.30 . . . . . .Fluorocarbon, PTFCE 2.1 0.30 1.3 0.19Fluorocarbon, ETFE and ECTFE; unreinforced 1.7 0.24 . . . . . .ABS/polyurethane 1.5 0.22 1.1 0.16Polypropylene, general purpose 1.5 0.22 1.1 0.16Polymethylpentene 1.4 0.21 . . . . . .Fluorocarbon, PVF 1.4 0.2 1.2 0.17Vinylidene chloride copolymer; oriented 1.38 0.20 . . . . . .Polypropylene, high impact 0.9 0.13 . . . . . .Polyethylene, high molecular weight 0.69 0.1 . . . . . .Fluorocarbon, FEP 0.5 0.07 0.3 0.05Fluorocarbon, PTFE 0.5 0.07 0.3 0.04Vinylidene chloride copolymer; unoriented 0.48 0.07 . . . . . .Polybutylene, homopolymer 0.25 0.036 0.23 0.034Polybutylene, copolymer 0.23 0.034 0.08 0.012Polyacrylate, unfilled 0.20 0.29 . . . . . .Polyethylenes, low density 0.19 0.027 0.14 0.020PVC, PVC-acetate, nonrigid 0.021 0.003 0.0027 0.0004


Index

A

Adhesive joints, tensile testing of 204–206, 205(F),206(F)

Aluminum and aluminum alloysdistribution curves 59(F)elastic behavior 116(F)plastic anisotropy factor 27(T)strain rate data 62(F)stress-strain curves 37(F), 132(F), 222(F)tensile properties 17(T), 94(T), 110(T), 119(T),

273–277(T)American Society of Mechanical Engineers (ASME)

115Anelasticity 116–118, 117(F), 118(F)Anisotropy. See also Plastic strain ratio

of plastic specimens 140–143, 142(F)of sheet metal specimens 25–28, 26(F), 27(F)(T), 103,

110(T)ASTM test standards 34, 39, 40, 41, 44, 45, 46, 47–59,

48(F), 51(F), 52(F), 53(F), 61(F), 69, 70, 75, 76, 77,81, 82, 83(T), 84, 86, 87–89, 88(T), 89(F)(T), 109,115, 137(T), 138, 158–159, 166, 179–180, 185,186–192, 198, 205–206, 246–247

B

Bauschinger effect 40, 40(F)Bolted joints, tensile testing of 195–204, 196(F), 197(F),

199(F)(T), 200(F)(T), 201(F), 202(F), 203(F), 204(F)Bridgman correction factor 23–24, 24(F)

C

Calibrationof load-measuring devices 75–77of test machines 85–87

Cavitation, during hot tensile testing 230–236, 231(F),232(F), 233(F), 234(F), 235(F), 236(F)(T)

Ceramics and ceramic-matrix compositescompressive strength 96(F)limitations of 163–164mechanical properties at low temperatures 240–241tensile testing of 34, 163–182Young’s modulus 275–277(T)

Chord modulus 43, 43(F)Cold work, and strain hardening 124–126, 124(F),

125(F), 126(F)Components, tensile testing of 195–208Composites. See Ceramics and ceramic-matrix

composites; Fiber-reinforced compositesComputerization, of test machines 68, 68(F)Constant extension rate testing. See Slow strain rate

testingCopper and copper alloys

annealing and hardness 127(F)cold rolled, grain structure 126(F)elastic behavior 116(F)plastic anisotropy factor 27(T)tensile properties 94(T), 110(T), 121(F), 125(F), 131(F),

273–277(T)Cost, designing for 93–94Cross slip 130Crosshead

displacement 71–72, 71(F), 245speed 69, 73–74, 225–226, 226(F)

Cryogenic tensile testing. See Low-temperature tensiletesting

Cryostats 243–245, 243(F), 244(F), 245(F), 248. See alsoEnvironmental chambers

D

Damping 118–119, 118(F)Data

analysis of 11–12, 147–150, 226–230, 259–260calculated 11raw 11, 148(F)recording of 11reduction of 68, 191–192reporting of 12utilization of 91–100, 150–152, 215–226

Definitions 34–36, 265–272Deformation. See Elastic deformation; Plastic deformationDesign, tensile testing for 91–100, 152, 192Deutsche Institut fur Normung (DIN) 47, 50, 82, 86,

