Springer Handbookof Experimental Solid Mechanics

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123

HandbookSpringerof Experimental Solid

MechanicsSharpe (Ed.)

With DVD-ROM, 874 Figures, 58 in four color and 50 Tables

Editor:

Professor William N. Sharpe, Jr.Department of Mechanical EngineeringRoom 126, Latrobe HallThe Johns Hopkins University3400 North Charles StreetBaltimore, MD 21218-2681, USAsharpe@jhu.edu

Library of Congress Control Number: 2008920731

ISBN: 978-0-387-26883-5 e-ISBN: 978-0-387-30877-7

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V

Preface to Handbook on Experimental Stress Analysis

Experimental science does not receive Truth from supe-rior Sciences: she is the Mistress and the other sciencesare her servants ROGER BACON: Opus Tertium.

Stress analysis has been regarded for some time asa distinct professional branch of engineering, the ob-ject of which is the determination and improvement ofthe mechanical strength of structures and machines. Ex-perimental stress analysis strives to achieve these aimsby experimental means. In doing so it does not remain,however, a mere counterpart of theoretical methods ofstress analysis but encompasses those, utilizing all theconclusions reached by theoretical considerations, andgoes far beyond them in maintaining direct contact withthe true physical characteristics of the problems underconsiderations.

Many factors make the experimental approach in-dispensable, and often the only means of access, inthe investigation of problems of mechanical strength.At our present state of knowledge it is remarkablehow quickly we can reach the limit of applicabilityof mathematical methods of stress analysis, and thereis a multitude of comparatively simple, and in prac-tice frequently occurring, stress problems for which notheoretical solutions have yet been obtained. In addi-tion to this, theoretical considerations are usually basedon simplifying assumptions which imply certain de-tachment from reality, and it can be decided only byexperimentation whether such idealization has not re-sulted in an undue distortion of the essential featuresof the problem. No such doubt needs to enter exper-imental stress analysis, especially if it is done underactual service conditions, where all the factors due tothe properties of the employed materials, the methodsof manufacture, and the conditions of operation arefully represented. The advantage of the experimentalapproach becomes especially obvious if we considerthat it is possible to determine experimentally the stressdistribution in a machine part in actual operation with-out knowing the nature of the forces acting on the partunder these circumstances, which proposition is clearlyinaccessible to any theoretical method of analysis. Tothese major advantages we may add one more, from thepoint of view of the average practicing engineer, whosemathematical preparation is not likely to enable him to

deal theoretically with some of the complex strengthproblems which he, nevertheless, is expected to settlesatisfactorily. To these men experimental methods con-stitute a recourse that is more readily accessible andthat, with proper care and perseverance, is most likelyto furnish the needed information.

Several principal methods and literally hundreds ofindividual tools and artifices constitute the “arsenal” ofthe experimental stress analyst. It is interesting to ob-serve, however, that each of these devices, no matterhow peculiar it sometimes appears to be, has its charac-teristic feature and, with it, some unique advantage thatmay render this tool most suitable for the investigationof a particular problem. The stress analyst cannot af-ford, therefore, to ignore any of these possibilities. Thiscircumstance, together with the ever-increasing demandon mechanical strength, will always tend to keep exper-imental stress analysis a distinct entity in the field oftechnical sciences.

There has been a long-felt need of a comprehen-sive reference book of this nature, but, at the sametime, it was recognized that no one person could pos-sibly write with authority on all the major experimentalprocedures that are being used at present in the investi-gation of mechanical strength. It was proposed thereforethat the problem could be solved only by a concertedeffort which might be initiated most suitably under theaegis of the Society for Experimental Stress Analysis,and the writer was appointed as editor with completefreedom to proceed with the organization of this under-taking. Invitations were sent to thirty eminent engineersand scientists who were best known for their outstand-ing contributions in one or more of the specific branchesof experimental stress analysis. It was most impressiveto witness the readiness and understanding with whichthese men, many of them not even associated with theSociety, responded to the request and joined the edi-tor in contributing their work, without remuneration, tothe furtherance of the aims of the Society, which thusbecomes the sole recipient of all royalties from thispublication.

This being the first comprehensive publication in itsfield, it may be of general interest to say a few wordsabout the method used in the planning and coordina-

VI

tion of the material. In inviting the contributors, I firstbriefly out-lined the subject to be covered requesting, inreturn, from each author a more detailed outline of whathe would propose on his respective subject. These au-thors’ outlines were subsequently collected in a booklet,a copy of which was sent to each participant, thus in-forming him in advance of projected contents of all theother parts of the book. This scheme proved of consid-erable help in assuring adequate coverage of all mattersof interest, without undue overlaps, repetition, or needof frequent cross references. In the final plan, as seenin the table of contents, the main body of the book wasdivided into 18 chapters, each dealing with either a prin-cipal method, from mechanical gages to x-ray analysis,or a major topic of interest, such as residual stresses,interpretation of service fractures, or analogies. In addi-tion to these, an appendix was devoted to the discussionof three theoretical subjects which are of fundamentalimportance in the planning and interpretation of exper-imental stress work. In the final outcome, not only thebook as a whole but also most of the individual chap-

ters turned out to be pioneering ventures in their ownrights, often constituting the first systematic expositionof their respective subject matter. Another innovationwas undertaken in the treatment of bibliographical ref-erences, where an effort was made to review briefly thecontents of each entry, since it was found that the meretitles of technical articles seldom convey a satisfactorypicture of their respective contents. Despite all precau-tions the book is bound to have errors and shortcomings,and it is the sincere hope of the editor that users ofthe book will not hesitate to inform him of possibilitiesof improvement which may be incorporated in a lateredition.

In the course of this work the editor was greatlyaided by advice from numerous friends and colleagues,among whom he wishes to acknowledge in particu-lar the invaluable help received from B. F. Langer,R. D. Mindlin, W. M. Murray, R. E. Peterson, andG. Pickett.

Evanston, Illinois April 1950 M. Hetenyi

VII

Preface to the Handbook on Experimental Mechanics, First Edition

The Handbook on Experimental Stress Analysis, whichwas published under the aegis of the Society forExperimental Stress Analysis in 1950, has been thecomprehensive and authoritative reference in our fieldfor more than thirty years. Under the able editorshipof the late M. Herenyi, 31 authors contributed with-out compensation 18 chapters and 3 appendices to thishandbook. It received international acclaim and broughtconsiderable income to the Society for ExperimentalMechanics.

