University of California, Berkeley

Lab3: Monotonic Tensile Loading

Andrew Mikhail, Eric Ocegueda, Felix Yoon, Lauren Farrell, Scout Heid, Xinyu Bian

Date Submitted: September 28, 2015

Date Performed: September 21, 2015

Lab Section: Lab 101 Monday 8-10 am

Lab GSI: Sayna Ebrahimi

Abstract

This laboratory assignment explores the measurement of the mechanical properties of materials

when subjected to monotonic loading (tensile) tests and provides opportunity to analyze and com-

pare the mechanical properties of 6061 Al and 1045 steel. Both test materials were tested as

standard ASTM tensile specimens (dog-bone shape). Using an Instron, the specimens were sub-

jected to tensile load while data on load applied and material elongation was captured via the

Instron and, for a subset of tests, via an extensometer (for greater accuracy). Critical results in-

clude lower elastic moduli for Al relative to steel; generally lower stress and strain values for Al

relative to steel (with the exception of yield strain); and lower strain energies for Al relative to

steel. This information indicates that steel is a stronger and tougher material; it also identified the

presence of a double yield point for steel due to the formation of slip bands.

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1 Introduction

The purpose of this experiment is to analyze and compare mechanical properties of 6061 Al alloy

and AISI 1045 steel. The properties of both materials are analyzed using engineering and true

stress-strain curves obtained from placing the materials under monotonic tensile loading – an axial

tensile load increasing linearly [1]. Engineering stress and strain use the geometry of the specimen

at the start of loading (initial area and length) while true stress and strain use the geometry at

the instant analysed (current area and current length) [1]. These curves offer information on the:

elastic modulus, yield stress under tension, ultimate stress under tension, elongation of fracture

under tension of both materials, and strain energy density. The elastic modulus is obtained by

determining the slope of elastic (reversible) deformation region from the graphs, the yield stress is

the value of the stress at the moment elastic deformation stops and plastic (irreversible) deformation

begins, ultimate stress is the highest value on the stress strain curve, and elongation of fracture is

the strain at the point of fracture (the rightmost point on the curve). The strain energy density

is a way of describing a material’s ductility; strain energy is determined by integrating the true

stress-strain curve.

The importance of obtaining comparative data on mechanical properties of these materials lies in

failure analysis and design. When designing a machine or structure, a lot of time is put into selecting

the appropriate material that can withstand the predicted loading without excessive fracturing or

deformation. In order to properly determine which material to use, the mechanical properties of

the material, including the elastic modulus, yield stress, and ultimate stress, play a major role in

the mechanical integrity and failure points a designer needs to account for. From these properties,

materials are compared on their effectiveness along with other parameters such as weight, cost,

and manufacturing time. Although many properties determined in this experiment are required in

the design analysis of structures and machines, more properties are often needed. Therefore, the

limitations in the data obtained lies in not knowing other mechanical properties of the materials in

other loadings – for example: ultimate and yield stress under compression and cyclic loading (either

compression or tension). In order to obtain these other properties, further testing is necessary, such

as monotonic compression loading and cyclic loading.

2 Theory

The experiment will focus on analyzing data on stress-strain curves and determining different

properties from the data. For this, an understanding of stress-strain curves, differences between en-

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gineering and true stress-strain, and ways of calculating certain mechanical properties are required.

Firstly, the parts of a stress-strain graph are: elastic region. yield point, and plastic region - which

includes strain hardening region, ultimate stress point, necking region, and fracture point. The

elastic region is the linear portion of the stress-strain curve and occurs when bonds stretch within

the material, which means the deformation is reversible [1] [2]. The yield point is the point where

elastic deformation ends and plastic deformation begins. Plastic deformation is when the curve is

no longer linear and signifies the breaking and reformation of bonds which means the deformation

is irreversible [2]. The ultimate stress point is the highest stress the specimen is placed in [2]. The

strain hardening region is between the yield point and the ultimate stress point [2]. The necking

region is after the ultimate stress point until fracture, during this region the area of the specimen

begins to decrease [2]. The final region, the fracture point, is the point when the specimen fractures

[2].

Secondly, the data determined from this experiment is engineering stress and strain not true stress

and strain. Engineering stress is defined as the normal force over the initial area it is acting on:

σ = PA 0

where P is measured in Newtons, A0 in meters,and in Pascals; engineering strain is defined

as the change in length from the initial length over the initial length: ε = l−l010 where l and l0 are

measured in millimeters and ε in mmmm [1]. The true strain on the other hand uses the area at the

instant the load is applied: σ = PA and the true strain use the change in length between to points

on the graph rather than the initial length: ε =∫ ll0ln( ll0 [1]. Both the true strain and stress can be

calculated from their engineering counterparts: σ = (1 + ε) and ε = ln(1 + ε) which will be used

to determine true stress-strain curves from experimental data [1].