88(T)Dewars. See CryostatsDuctility 5–7, 16–17, 44–47, 129–130, 216–220




E

Elastic deformation 3–5, 4(F), 37–39Elastic limit 5, 15, 15(F), 39Elastic modulus. See Young’s modulusElastomers

manufacture of 155, 157mechanical properties 156(T)molecular structure 156–157tear strength 96(F)tensile properties 159–161tensile testing of 34, 155–162

Elevated-temperature tensile testing. See Hot tensiletesting

Elongation 35, 40, 44–46, 44(F), 45(F), 46(F), 109–110,156, 156(T), 161, 203, 235–236, 235(F), 236(F)

Environmental chambers 84–85, 85(F), 213–214, 215(F),244. See also Cryostats

Equipment, tensile testing 54–56, 65–89, 210–215,243–246. See also Extensometers; Gripping; Straingages; Tensile testing machines

Expanding ring test 254–255Extension-under-load yield strength 42, 42(F), 44,

202–203, 203(F)Extensometers 36, 56, 77–83, 78(F), 79(F), 80(F), 81(F),

82(F), 83(F)(T), 84(F), 109, 146–147, 245, 246

F

Failure stress 97–98Fasteners, threaded, tensile testing of 195–204, 196(F),

197(F), 199(F)(T), 200(F)(T), 201(F), 202(F), 203(F),204(F)

Fiber-reinforced compositesmechanical properties at low temperatures 241tensile properties 96(F), 275–277(T)tensile testing of 183–193, 247–248

Filaments. See Fiber-reinforced compositesFlexure tests 171–175, 173(F), 174(F), 176, 177(F)Flow curves 20–21, 20(F)(T)Flyer plates 255–257, 255(F), 256(F), 257(F)Foot correction 43, 43(F)Force 34–35, 85–87, 149(F), 245Formability. See Sheet formabilityForming limit diagrams 103–104, 103(F), 104(F), 105(F)Fractures

brittle 29, 29(F), 30–31characterization 134–136, 135(F), 136(F)cup-and-cone 29–30, 29(F), 30(F)ductile 28–30, 29(F), 30(F)

G

Gage length 44, 44(F), 45, 45(F), 50(F), 51–53, 51(F),52(F), 109–110, 199(F), 226, 227(F)

Gleeble testing 210–213, 210(F), 211(F), 212(F),215–220, 216(T), 217(F), 218(F), 219(F), 220(F),221(F)

Glossary of terms 265–272

Grain size, and tensile properties 122(F), 123–124,124(F), 225(F)

Gripping, of specimens 2, 2(F), 9, 9(F), 10(F), 54–55,55(F), 57(F), 58, 83–84, 84(F), 144–145, 166–171,169(F), 176–177, 177(F), 185(F)

H

Hardnesscorrelation with strength 99–100, 99(F)(T), 100(T)of fasteners and studs 198, 199

High strain rate tensile testing 251–263High-temperature tensile testing. See Hot tensile testingHooke’s modulus. See Young’s modulusHopkinson pressure bar. See Split-Hopkinson pressure

barHot tensile testing 175–180, 209–238

I

Indirect tensile testing 171–175, 172(F), 173(F), 174(F)Inertia, effects of 252–253International Organization for Standardization (ISO)

43, 46, 47, 48, 49, 49(F), 50, 75, 82, 88(T), 137(T)Iron

elastic behavior 116(F)interstitial sites in lattice 116(F)tensile properties 93(T), 121(F), 275–277(T)

J

Japanese Industrial Standards (JIS) 47, 50, 88(T)Joints. See Adhesive joints; Bolted joints; Welded joints

L

Laminates. See Fiber-reinforced compositesLoad 34–35Load cells 75, 76–77, 77(F), 87, 109Load measurement 74–77, 76(F), 77(F), 109Low-temperature tensile testing 239–249Luders bands 16, 16(F), 123

M

Magnesium and magnesium alloysplastic anisotropy factor 27(T)tensile properties 94(T), 273–277(T)

Metal-matrix composites. See Fiber-reinforcedcomposites

Metals and alloys. See also Steel; various alloy systemselastic constants 98(T)mechanical behavior under tensile loads 13–31mechanical properties at low temperatures 240, 240(F)tensile properties 96(F), 273–277(T)tensile testing of 33–63, 101–114, 115–136, 209–238,