Since 1950, new experimental techniques, suchas holography, laser speckle interferometry, geometricmoire, moire interferometry, optical heterodyning, andmodal analysis, have emerged as practical tools in thebroader field of experimental mechanics. The emer-gence of new materials and new disciplines, such ascomposite materials and fracture mechanics, resulted inthe evolution of traditional experimental techniques tonew fields such as orthotropic photoelasticity and exper-imental fracture mechanics. These new developments,together with the explosive uses of on/off-line comput-ers for rapid data processing and the combined use ofexperimental and numerical techniques, have expandedthe capabilities of experimental mechanics far beyondthose of the 1950s.

Sensing the need to update the handbook, H. F.Brinson initiated the lengthy process of revising the

handbook during his 1978-79 presidency of the Society.Since M. Hetenyi could not undertake the contemplatedrevision at that time, the decision was made to pub-lish a new handbook under a new editor. Opinionsranging from topical coverage to potential contributorswere solicited from various SEM members, and aftera short respite I was chosen as editor by the ad hocHandbook Committee chaired by J. B. Ligon. Despitethe enormous responsibility, our task was made eas-ier by inheriting the legacy of the Herenyi Handbookand the numerous suggestions that were collected byH. Brinson.

The new handbook, appropriately entitled Hand-book on Experimental Mechanics, is dedicated toDr. Hetenyi. Twenty-five authors have contributed 21chapters that include, among others, the new disci-plines and developments that are mentioned above. Thehandbook emphasizes the principles of the experimen-tal techniques and de-emphasizes the procedures thatevolve with time. I am grateful to the contributors,who devoted many late afterhours in order to meet themanuscript deadlines and to J. B. Ligon who readilyprovided welcomed assistance during the trying timesassociated with this editorship.

Albert S. Kobayashi 1987

VIII

Preface to the Handbook on Experimental Mechanics, Second Edition

Since the publication of the first edition, considerableprogress has been made in automated image process-ing, greatly reducing the heretofore laborious task ofevaluating photoelastic and moire fringe patterns. It istherefore appropriate to add Chapter 21: “Digital ImageProcessing” before the final chapter, “Statistical Analy-sis of Experimental Data.” Apart from the new chapter,this second edition is essentially same as the first edi-tion with minor corrections and updating. Exceptions tothis are the addition of a section on optical fiber sensorsin Chapter 2: “Strain Gages,” and extensive additions to

Chapter 14, which is retitled “Thermal Stress Analysis,”and to Chapter 16: “Experimental Modal Analysis.”

To reiterate, the purpose of this handbook is to docu-ment the principles involved in experimental mechanicsrather than the procedures and hardware, which evolveover time. To that extent, we, the twenty-seven authors,judging from the many appreciative comments whichwere received upon the publication of the first edition,have succeeded.

Albert S. Kobayashi April 1993

IX

Preface

This handbook is a revision and expansion of theHandbook on Experimental Mechanics published bythe Society for Experimental Mechanics in 1987 witha second edition in 1993 – both edited by AlbertKobayashi. All three of these trace a direct lineage tothe seminal Handbook of Experimental Stress Analysisconceived and edited by Miklós Hetényi in 1950 andthey encapsulate the history of the field. In 1950, the ca-pability of measuring strains on models and structureswas just becoming widely available. Engineers werestill making their own wire resistance foil gages, andphotoelasticity measurements required film processing.Conversion of these measurements to stresses reliedon slide rules and graph paper. Now, foil resistancegages are combined with automatic data acquisition,and photoelasticity is just as automated. Input from bothexperimental methods is combined with finite elementanalysis to present stress variations in color on a com-puter screen. The focus then was on large structuressuch as airframes; in fact, the efforts of the Society forExperimental Stress Analysis (founded in 1938) werecrucial to the rapid development of aircraft in the 1940s.While measurements on large structures continue tobe important, researchers today also measure the me-chanical properties of specimens smaller than a humanhair.

The field is completely different now. Experimentaltechniques and applications have expanded (or con-tracted if you prefer) from stress analysis of largestructures to include the electromechanical analysis ofmicron-sized sensors and actuators. Those changes –occurring gradually over the early years but now morerapidly – led to a change in the society name to the So-ciety for Experimental Mechanics. Those changes alsohave led to the expansion of the current volume withthe deletion of some topics and the addition of others

in order to address these emerging topics in the “microworld”. This volume presents experimental solid me-chanics as it is practiced in the early part of the 21stcentury. It is a field that is important as a technologyand rich in research opportunities.

A striking feature of this handbook is that 20of the 36 chapters are on topics that have arisen ormatured in the 15 years since the last edition; and,in most cases, these have been written by relativelyyoung researchers and practitioners. Consider micro-electromechanical systems (MEMS), for example. Thattechnology, originated by electrical engineers only 25years ago, now permeates our lives. It was soon learnedthat designers and manufacturers needed better un-derstanding of the mechanical properties of the newmaterials involved, and experimental mechanists be-came involved only 15 years ago. That is just oneexample; several of the chapters speak to it as well assimilar completely new topics. The reader will find inthis volume not only information on the traditional ar-eas of experimental solid mechanics, but on new andemerging topics as well.

This revision was initiated by the Executive Boardof the Society and managed by the very capable staffat Springer, in particular Elaine Tham, Werner Sko-laut, and Lauren Danahy. Sound advice was providedover the course of the effort by Jim Dally and TomProulx. However, the real work was done by the authors.Each chapter was written by authors, who are not onlyexperts, but who volunteered to contribute to this Hand-book. Although they are thoroughly familiar with thetechnical details, it still required a major effort on theirpart to prepare a chapter. On behalf of the Society andSpringer, I acknowledge and thank them.

Baltimore June 2008 William N. Sharpe, Jr.