Lastly, many properties typically calculated for materials are: elastic modulus, yield strength,

ultimate tensile strength, strength and strain at fracture, total strain at necking, strain energy

at fracture, percent reduction in area at both necking and fracture. The first property, elastic

modulus, is the constant of proportionality during the elastic region and signifies the stiffness of

a material [2]. Soft and ductile material typically have small E values since they deform easily,

while hard and brittle material have large E values since they resist deformation. The next value

is the yield strength, which is the value of stress where plastic deformation begins [2]. Ultimate

tensile strength is found on the engineering stress-strain curve as the highest point on the graph [2].

The strength and strain at fracture are values of the stress and strain at the instant the specimen

fractures (final point on graph) [2]. Total strain at necking is the strain that occurs up to the

start of necking: εn = lu−l0l0

where lu is the length at ultimate stress. Ductile materials have large

necking strain, while brittle materials have small necking due to their resistance to stretching. The

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strain energy density is the area under the true stress-strain curve and is useful for determining

ductility of materials; the value at fracture is used with the assumption that εf >> εY : uf ≈σf εfn+1

where n ≈ εu (strain hardening exponent) and uf is measured in Pa [1]. A higher strain energy

indicates a more ductile material (since there will be more area under the curve), while a lower

strain energy indicates a more brittle material (since there will be less plastic deformation). The

percent reduction in area is the change in area over the initial: %RA = A0−AA0

[1]. The larger a

percent reduction of area the more ductile a material is since it easily deformed.

3 Experimental Procedure

3.1 Experimental Instrumentation

In order to test the tensile strength of the two materials given to us, we used the instruments

described in Appendix A-1. The primary tool used was the Instron series 5500 Twin Column

Table Top Model, located in 70 Hesse. The Instron device samples data at 40kHz and has a point

measurement accuracy of ±0.02 mm, or 0.05% of displacement. Further detailed specifications can

be found in can be found in the 5500 Instron machine manual [3]. We also used the corresponding

control panel for inputting and generating data, and an Accuracy Class 0.5 extensometer to measure

the elongation of the specimen [3].

Table 1: Table of the Specimen and some details about them.

3.2 Experimental Procedure

We began by measuring and recording the initial dimensions of the tensile test specimen. Some of

the dimensions varied, but the difference was very small. The dimensions of each test specimen can

be found in Table 1. Since the Instron machine was already on, we moved on to open the Instron

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software in the control computer. We went to save ”File → Open method” and loaded the tensile

test program ”ME108 Tensile Test.mtM”. Then we set all the parameters required by the software,

including specimen dimensions, loading speed (elongation rate), etc. When finished, we went to

”OK → Run method” to return to the data acquisition interface. We pressed the ”Return” button

on the Instron control panel next to the machine to bring the fixture to the original position. Next,

we loaded the tensile specimen and clamped it tightly with the fixture, and zeroed the load and

the strain on the machine control panel. For specimens 1, 3, and 5 we pressed Start on the control

panel to start the tensile test and monitored the load and strain data output until fracture. For

specimens 2, 4,and 6 we attached the extensometer before pressing ”Start” and measured specimen

elongation until the hardening region in order to avoid the inaccurate data that occurs during

necking. After saving the raw data file that is generated into our own folder through ”File → Data

→ End & Save,” we carefully removed the fractured specimen and moved onto the next specimen.

4 Results

We measured load and extension for samples with and without an extensometer. Those without an

extensometer were loaded until break, while samples measured with an extensometer were loaded

to a strain of 10% to avoid damage to the sensor. True stress and true strain values were calculated

from the measured values using the equations σ = σ(1+ε) and ε = ln(1+ε) respectively. Results of

the tensile loading tests are graphed and tabulated in Figures 1-7 and Table 2. Figures 5-7 show

the stress and strain points of each material at yield, necking, and fracture. A best-fit trendline

was used in the elastic region of each response to find the elastic modulus, E, which is equal to

the slope in the region. Yield values were determined using an offset yield strength by finding

the intersection of the stress-strain response and a line with slope E passing through 0.2% strain.

Strain energy density (uf ) is also shown as the area under the true stress vs. true strain curve.

Strain energy density was calculated using the equation uf ≈(σf )(εf )n+1 and %RA was calculated

using %RA = A0−AA0

. Area at fracture (A) was found using the true strain value equation ε = lnA0A .