246–247Modulus of elasticity. See Young’s modulus



Index / 281

Modulus of resilience. See ResilienceModulus of toughness. See Toughness

N

National Institute of Standards and Technology (NIST)77

Necking 14(F), 20, 22–25, 23(F), 24(F), 45, 143, 143(F),226–227, 260

Nickel and nickel alloysstress-strain curves 124(F)tensile properties 119(T), 273–277(T)

Notch sensitivity 28, 28(F)Notch tensile testing 28, 28(F), 133

O

Oak Ridge National Laboratory 169Offset yield strength 5, 14(F), 15, 15(F), 42–43, 42(F),

44, 202(F)Olsen, Tinius 65Open hole tensile testing 188(F), 189–190, 190(F)

P

Plane-strain tensile testing 111–112, 112(F)Plastic deformation 3–5, 4(F), 39Plastic strain ratio 40, 101, 103, 103(F), 110(T), 111,

223–224, 224(F). See also AnisotropyPlastics

mechanical properties at low temperatures 241mechanical test standards 137(T)stress-strain curves 37(F)tensile properties 18(F), 95(T), 150(T), 273–277(T)tensile testing of 34, 137–153, 247–248

Poisson’s ratio 4, 40, 98, 98(T), 192Polymers. See PlasticsProduct design 91–92Proof-load test 198–199Proof stress. See Offset yield strengthProportional limit 5, 15, 15(F), 39, 119, 119(F)Proving rings 75–77, 76(F), 87

R

Reduction of area 40, 46–47, 47(F), 109, 204, 212(F),215–216(T), 217(F)

Reloading 39–40Resilience 17–18, 17(F)Rotating wheel test 260–262, 261(F)Rubber. See Elastomers

S

Safetyin cryogenic testing 248–249, 248(T)factor of 92–93

Samples. See Specimens, tensile

Shear fracture 104Sheet formability 101–114Silver and silver alloys, tensile properties 119(T),

273–277(T)Slow strain rate testing 133–134, 134(F)Spall stress 256–257, 257(F)Specimens, tensile

adhesive joint 204–206, 205(F), 206(F)alignment of 55–56, 109, 144–145, 246anisotropy in 25–28, 26(F), 27(F)(T), 103, 110(T),

140–143, 142(F)composite 185–191, 186(F), 188(F), 190(F), 191(F)dimension measurements 52dimensions, effect on elongation 45–46, 46(F)gage length of 1–2, 1(F), 44, 44–46, 44(F), 45, 45(F),

50(F), 51–53, 51(F), 52(F)geometry of 50–54, 50(F), 166, 167(F), 168(F), 188(F),

190(F), 205(F), 214–215, 215(F), 247(F)Gleeble 210(F), 211(F)gripping of 2, 2(F), 9, 9(F), 10(F), 54–55, 55(F), 57(F),

58, 83–84, 84(F), 144–145, 166–171, 169(F),176–177, 177(F), 185(F)

for indirect testing 171–175, 172(F)for low-temperature testing 247, 247(F)notched 28, 53–54, 53(F), 133open hole 189–190, 190(F)orientation of 49, 49(F), 50(T)plane-strain 112(F)plastic 144–145preparation of 8, 108–109, 157, 187, 189rough 48–49, 49(F)sample selection 8, 49–50sheet 107(F)split-Hopkinson pressure bar 260surface finish of 54terminology 48–49, 49(F), 50(F)

Split-Hopkinson pressure bar 257–260, 258(F), 259(F)Springback 104–106, 105(F)Stainless steel

dislocations 121(F)microstructure 120(F)tensile properties 17(T), 110(T), 273–277(T)

Steel. See also Metals and alloyscold work effects 125(F)contour maps 59(F)forming limit diagram 103(F)Gleeble curves 219(F), 220(F)hot-workability ratings 216(T)Luders bands 16(F)plastic anisotropy factor 27(T)spall data 257(F)stress-strain curves 37(F), 38(F), 39(F), 97(F), 108(F),

130(F)stress-time diagrams 262(F)tensile properties 15(F), 17(F)(T), 18(F), 93(T), 110(T),