XI

About the Editor

William N. Sharpe, Jr. holds the Alonzo G. Decker Chair in Mechanical Engineeringat the Johns Hopkins University where he served as department chairman for 11-1/2years. His early research focused on laser-based strain measurement over very shortgage lengths to study plasticity and fracture behavior. The past fifteen years have beendevoted to development and use of experimental methods to measure the mechanicalproperties of materials used in microelectromechanical systems. He is a Fellow andPast President of the Society for Experimental Mechanics from which he received theMurray Medal. The American Society of Mechanical Engineers awarded him the NadaiAward as well as Fellow grade. He has received an Alexander von Humboldt Awardalong with the Roe Award from the American Society of Engineering Education.

XIII

List of Authors

Jonathan D. AlmerArgonne National Laboratory9700 South Cass AvenueArgonne, IL 60439, USAe-mail: almer@aps.anl.gov

Archie A.T. AndonianThe Goodyear Tire & Rubber Co.D/410F 142 Goodyear BoulevardAkron, OH 44305, USAe-mail: aandonian@goodyear.com

Satya N. AtluriUniversity of CaliforniaDepartment of Mechanical & AerospaceEngineering, Center for Aeorspace Research& Education5251 California Avenue, Suite 140Irvine, CA 92612, USA

David F. BahrWashington State UniversityMechanical and Materials EngineeringPullman, WA 99164, USAe-mail: dbahr@wsu.edu

Chris S. BaldwinAither Engineering, Inc.4865 Walden LaneLanham, MD 20706, USAe-mail: cbaldwin@aitherengineering.com

Stephen M. BelkoffJohns Hopkins UniversityInternational Center for OrthopaedicAdvancement, Department of OrthopaedicSurgery, Bayview Medical Center5210 Eastern AvenueBaltimore, MD 21224, USAe-mail: sbelkoff@jhmi.edu

Hugh BruckUniversity of MarylandDepartment of Mechanical EngineeringCollege Park, MD 20742, USAe-mail: bruck@umd.edu

Ioannis ChasiotisUniversity of Illinois at Urbana-ChampaignAerospace EngineeringTalbot Lab, 104 South Wright StreetUrbana, IL 61801, USAe-mail: chasioti@uiuc.edu

Gary CloudMichigan State UniversityMechanical Engineering DepartmentEast Lansing, MI 48824, USAe-mail: cloud@egr.msu.edu

Wendy C. CroneUniversity of WisconsinDepartment of Engineering Physics1500 Engineering DriveMadison, WI 53706, USAe-mail: crone@engr.wisc.edu

James W. DallyUniversity of Maryland5713 Glen Cove DriveKnoxville, TN 37919, USAe-mail: jdally0829@comcast.net

James F. DoylePurdue UniversitySchool of Aeronautics & AstronauticsWest Lafayette, IN 47907, USAe-mail: jfdoyle@purdue.edu

Igor EmriUniversity of LjubljanaCenter for Experimental MechanicsCesta na brdo 85Lubljana, SI-1125, Sloveniae-mail: ie@fs.uni-lj.si

Yimin GanUniversität GH KasselFachbereich 15 – MaschinenbauMönchebergstr. 734109 Kassel, Germanye-mail: ganyimin@uni-kassel.de

XIV List of Authors

Ashok Kumar GhoshNew Mexico TechMechanical Engineering and Civil EngineeringSocorro, NM 87801, USAe-mail: ashok@nmt.edu

Richard J. GreeneThe University of SheffieldDepartment of Mechanical EngineeringMappin StreetSheffield, S1 3JD, UKe-mail: r.j.greene@sheffield.ac.uk

Bongtae HanUniversity of MarylandMechanical Engineering DepartmentCollege Park, MD 20742, USAe-mail: bthan@eng.umd.edu

M. Amanul HaquePennsylvania State UniversityDepartment of Mechanical Engineering317A Leonhard BuildingUniversity Park, PA 16802, USAe-mail: mah37@psu.edu

Craig S. HartleyEl Arroyo Enterprises LLC231 Arroyo Sienna DriveSedona, AZ 86332, USAe-mail: cmcshartley@msn.com

Roger C. HautMichigan State UniversityCollege of Osteopathic Medicine, OrthopaedicBiomechanics LaboratoriesA407 East Fee HallEast Lansing, MI 48824, USAe-mail: Haut@msu.edu

Jay D. HumphreyTexas A&M UniversityDepartment of Biomedical Engineering335L Zachry Engineering Center, 3120 TAMUCollege Station, TX 77843-3120, USAe-mail: jhumphrey@tamu.edu

Peter G. IfjuUniversity of FloridaMechanical and Aerospace EngineeringGainesville, FL 32611, USAe-mail: ifju@ufl.edu

Wolfgang G. KnaussCalifornia Institute of Technology-GALCIT 105-501201 East California BoulevardPasadena, CA 91125, USAe-mail: wgk@aero.caltech.edu

Albert S. KobayashiUniversity of WashingtonDepartment of Mechanical EngineeringSeattle, Washington 98195-2600, USAe-mail: ask@u.washington.edu

Sridhar KrishnaswamyNorthwestern UniversityCenter for Quality Engineering & Failure PreventionEvanston, IL 60208-3020, USAe-mail: s-krishnaswamy@northwestern.edu

Yuri F. KudryavtsevIntegrity Testing Laboratory Inc.PreStress Engineering Division80 Esna Park DriveMarkham, Ontario L3R 2R7, Canadae-mail: ykudryavtsev@itlinc.com

Pradeep LallAuburn UniversityDepartment of Mechanical EngineeringCenter for Advanced Vehicle Electronics201 Ross HallAuburn, AL 36849-5341, USAe-mail: lall@eng.auburn.edu

Kenneth M. LiechtiUniversity of TexasAerospace Engineering and Engineering MechanicsAustin, TX 78712, USAe-mail: kml@mail.utexas.edu

List of Authors XV

Hongbing LuOklahoma State UniversitySchool of Mechanical and Aerospace Engineering218 Engineering NorthStillwater, OK 74078, USAe-mail: hongbing.lu@okstate.edu

Ian McEnteggartInstronCoronation Road, High WycombeBuckinghamshire, HP12 3SY, UK

Dylan J. MorrisNational Institute of Standards and TechnologyMaterials Science and Engineering LaboratoryGaithersburg, MD 20877, USAe-mail: dylan.morris@nist.gov