Both uf and %RA are tabulated in Table 2.

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Table 2: Calculated stress and strain values indicated on Figures 5-7

5 Discussion

Using these results, we can compare the mechanical properties of 6061 Al loaded with different

elongation rates as well as compare the properties of 1045 steel to 6061 Al. For the former compar-

ison, the data from Figure 1 and Figure 2 show no significant difference in mechanical properties

between 3mm/min elongation and 6mm/min elongation, suggesting 6061 Al does not exhibit strain

rate sensitivity in this range. From Figure 4 and Table 2, we can see the response of 6061 Al

compared to steel is weaker and less ductile, indicating 1045 steel is the stronger and tougher ma-

terial. 1045 Steel also shows an interesting characteristic not seen in 6061 Al. Around 4% strain,

1045 steel exhibits a double yield point, a phenomena common in low carbon steels. This is due

to the formation of Luder bands, which are localized bands of deformation caused by strain lo-

calization from alloys carbon. At the upper yield point, the formation of these bands begins, and

because carbon can diffuse relatively easily through the steel, there is a load drop and burst of

plastic strain at a constant applied load as the bands fully propagate [4]. This behavior is not seen

in 6061 Al because conventional work hardening prevents dislocation/strain localization. We also

noticed the steel samples were warmer after fracture than the Al samples. As the tougher material,

steel has higher stored energy, which was released upon fracture as heat. Figures 1-3 also show

a difference in strain measurement between data taken from Instron and from the extensometer.

The extensometer was able to take very accurate elongation data from the area of interest in the

sample. The Instron measured elongation of the entire sample, which introduces more error to the

measurements since there may have been some slip between the sample and Instron vice fixture as

well as some deformation of the material not in the section of interest, adding to the overall strain

of the measured data.

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6 Conclusion

Based on the values of stress and strain for yield, ultimate, and fracture points on the stress-strain

curve created using the Instron’s data output, this lab demonstrates the toughness of (1045) steel

relative to (6065) aluminum. While there is a slight dip in the yield strain associated with the

steel samples, this is due to the carbon composition of steel and the resulting slip bands; overall,

the steel samples had a higher elastic modulus and also required more strain energy to fracture.

This lab also identifies the importance of measurement tools in determining the accuracy of results:

usage of a more precise tool – i.e. the extensometer – yielded appreciably distinct results indicating

a lesser degree of precision in using ”just” the Instron.

7 References

1. Kyriakos Komvopoulos, Mechanical Testing of Engineering Materials. (San Diego, CA:

Cognella Academic Publishing, 2010).

2. N. E. Dowling, Mechanical Behavior of Materials: Engineering Methods for Deformation,

Fracture, and Fatigue. (Upper Saddle River, NJ: Prentice Hall, 2012).

3. Instron, 5500 Series: Advanced materials testing systems brochure. (INTERNET, 2007).

4. Plane Stress. Universtiy of Cambridge DoITPoMS [Internet]. Creative Commons: UK, 2015

[cited 2015 September 26] Available from: http://www.doitpoms.ac.uk/tlplib/metal-forming-

3/plane stress.php

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8 Appendix

8.1 Appendix A: Instrumentation

Appendix A-1: Photographs of tensile testing machine and important components: (A) Instron

machine, (B) control system, (C) safety grip, (D) fi xture, (E) control panel, (F) emergency stop,

(G) extensometer, and (H) load cell.[1]

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8.2 Appendix B: Figures depicting lab results

Figure 1: True stress vs. true strain and engineering stress vs. engineering strain responses for

6061 Al alloy for an elongation rate of 3mm/min obtained with and without and extensometer.

Figure 2: True stress vs. true strain and engineering stress vs. engineering strain responses for

6061 Al alloy for an elongation rate of 6mm/min obtained with and without and extensometer.

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Figure 3: True stress vs. true strain and engineering stress vs. engineering strain responses for

1045 steel for an elongation rate of 6mm/min obtained with and without and extensometer.

Figure 4: Comparison of engineering stress-strain curves of 1045 steel and 6061 Al for an

elongation rate of 6mm/min obtained with and without and extensometer.

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Figure 5: Critical values of the stress-strain response of 6061 Al loaded until fracture for an

elongation rate of 3mm/min

Figure 6: Critical values of the stress-strain response of 6061 Al loaded until fracture for an

elongation rate of 6mm/min

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Figure 7: Critical values of the stress-strain response of 1045 steel loaded until fracture for an

elongation rate of 6mm/min

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