119(T), 275–277(T)Stiffness

designing for 95–97of test machines 71–72, 71(F), 73(T)

Strain 35




Strain concentrations 59–61, 60(F)Strain gages 79–80, 79(F), 82(F), 146–147, 245–246Strain hardening 124–126, 131Strain-hardening exponent (coefficient) 20–21, 20(F)(T),

40, 101–102, 110–111, 110(T), 130, 222–223Strain measurement 77–83, 177–178, 245, 251, 253–254Strain rate 21–22, 21(T), 22(F), 57–58, 58(F), 60(F),

61–62, 61(F), 62(F), 69–74, 69(T), 110, 131–133,131(F), 132(F), 211, 224–225, 225(F)

Strain rate sensitivity 101, 102–103, 110(T), 111, 111(F),223, 223(F), 225(F), 251

Strain sensors 65–89, 145–147Strength, designing for 93–95, 93(T), 94(T), 95(T), 96(F)Strength coefficient 20–21, 20(F)(T)Stress 35, 36Stress rate 57–58, 58(F)Stress-strain curves

engineering 3–7, 4(F), 5(F), 6(F), 8(F), 13–18, 14(F),15(F), 17(F), 18(F), 19(F), 36–47, 37(F), 38(F),41(F), 42(F), 43(F), 44(F), 108(F), 130–131,130(F), 220–221, 221(F), 229(F), 233–234, 233(F)

true 7, 8(F), 18–20, 19(F), 20(F), 108(F), 130–131,130(F), 221–222, 222(F)

Stretcher strains 123Studs. See Fasteners, threadedSuperalloys

Gleeble curves 219(F), 220(F), 221(F)hot-workability ratings 216(T)tensile properties 93(T), 273–277(T)

T

Tangent modulus 43, 43(F)Temperature, effect of 22, 56, 106–107, 131–133,

131(F), 132(F), 158. See also Hot tensile testing;Low-temperature tensile testing

Tensile strength 5, 6(F), 14–15, 14(F), 40–41, 59, 59(F),61(F), 92–95, 93(T), 94(T), 95(T), 96(F), 126–127,155–156, 156(T), 159–161, 191, 203, 217–220

Tensile testingof adhesive joints 204–206, 205(F), 206(F)of ceramics and ceramic-matrix composites 34, 163–182of components 195–208for design 91–100, 152, 192of elastomers 34, 155–162equipment for 54–56, 65–89, 210–215expanding ring 254–255of fiber-reinforced composites 183–193, 247–248flat plate impact 255–257, 255(F), 256(F), 257(F)flexure 171–175, 173(F), 174(F), 176, 177(F)Gleeble 210–213, 210(F), 211(F), 212(F), 215–220,

216(T), 217(F), 218(F), 219(F), 220(F), 221(F)high strain rate 251–263high-temperature (hot) 175–180, 209–238indirect 171–175, 172(F), 173(F), 174(F)low-temperature 239–249mechanical behavior 13–31of metals and alloys 33–63, 101–114, 115–136,

209–238, 246–247methodology 8–12, 47–58

notch 28, 28(F), 133open hole 188(F), 189–190, 190(F)overview 1–24plane-strain 111–112, 112(F)of plastics 34, 137–153, 247–248post-test measurements 58–59procedures 10–11, 56–58proof-load 198–199rotating wheel 260–262, 261(F)setup 8–10, 54–56for sheet formability determination 101–114slow strain rate 133–134, 134(F)speed 56–58split-Hopkinson pressure bar 257–260, 258(F), 259(F)strain sensors 65–89temperature control 56test standards 47–59, 87–89, 88(T), 89(F)(T). See also

ASTM test standardsof threaded fasteners and bolted joints 195–204, 196(F),

197(F), 199(F)(T), 200(F)(T), 201(F), 202(F),203(F), 204(F)

total extension at fracture 204, 204(F)uniaxial 33–63, 107–111vs. compression testing 241–243wedge 200–201, 200(F)(T), 201(F)of welded joints 206–208

Tensile testing machines. See also Equipmentcalibration of 85–87computerization of 68, 68(F)control modes 72–74early models 65, 65(F)electromechanical (gear-driven or screw-driven) 2, 3,

66–67, 67(F), 213–214, 243frame-furnace 213–214, 214(F), 215(F)Gleeble 210–211, 210(F)hydraulic/servohydraulic 2–3, 3(F), 66, 67–68, 68(F),