Sia Nemat-NasserUniversity of CaliforniaDepartment of Mechanical and AerospaceEngineering9500 Gilman DriveLa Jolla, CA 92093-0416, USAe-mail: sia@ucsd.edu

Wolfgang OstenUniversität StuttgartInstitut für Technische OptikPfaffenwaldring 970569 Stuttgart, Germanye-mail: osten@ito.uni-stuttgart.de

Eann A. PattersonMichigan State UniversityDepartment of Mechanical Engineering2555 Engineering BuildingEast Lansing, MI 48824-1226, USAe-mail: eann@egr.msu.edu

Daniel PostVirginia Polytechnic Institute and State University(Virginia Tech)Department of Engineering Science and MechanicsBlacksburg, VA 24061, USAe-mail: danpost@vt.edu

Ryszard J. PryputniewiczWorcester Polytechnic InstituteNEST – NanoEngineering, Science, and TechnologyCHSLT – Center for Holographic Studies and LaserMicro-MechatronicsWorcester, MA 01609, USAe-mail: rjp@wpi.edu

Kaliat T. RameshJohns Hopkins UniversityDepartment of Mechanical Engineering3400 North Charles StreetBaltimore, MD 21218, USAe-mail: ramesh@jhu.edu

Krishnamurthi RameshIndian Institute of Technology MadrasDepartment of Applied MechanicsChennai, 600 036, Indiae-mail: kramesh@iitm.ac.in

Krishnaswamy Ravi-ChandarUniversity of Texas at Austin1 University Station, C0600Austin, TX 78712-0235, USAe-mail: kravi@mail.utexas.edu

Guruswami RavichandranCalifornia Institute of TechnologyGraduate Aeronautical LaboratoriesPasadena, CA 91125, USAe-mail: ravi@caltech.edu

Robert E. RowlandsUniversity of WisconsinDepartment of Mechanical Engineering1415 Engineering DriveMadison, WI 53706, USAe-mail: rowlands@engr.wisc.edu

Taher SaifUniversity of Illinois at Urbana-ChampaignMicro and Nanotechnology Laboratory, 2101DMechanical Engineering Laboratory1206 West Green StreetUrbana, IL 61801, USAe-mail: saif@uiuc.edu

Wolfgang Steinchen (deceased)

XVI

Jeffrey C. SuhlingAuburn UniversityDepartment of Mechanical Engineering201 Ross HallAuburn, AL 36849-5341, USAe-mail: jsuhling@eng.auburn.edu

Michael A. SuttonUniversity of South CarolinaCenter for Mechanics, Materials and NDEDepartment of Mechanical Engineering300 South Main StreetColumbia, SC 29208, USAe-mail: sutton@sc.edu

Robert B. WatsonVishay Micro-MeasurementsSensors Engineering DepartmentRaleigh, NC, USAe-mail: bob.watson@vishay.com

Robert A. WinholtzUniversity of MissouriDepartment of Mechanical and AerospaceEngineeringE 3410 Lafferre HallColumbia, MO 65211, USAe-mail: winholtz@missouri.edu

XVII

Contents

List of Abbreviations ................................................................................. XXVII

Part A Solid Mechanics Topics

1 Analytical Mechanics of SolidsAlbert S. Kobayashi, Satya N. Atluri .......................................................... 31.1 Elementary Theories of Material Responses ..................................... 41.2 Boundary Value Problems in Elasticity ............................................ 111.3 Summary ...................................................................................... 14References .............................................................................................. 14

2 Materials Science for the Experimental MechanistCraig S. Hartley ........................................................................................ 172.1 Structure of Materials .................................................................... 172.2 Properties of Materials................................................................... 33References .............................................................................................. 47

3 Mechanics of Polymers: ViscoelasticityWolfgang G. Knauss, Igor Emri, Hongbing Lu............................................ 493.1 Historical Background .................................................................... 493.2 Linear Viscoelasticity ..................................................................... 513.3 Measurements and Methods .......................................................... 693.4 Nonlinearly Viscoelastic Material Characterization ........................... 843.5 Closing Remarks ............................................................................ 893.6 Recognizing Viscoelastic Solutions if the Elastic Solution is Known ... 90References .............................................................................................. 92

4 Composite MaterialsPeter G. Ifju ............................................................................................. 974.1 Strain Gage Applications ................................................................ 984.2 Material Property Testing ............................................................... 1024.3 Micromechanics ............................................................................ 1074.4 Interlaminar Testing ...................................................................... 1114.5 Textile Composite Materials ............................................................ 1144.6 Residual Stresses in Composites ..................................................... 1174.7 Future Challenges .......................................................................... 121References .............................................................................................. 121

5 Fracture MechanicsKrishnaswamy Ravi-Chandar ................................................................... 1255.1 Fracture Mechanics Based on Energy Balance ................................. 1265.2 Linearly Elastic Fracture Mechanics ................................................. 128

XVIII Contents

5.3 Elastic–Plastic Fracture Mechanics .................................................. 1325.4 Dynamic Fracture Mechanics .......................................................... 1375.5 Subcritical Crack Growth ................................................................ 1405.6 Experimental Methods ................................................................... 140References .............................................................................................. 156

6 Active MaterialsGuruswami Ravichandran........................................................................ 1596.1 Background .................................................................................. 1596.2 Piezoelectrics ................................................................................ 1616.3 Ferroelectrics ................................................................................ 1626.4 Ferromagnets ................................................................................ 166References .............................................................................................. 167

7 Biological Soft TissuesJay D. Humphrey ..................................................................................... 1697.1 Constitutive Formulations – Overview ............................................ 1717.2 Traditional Constitutive Relations ................................................... 1727.3 Growth and Remodeling – A New Frontier ...................................... 1787.4 Closure ......................................................................................... 1827.5 Further Reading ............................................................................ 182References .............................................................................................. 183

8 Electrochemomechanics of Ionic Polymer–Metal CompositesSia Nemat-Nasser .................................................................................... 1878.1 Microstructure and Actuation ......................................................... 1888.2 Stiffness Versus Solvation ............................................................... 1918.3 Voltage-Induced Cation Distribution .............................................. 1938.4 Nanomechanics of Actuation ......................................................... 1958.5 Experimental Verification .............................................................. 1978.6 Potential Applications ................................................................... 199References .............................................................................................. 199

