Tensile testing-laboratory

1
Tensile Testing Laboratory
By
Stephan Favilla
0723668
ME 354 AC
Date of Lab Report Submission: February 11th
2010
Date of Lab Exercise: January 28th
2010

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Executive Summary
Tensile tests are fundamental for understanding properties of different materials, and how
they will behave under load. This lab tested four different materials, including A-36 hot
rolled steel, 6061-T6 Aluminum, polycarbonate, and polymethylmethacrylate (PMMA).
Each material was tested three times using an Instron load frame and the BlueHill data
acquisition software. The data from each test was used to determine valuable material
properties such as ultimate tensile strength, modulus of elasticity, and yield strength.
Other calculated properties included true fracture strength, percent reduction of area, and
percent elongation. These material properties were used for comparing the materials to
each other, and to define the material as brittle or ductile.
The true stress and true strain were calculated for one sample of 6061-T6 aluminum to
show the difference between the engineering stress and strain, and the true values. The
engineering stress is an assumption that uses the initial area of the cross section, ignoring
the effects of transverse strain and the changing cross section. This assumption results in
the drop of the engineering stress-strain curve after the ultimate tensile strength, where
necking occurs.
Using the values of the true strain, the true plastic strain was determined for one sample
of Aluminum (Sample #2) by subtracting the contribution of the true elastic strain, as
outlined in Appendix E. Plotting the logarithm of the true stress versus the logarithm of
the true plastic strain allowed the plastic portion of the true stress-strain curve to be
modeled by the Ramberg-Osgood model, as detailed in Appendix F. While the model did
poorly at low plastic strains near yielding, it did an excellent job just before necking and
the ultimate tensile strain.
The results of the tensile tests showed that the A-36 hot rolled steel was the strongest
material. It had the highest ultimate tensile strength (527.9 MPa), the greatest modulus of
toughness (174.6 MPa), and the largest true fracture strength (1047 MPa). The 6061-T6
aluminum had a higher yield (356.3 MPa) than the steel (355.6), but a lower ultimate
tensile strength (374.9 MPa) and true fracture strength (571.8 MPa) due to tempering and
precipitation hardening. All of the materials besides the PMMA proved to be ductile,
especially the polycarbonate, which had a percent elongation of 82.2% The PMMA
samples averaged a percent elongation of only 0.7333%.

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A. Introduction
Tensile testing is one of the most fundamental tests for engineering, and provides
valuable information about a material and its associated properties. These properties can
be used for design and analysis of engineering structures, and for developing new
materials that better suit a specified use.
The tensile testing laboratory was conducted using an Instron load frame and the BlueHill
data acquisition software. Four different materials were tested, including 6061-T6
Aluminum Alloy, A-36 hot rolled steel, polymethylmethacrylate (PMMA, cast acrylic),
and polycarbonate. The samples were cylindrical in cross section, with a reduced gage
section. The reduced gage section ensured that the highest stresses occurred within the
gage, and not near the grips of the Instron load frame, preventing strain and fracture of
the specimen near or in the grips. The reduced gage section of each specimen was about
12.7 mm (0.5 inches). The samples were already machined to the proper dimensions
required for the test, according to ASTM standards.
Three samples of each material were tested in the Instron load frame, and the data
gathered into an Excel spreadsheet. The data was used to calculate various properties of
each material, including the elastic modulus, yield strength, ultimate tensile strength. The
data was then plotted on engineering stress-strain curves to compare the samples. The
purpose of this experiment was to gather information about each material so that
important mechanical properties could be determined. This experiment also familiarized
the students with the Instron load frame, BlueHill data acquisition software, and the
general steps to performing a tensile test on a reduced gage section specimen. The data
used for this lab report was not gathered from the student run experiments, but rather
from standardized testing performed by the laboratory professor, to ensure accurate and
consistent results.