213, 243load measurement 74–77, 76(F), 77(F)for low-temperature testing 243–246, 243(F), 244(F),

245(F)for plastics 144–145stiffness of 71–72, 71(F), 73(T)strain measurement 77–83universal 2, 65, 65(F), 66–77, 85–87, 213, 214(F)

Tension set, for elastomers 156, 161Terminology 34–36, 48–49, 49(F), 50(F), 265–272Test pieces. See Specimens, tensileThermocouples 246Threaded fasteners. See Fasteners, threadedTitanium and titanium alloys

flow stress 124(F)plastic anisotropy factor 27(T)stress-strain curves 221(F), 222(F)tensile properties 95(T), 119(T), 132(F), 273–277(T)

Total extension at fracture test 204, 204(F)Toughness 17(F), 18, 127–129, 129(F)Tows. See Fiber-reinforced compositesTrue stress and strain. See Stress-strain curves, true

UUniaxial tensile testing 33–63, 107–111Upper yield strength 41–42, 41(F)



Index / 283

V

Viscoelasticity 138–140, 139(F), 142(F)Vulcanization 155, 157–158

W

Wave propagation, effects of 252–253Wedge tensile testing 200–201, 200(F)(T), 201(F)Weight, designing for 93–94Welded joints, tensile testing of 206–208Work hardening 143, 143(F)Wrinkling 104

Y

Yield point 5, 15–16, 15(F), 16(F), 41–42, 122–123,201–202, 202(F), 203(F)

Yield strength 5, 6(F), 40–44, 59, 59(F), 61(F), 92–95,93(T), 94–95(T), 96(F), 119–133, 119(T), 199, 203,203(F), 273–274(T)

Young’s modulus 4, 15(F), 17, 17(T), 37–39, 40, 44(F),97–99, 98(T), 115–116, 119(T), 156, 191–192,275–277(T)

Z

Zirconium and zirconium alloysplastic anisotropy factor 27(T)tensile properties 273–277(T)



ASM International is the society for materials engineers and scientists, a worldwide network dedicated to advancing industry, technology, and applications of metals and materials. ASM International, Materials Park, Ohio, USA www.asminternational.org

This publication is copyright © ASM International®. All rights reserved.

Publication title Product code Tensile Testing #05106G

To order products from ASM International:

Online Visit www.asminternational.org/bookstore

Telephone 1-800-336-5152 (US) or 1-440-338-5151 (Outside US) Fax 1-440-338-4634

Mail Customer Service, ASM International 9639 Kinsman Rd, Materials Park, Ohio 44073-0002, USA

Email [email protected]

In Europe

American Technical Publishers Ltd. 27-29 Knowl Piece, Wilbury Way, Hitchin Hertfordshire SG4 0SX, United Kingdom Telephone: 01462 437933 (account holders), 01462 431525 (credit card) www.ameritech.co.uk

In Japan Neutrino Inc. Takahashi Bldg., 44-3 Fuda 1-chome, Chofu-Shi, Tokyo 182 Japan Telephone: 81 (0) 424 84 5550

Terms of Use. This publication is being made available in PDF format as a benefit to members and customers of ASM International. You may download and print a copy of this publication for your personal use only. Other use and distribution is prohibited without the express written permission of ASM International. No warranties, express or implied, including, without limitation, warranties of merchantability or fitness for a particular purpose, are given in connection with this publication. Although this information is believed to be accurate by ASM, ASM cannot guarantee that favorable results will be obtained from the use of this publication alone. This publication is intended for use by persons having technical skill, at their sole discretion and risk. Since the conditions of product or material use are outside of ASM's control, ASM assumes no liability or obligation in connection with any use of this information. As with any material, evaluation of the material under end-use conditions prior to specification is essential. Therefore, specific testing under actual conditions is recommended. Nothing contained in this publication shall be construed as a grant of any right of manufacture, sale, use, or reproduction, in connection with any method, process, apparatus, product, composition, or system, whether or not covered by letters patent, copyright, or trademark, and nothing contained in this publication shall be construed as a defense against any alleged infringement of letters patent, copyright, or trademark, or as a defense against liability for such infringement.

asm - tensile testing

Documents