9 A Brief Introduction to MEMS and NEMSWendy C. Crone ........................................................................................ 2039.1 Background .................................................................................. 2039.2 MEMS/NEMS Fabrication ................................................................. 2069.3 Common MEMS/NEMS Materials and Their Properties ....................... 2069.4 Bulk Micromachining versus Surface Micromachining ...................... 2139.5 Wafer Bonding .............................................................................. 2149.6 Soft Fabrication Techniques ........................................................... 2159.7 Experimental Mechanics Applied to MEMS/NEMS .............................. 2179.8 The Influence of Scale .................................................................... 2179.9 Mechanics Issues in MEMS/NEMS ..................................................... 2219.10 Conclusion .................................................................................... 224References .............................................................................................. 225

Contents XIX

10 Hybrid MethodsJames F. Doyle ......................................................................................... 22910.1 Basic Theory of Inverse Methods .................................................... 23110.2 Parameter Identification Problems ................................................. 23510.3 Force Identification Problems ........................................................ 24010.4 Some Nonlinear Force Identification Problems ................................ 24610.5 Discussion of Parameterizing the Unknowns ................................... 255References .............................................................................................. 257

11 Statistical Analysis of Experimental DataJames W. Dally ........................................................................................ 25911.1 Characterizing Statistical Distributions ............................................ 26011.2 Statistical Distribution Functions .................................................... 26311.3 Confidence Intervals for Predictions ............................................... 26711.4 Comparison of Means .................................................................... 27011.5 Statistical Safety Factor .................................................................. 27111.6 Statistical Conditioning of Data ...................................................... 27211.7 Regression Analysis ....................................................................... 27211.8 Chi-Square Testing ........................................................................ 27711.9 Error Propagation .......................................................................... 278References .............................................................................................. 279

Part B Contact Methods

12 Bonded Electrical Resistance Strain GagesRobert B. Watson ..................................................................................... 28312.1 Standardized Strain-Gage Test Methods ......................................... 28412.2 Strain and Its Measurement ........................................................... 28412.3 Strain-Gage Circuits....................................................................... 28512.4 The Bonded Foil Strain Gage .......................................................... 29112.5 Semiconductor Strain Gages ........................................................... 325References .............................................................................................. 332

13 ExtensometersIan McEnteggart ...................................................................................... 33513.1 General Characteristics of Extensometers ........................................ 33613.2 Transducer Types and Signal Conditioning ...................................... 33713.3 Ambient-Temperature Contacting Extensometers ............................ 33813.4 High-Temperature Contacting Extensometers ................................. 34113.5 Noncontact Extensometers ............................................................. 34313.6 Contacting versus Noncontacting Extensometers ............................. 34513.7 Conclusions ................................................................................... 346References .............................................................................................. 346

XX Contents

14 Optical Fiber Strain GagesChris S. Baldwin ...................................................................................... 34714.1 Optical Fiber Basics ........................................................................ 34814.2 General Fiber Optic Sensing Systems ............................................... 35114.3 Interferometry .............................................................................. 35414.4 Scattering ..................................................................................... 35914.5 Fiber Bragg Grating Sensors ........................................................... 36114.6 Applications of Fiber Optic Sensors ................................................. 36714.7 Summary ...................................................................................... 368References .............................................................................................. 369

15 Residual StressYuri F. Kudryavtsev .................................................................................. 37115.1 Importance of Residual Stress ........................................................ 37115.2 Residual Stress Measurement ......................................................... 37315.3 Residual Stress in Fatigue Analysis ................................................. 38115.4 Residual Stress Modification .......................................................... 38315.5 Summary ...................................................................................... 386References .............................................................................................. 386

16 Nanoindentation: Localized Probes of Mechanical Behaviorof MaterialsDavid F. Bahr, Dylan J. Morris .................................................................. 38916.1 Hardness Testing: Macroscopic Beginnings...................................... 38916.2 Extraction of Basic Materials Properties

from Instrumented Indentation ..................................................... 39216.3 Plastic Deformation at Indentations ............................................... 39616.4 Measurement of Fracture Using Indentation ................................... 39916.5 Probing Small Volumes

to Determine Fundamental Deformation Mechanisms ..................... 40216.6 Summary ...................................................................................... 404References .............................................................................................. 404

17 Atomic Force Microscopy in Solid MechanicsIoannis Chasiotis ..................................................................................... 40917.1 Tip–Sample Force Interactions in Scanning Force Microscopy ........... 41117.2 Instrumentation for Atomic Force Microscopy.................................. 41217.3 Imaging Modes by an Atomic Force Microscope ............................... 42317.4 Quantitative Measurements in Solid Mechanics with an AFM ........... 43217.5 Closing Remarks ............................................................................ 43817.6 Bibliography ................................................................................. 439References .............................................................................................. 440

Contents XXI

Part C Noncontact Methods

18 Basics of OpticsGary Cloud............................................................................................... 44718.1 Nature and Description of Light ..................................................... 44818.2 Interference of Light Waves ........................................................... 44918.3 Path Length and the Generic Interferometer ................................... 45118.4 Oblique Interference and Fringe Patterns ....................................... 45318.5 Classical Interferometry ................................................................. 45518.6 Colored Interferometry Fringes ....................................................... 46118.7 Optical Doppler Interferometry ....................................................... 46418.8 The Diffraction Problem and Examples ........................................... 46818.9 Complex Amplitude ....................................................................... 47018.10 Fraunhofer Solution of the Diffraction Problem ............................... 47218.11 Diffraction at a Clear Aperture ........................................................ 47418.12 Fourier Optical Processing .............................................................. 47618.13 Further Reading ............................................................................ 479References .............................................................................................. 479

19 Digital Image Processing for Optical MetrologyWolfgang Osten ....................................................................................... 48119.1 Basics of Digital Image Processing .................................................. 48319.2 Techniques for the Quantitative Evaluation of Image Data

in Optical Metrology ...................................................................... 48519.3 Techniques for the Qualitative Evaluation of Image Data

in Optical Metrology ...................................................................... 545References .............................................................................................. 557

20 Digital Image Correlation for Shapeand Deformation MeasurementsMichael A. Sutton .................................................................................... 56520.1 Background .................................................................................. 56620.2 Essential Concepts in Digital Image Correlation ............................... 56820.3 Pinhole Projection Imaging Model.................................................. 56920.4 Image Digitization ......................................................................... 57320.5 Intensity Interpolation .................................................................. 57320.6 Subset-Based Image Displacements ............................................... 57520.7 Pattern Development and Application ............................................ 57720.8 Two-Dimensional Image Correlation (2-D DIC) ................................. 57920.9 Three-Dimensional Digital Image Correlation .................................. 58120.10 Two-Dimensional Application:

Heterogeneous Material Property Measurements............................. 58520.11 Three-Dimensional Application:

Tension Torsion Loading of Flawed Specimen .................................. 58820.12 Three-Dimensional Measurements – Impact Tension Torsion

Loading of Single-Edge-Cracked Specimen ..................................... 59320.13 Closing Remarks ............................................................................ 597

XXII Contents

20.14 Further Reading ............................................................................ 597References .............................................................................................. 599

21 Geometric MoiréBongtae Han, Daniel Post ........................................................................ 60121.1 Basic Features of Moiré .................................................................. 60121.2 In-Plane Displacements ................................................................ 60721.3 Out-Of-Plane Displacements: Shadow Moiré .................................. 61121.4 Shadow Moiré Using the Nonzero Talbot Distance (SM-NT) ............... 61721.5 Increased Sensitivity ...................................................................... 623References .............................................................................................. 626

22 Moiré InterferometryDaniel Post, Bongtae Han ........................................................................ 62722.1 Current Practice ............................................................................. 63022.2 Important Concepts ....................................................................... 63422.3 Challenges .................................................................................... 64422.4 Characterization of Moiré Interferometry ........................................ 64522.5 Moiré Interferometry in the Microelectronics Industry ..................... 646References .............................................................................................. 652

23 Speckle MethodsYimin Gan, Wolfgang Steinchen (deceased)............................................... 65523.1 Laser Speckle ................................................................................ 65523.2 Speckle Metrology ......................................................................... 65823.3 Applications .................................................................................. 66823.4 Bibliography ................................................................................. 672References .............................................................................................. 672

24 HolographyRyszard J. Pryputniewicz .......................................................................... 67524.1 Historical Development.................................................................. 67624.2 Fundamentals of Holography ......................................................... 67724.3 Techniques of Hologram Interferometry.......................................... 67924.4 Representative Applications of Holography ..................................... 68524.5 Conclusions and Future Work ......................................................... 696References .............................................................................................. 697

25 PhotoelasticityKrishnamurthi Ramesh ............................................................................ 70125.1 Preliminaries ................................................................................ 70425.2 Transmission Photoelasticity .......................................................... 70525.3 Variants of Photoelasticity ............................................................. 71025.4 Digital Photoelasticity .................................................................... 71925.5 Fusion of Digital Photoelasticity Rapid Prototyping

and Finite Element Analysis ........................................................... 73225.6 Interpretation of Photoelasticity Results ......................................... 734

Contents XXIII

25.7 Stress Separation Techniques ......................................................... 73525.8 Closure ......................................................................................... 73725.9 Further Reading ............................................................................ 73725.A Appendix ...................................................................................... 738References .............................................................................................. 740

26 Thermoelastic Stress AnalysisRichard J. Greene, Eann A. Patterson, Robert E. Rowlands ......................... 74326.1 History and Theoretical Foundations .............................................. 74426.2 Equipment .................................................................................... 74526.3 Test Materials and Methods ........................................................... 74726.4 Calibration .................................................................................... 74926.5 Experimental Considerations.......................................................... 74926.6 Applications .................................................................................. 75326.7 Summary ...................................................................................... 75926.A Analytical Foundation of Thermoelastic Stress Analysis .................... 76026.B List of Symbols .............................................................................. 762References .............................................................................................. 763

27 Photoacoustic Characterization of MaterialsSridhar Krishnaswamy ............................................................................. 76927.1 Elastic Wave Propagation in Solids ................................................. 77027.2 Photoacoustic Generation .............................................................. 77727.3 Optical Detection of Ultrasound ...................................................... 78327.4 Applications of Photoacoustics ....................................................... 78927.5 Closing Remarks ............................................................................ 798References .............................................................................................. 798

28 X-Ray Stress AnalysisJonathan D. Almer, Robert A. Winholtz ..................................................... 80128.1 Relevant Properties of X-Rays ........................................................ 80228.2 Methodology ................................................................................. 80428.3 Micromechanics of Multiphase Materials ........................................ 80728.4 Instrumentation ............................................................................ 80928.5 Experimental Uncertainties ............................................................ 81028.6 Case Studies .................................................................................. 81328.7 Summary ...................................................................................... 81728.8 Further Reading ............................................................................ 818References .............................................................................................. 818

Part D Applications

29 Optical MethodsArchie A.T. Andonian ............................................................................... 82329.1 Photoelasticity .............................................................................. 82429.2 Electronic Speckle Pattern Interferometry ....................................... 828

XXIV Contents

29.3 Shearography and Digital Shearography ......................................... 83029.4 Point Laser Triangulation ............................................................... 83129.5 Digital Image Correlation ............................................................... 83229.6 Laser Doppler Vibrometry ............................................................... 83429.7 Closing Remarks ............................................................................ 83529.8 Further Reading ............................................................................ 836References .............................................................................................. 836

30 Mechanical Testing at the Micro/NanoscaleM. Amanul Haque, Taher Saif ................................................................... 83930.1 Evolution of Micro/Nanomechanical Testing .................................... 84030.2 Novel Materials and Challenges ...................................................... 84130.3 Micro/Nanomechanical Testing Techniques ..................................... 84230.4 Biomaterial Testing Techniques ...................................................... 85630.5 Discussions and Future Directions .................................................. 85930.6 Further Reading ............................................................................ 862References .............................................................................................. 862

31 Experimental Methods in Biological Tissue TestingStephen M. Belkoff, Roger C. Haut ............................................................ 87131.1 General Precautions ...................................................................... 87131.2 Connective Tissue Overview ............................................................ 87231.3 Experimental Methods on Ligaments and Tendons .......................... 87331.4 Experimental Methods in the Mechanical Testing

of Articular Cartilage ...................................................................... 87631.5 Bone ............................................................................................ 87831.6 Skin Testing .................................................................................. 883References .............................................................................................. 884

32 Implantable Biomedical Devicesand Biologically Inspired MaterialsHugh Bruck ............................................................................................. 89132.1 Overview....................................................................................... 89232.2 Implantable Biomedical Devices..................................................... 89932.3 Biologically Inspired Materials and Systems .................................... 90932.4 Conclusions ................................................................................... 92332.5 Further Reading ............................................................................ 924References .............................................................................................. 924

33 High Rates and Impact ExperimentsKaliat T. Ramesh...................................................................................... 92933.1 High Strain Rate Experiments ......................................................... 93033.2 Wave Propagation Experiments ...................................................... 94533.3 Taylor Impact Experiments ............................................................. 94933.4 Dynamic Failure Experiments ......................................................... 94933.5 Further Reading ............................................................................ 953References .............................................................................................. 954

Contents XXV

34 Delamination MechanicsKenneth M. Liechti ................................................................................... 96134.1 Theoretical Background ................................................................. 96234.2 Delamination Phenomena ............................................................. 96834.3 Conclusions ................................................................................... 980References .............................................................................................. 980

35 Structural Testing ApplicationsAshok Kumar Ghosh................................................................................. 98535.1 Past, Present, and Future of Structural Testing ................................ 98735.2 Management Approach to Structural Testing ................................... 99035.3 Case Studies .................................................................................. 99735.4 Future Trends ................................................................................ 1012References .............................................................................................. 1013

36 Electronic Packaging ApplicationsJeffrey C. Suhling, Pradeep Lall ................................................................. 101536.1 Electronic Packaging ...................................................................... 101736.2 Experimental Mechanics in the Field of Electronic Packaging ........... 101936.3 Detection of Delaminations ........................................................... 102236.4 Stress Measurements in Silicon Chips and Wafers ............................ 102436.5 Solder Joint Deformations and Strains ............................................ 103136.6 Warpage and Flatness Measurements

for Substrates, Components, and MEMS .......................................... 103636.7 Transient Behavior of Electronics During Shock/Drop ....................... 103936.8 Mechanical Characterization of Packaging Materials ........................ 1041References .............................................................................................. 1042

Acknowledgements ................................................................................... 1045About the Authors ..................................................................................... 1049Detailed Contents ...................................................................................... 1059Subject Index ............................................................................................. 1083

XXVII

List of Abbreviations

A

AASHTO Association of State HighwayTransportation Officials

ABS American Bureau of ShippingACES analytical, computational, and

experimental solutionAC alternating currentAFM atomic force microscopyAFNOR Association Française de NationalAISC American Institute of Steel ConstructionALT accelerated lift testingAREA American Railway Engineering

AssociationASTM American Society for Testing and

Materials

B

bcc body-centered cubicBGA ball grid arrayBHN Brinell hardness numberBIL boundary, initial, and loadingBSI British Standards InstituteBS beam-splitterBrUTS bromoundecyltrichlorosilane

C

CAD computer-aided designCAE computer-aided engineeringCAM computer-aided manufacturingCAR collision avoidance radarCBGA ceramic ball grid arrayCCD charge-coupled deviceCCS camera coordinate systemCDC Centers for Disease ControlCD compact discCGS coherent gradient sensingCHS coefficient of hygroscopic swellingCMC ceramic matrix compositeCMM coordinate measuring machineCMOS complementary

metal–oxide-semiconductorCMP chemical–mechanical polishingCMTD composite materials technical divisionCNC computer numerical controlCNT carbon nanotubeCOD crack opening displacementCOI crack opening interferometryCP conductive polymer

CSK cytoskeletonCSM continuous stiffness moduleCTE coefficient of thermal expansionCTOD crack-tip opening displacementCVD chemical vapor depositionCVFE cohesive-volumetric finite elementsCW continuous waveCZM cohesive zone model

D

DBS directional beam-splitterDCB double-cantilever beamDCPD dicyclopentadieneDC direct currentDEC diffraction elastic constantDGL Devonshire–Ginzburg–LandauDIC digital image correlationDIN Deutsches Institut für NormungDMA dynamical mechanical analyzersDMD digital micromirror deviceDMT Derjaguin–Muller–ToporovDNP distance from the neutral pointDPH diamond pyramid hardnessDPN dip-pen nanolithographyDPV Doppler picture velocimetryDRIE deep reactive-ion etchingDR deviation ratioDSC digital speckle correlationDSPI digital speckle-pattern interferometryDSPSI digital speckle-pattern shearing

interferometryDSP digital speckle photographyDTA differential thermal analyzerDTS distributed temperature sensingDTS dodecyltrichlorosilane

E

EAP electroactive polymerECM extracellular matrixECO poly(ethylene carbon monoxide)

copolymerEDM electric-discharge machiningEDP ethylenediamine pyrochatecholEFM electrostatic force microscopyEFPI extrinsic Fabry–Pérot interferometerEMI electromagnetic interferenceENF end-notched flexureEPFM elastic–plastic fracture mechanicsEPL electron-beam projection lithography

XXVIII List of Abbreviations

ESIS European Structural Integrity SocietyESPI electronic speckle pattern interferometryESSP electrostatically stricted polymerES expert systemET emerging technologiesEW equivalent weightEXAFS extended x-ray absorption fine structure

F

FAC focal adhesion complexFBGA fine-pitch ball grid arrayFBG fiber Bragg gratingFC-BGA flip-chip ball grid arrayfcc face-centered cubicFC-PBGA flip-chip plastic ball grid arrayFDA Food and Drug AdministrationFEM finite element modelingFE finite elementFFT fast Fourier transformFFV full field of viewFGM functionally graded materialFIB focused ion beamFMM force modulation microscopyFMT Fillers–Moonan–TschoeglFM frequency modulationFSW friction stir weldsFTE Fourier-transform methodFoV field of view

G

GF growth factorGMR giant magnetoresistanceGPS global positioning sensingGRP glass-reinforced plasticGUM Guide for the Expression of Uncertainty

in MeasurementG&R growth and remodeling

H

HAZ heat-affected zonehcp hexagonal close-packedHDI high-density interconnectHEMA 2-hydroxyethyl methacrylateHFP half-fringe photoelasticityHNDE holographic nondestructive evaluationHRR Hutchinson–Rice–RosengreenHSRPS high strain rate pressure shearHTS high-temperature storage

I

IBC International Building CodeIC integrated circuits

IEC ion exchange capacityIFM interfacial force microscopeIMU inertial measurement unitIPG ionic polymer gelIPMC ionomeric polymer–metal compositeIP image processingIR-GFP infrared grey-field polariscopeISDG interferometric strain/displacement gageISO International Organization for

StandardizationISTS impulsive stimulated thermal scatteringIT interferometer

J

JIS Japanese Industrial Standards

L

LAN local area networkLASIK laser-based corneal reshapingLCE liquid crystal elastomerLDV laser Doppler vibrometryLED light-emitting diodeLEFM linear elastic fracture mechanicsLFM lateral-force AFMLIGA lithography galvanoforming moldingLMO long-working-distance microscopeLORD laser occlusive radius detectorLPCVD low-pressure CVDLPG long-period gratingLVDT linear variable differential transformerLVDT linear variable displacement transducer

M

MBS model-based simulationMEMS micro-electromechanical systemMFM magnetic force microscopymicro-CAT micro computerized axial tomographyMITI Ministry of International Trade and

IndustryMLF metal leadframe packageMMC metal matrix compositesMOEMS microoptoelectromechanical systemsMOSFET metal-oxide semiconductor field-effect

transistorMO microscope objectiveM-TIR modified total internal reflectionμPIV microparticle image velocimetryMPB morphotropic phase boundaryMPCS most probable characteristics strengthMPODM multipoint overdeterministic methodMW(C)NT multiwalled (carbon) nanotubes

List of Abbreviations XXIX

N

NA numerical apertureNC-AFM noncontact AFMNCOD normal crack opening displacementNC nanocrystallineNDE nondestructive evaluationNDT/NDE nondestructive testing/evaluationNEMS nanoelectromechanical systemNEPA National Environmental Policy ActNHDP The National Highways Development

ProjectNIST National Institute of Standard and

TechnologyNMR nuclear magnetic resonanceNSF National Science FoundationNSOM near-field scanning optical microscopyNVI normal velocity interferometer

O

O/DFM optical/digital fringe multiplicationOCS object coordinate systemODF orientation distribution functionOEH optoelectronic holographyOELIM optoelectronic laser interferometric

microscopeOFDR optical frequency-domain reflectometryOIML Organisation Internationale de

Metrologie LegaleOIM orientation imaging microscopyOMC organic matrix compositesONDT optical nondestructive testingOPD optical path differenceOPS operations per secondOSHA Occupational Safety and Health

Administration

P

PBG photonic-bandgapPBS phosphate-buffered salinePCB printed circuit boardPCF photonic-crystal fiberPDMS polydimethylsiloxanePECVD plasma-enhanced CVDPE pulse-echoPID proportional-integral-derivativePIN p-type intrinsic n-typePIV particle image velocimetryPLA polylactic acidPLD path length differencePLZT Pb(La,Zr,Ti)O3PL path lengthPM fiber polarization maintaining fiberPMC polymer matrix composites

PMI phase-measurement interferometryPMMA polymethyl methacrylatePMN Pb(MgxNb1−x )O3PM polarization maintainingPM power meterPQFP plastic quad flat packagePRC photorefractive crystalPSF point spread functionPST phase shifting techniquePTH plated-through holesPVC polyvinyl chloridePVDF polyvinylidene fluoridePVD physical vapor depositionPVS phase velocity scanningPZT Pb(Zr,Ti)O3

Q

QC quality-controlQFP quad flat packQLV quasilinear viscoelastic theory

R

RCC reinforced cement concreteRCRA Resource Conservation and Recovery ActRF radiofrequencyRIBS replamineform inspired bone structuresRMS root-mean-squareRPT regularized phase trackingRSG resistance strain gageRSM residual stress managementRS residual stressRVE representative volume elementR&D research and development

S

S-T-C self-temperature compensationS/N signal to noiseSAC Sn–Ag–CuSAM scanning acoustic microscopySAM self-assembled monolayerSAR synthetic-aperture radarSAW surface acoustic waveSCF stress concentration factorSCS sensor coordinate systemSC speckle correlationSDF structure data filesSD standard deviationSEM scanning electron microscopySEM Society for Experimental MechanicsSHPB split-Hopkinson pressure barSIF stress intensity factorSI speckle interferometrySLC surface laminar circuit

XXX List of Abbreviations

SLL surface laminar layerSMA shape-memory alloySNL Sandia National LaboratoriesSNR signal-to-noise ratioSOI silicon on insulatorSOTA state-of-the-artSPATE stress pattern analysis by thermal

emissionsSPB space–bandwidth productSPM scanning probe microscopeSPSI speckle pattern shearing

interferometrySPS spatial phase shiftingSP speckle photographySQUID superconducting quantum interface

deviceSRM sensitivity response methodSSM sacrificial surface micromachiningSTC self-temperature compensatedSTM scanning tunneling microscopeSThM scanning thermal microscopyST structural testSW(C)NT single-walled (carbon) nanotubes

T

TBC thermal barrier coatingsTCE temperature coefficient of expansionTCR temperature coefficient of resistanceTDI transverse displacement interferometerTDM time division multiplexingTEC thermoelectric coolerTEM transmission electron microscopyTERSA thermal evaluation for residual stress

analysisTFE tetrafluoroethylene

TIG tungsten inert gasTIM thermal interface materialsTIR total internal reflectionTMAH tetramethylammonium hydroxideTM thermomechanicalTPS temporal phase shiftingTSA thermoelastic stress analysisTS through scanTWSME two-way shape memory effectTerfenol-D Tb0.3Dy0.7Fe2TrFE trifluoroethylene

U

UCC ultrasonic computerized complexUDL uniformly distributed loadUHV ultrahigh vacuumULE ultralow expansion

UP ultrasonic peening

V

VCCT virtual crack closure techniqueVDA video dimension analysisVISAR velocity interferometer system for any

reflectorVLE vector loop equations

W

WCS world coordinate systemWDM wavelength-domain multiplexingWFT windowed Fourier transformWLF Williams–Landel–FerryWM wavelength meterWTC World Trade Center