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B. Procedure
Each specimen was measured with the calipers to determine the diameter of the cross
section. A gage length was determined (typically 50.00 mm) and scribed into the
specimen so that the distance between the two marks could be measured after the tensile
test was completed. A typical reduced gage section specimen is shown in Figure 1, on the
following page. The BlueHill data acquisition software was started, and the correct
material was chosen. The load cell was zeroed to ensure that the software only measured
the tensile load applied to the specimen.
The specimen was loaded into the jaws of the Instron load frame so that it was equally
spaced between the two clamps. The axial and transverse extensometers were attached to
the reduced gage section of the specimen, ensuring that the axial extensometer was set
correctly when attaching it to the gage and that the transverse extensometer was across
the complete diameter of the specimen. This precaution results in better data and prevents
damage to the extensometers.
The Instron load frame, shown in Figure 2 on the following page, was preloaded using
the scroll wheel to ensure that the specimen was properly loaded in the frame, and that it
wasn’t slipping in the jaws. The load was released, and the extensometers were zeroed
using the software. The test was started, and the specimen was loaded, resulting in a
measureable strain. For the steel and aluminum samples, the crosshead was initially set to
move upward at 1.27 mm/min, then at 15 mm/min at a specified state beyond yielding.
This increase in the rate of strain sped up the test, but may have also introduced some
error. The polycarbonate sample started at 5 mm/min and was later sped up to 30
mm/min. The PMMA samples were pulled at a constant rate of 10 mm/min.
The data was gathered using the software, and loaded into a spreadsheet. At a set value of
strain (past the yield strain), the software stopped using data from the extensometers, and
started gathering the strain information using the position of the moving crosshead. A
warning message came up on the computer screen, instructing the operator to remove the

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extensometers to prevent damage. The test continued until fracture, where the software
stopped the moving crosshead, and finished gathering data. The specimen was removed,
and the crosshead was reset to the initial position to start another tensile test. The testing
procedure was repeated for the rest of the specimens.
Figure 1: A reduced gage section specimen made from 6061-T6 aluminum, ready for tensile
testing.
Figure 2: A typical Instron load frame used for tensile testing.

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C. Results
C.1 Engineering Stress and Engineering Strain
The data from the tensile tests was plotted on separate graphs according to material. Each
graph shows the engineering stress versus the engineering strain, as calculated per
Appendix A. Figure 3 shows the three tests for the A-36 hot rolled steel samples, and
Figure 4 shows the three tensile tests of the 6061-T6 aluminum samples. Figure 5 and
Figure 6 show the test results of the polycarbonate and the PMMA, respectively.
Figure 3: The engineering stress versus the engineering strain for A-36 steel.
Figure 4: The engineering stress versus the engineering strain for 6061-T6 aluminum.
0
100
200
300
400
500
600
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Stress(MPa)
Strain (m/m)
Steel 1
Steel 2
Steel 3
0
50
100
150
200
250
300
350
400
0 0.03 0.06 0.09 0.12 0.15 0.18 0.21
Stress(MPa)
Strain (m/m)
Aluminum 1
Aluminum 2
Aluminum 3

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Figure 5: The engineering stress versus the engineering strain for polycarbonate.
Figure 6: The engineering stress versus the engineering strain for PMMA.
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Stress(MPa)
Strain (m/m)
Polycarbonate 1
Polycarbonate 2
Polycarbonate 3
0
10
20
30
40
50
60
70
80
90
0 0.01 0.02 0.03 0.04 0.05 0.06
Stress(MPa)
Strain (m/m)
PMMA 1
PMMA 2
PMMA 3

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C.2 Material Properties
The ultimate tensile strength for each material is listed in Table 1. The value of the
ultimate tensile strength was found using the process in Appendix B. The strain
corresponding to the ultimate tensile strength is where necking begins to occur.
Table 1: The ultimate tensile strength for the four materials.
Sample
Material
Ultimate Tensile
Strength, (MPa)
Standard Deviation,
StDev (MPa)
A-36 Steel 527.9 1.161
6061-T6 374.9 2.218
Polycarbonate 59.18 0.3217
PMMA 77.62 2.606
The modulus of elasticity and the yield strengths were calculated for steel and aluminum.
The corresponding standard deviations for both values were also calculated using the
procedure outlined in Appendix B. All of these values are shown in Table 2.
Table 2: The modulus of elasticity, yield strength, and standard deviations for steel and
aluminum.
Sample
Material
Modulus of
Elasticity,
E (MPa)
Standard
Deviation
of E (MPa)
Yield Strength,
(MPa)
Standard
Deviation
of (MPa)
A-36 Steel 209300 1966 355.6 1.357
6061-T6 69460 337 356.3 1.979
The modulus of resilience and the modulus of toughness were calculated from the area
under the engineering stress versus engineering strain curves, as outlined in Appendix C.
Both are useful for determining the amount of energy the material can absorb before
yielding and fracture. The values of both are shown in Table 3.
Table 3: The modulus of resilience and the modulus of toughness for the materials.
Sample
Material
Modulus of Resilience
(MPa)
Modulus of Toughness
(MPa)
A-36 Steel 0.9725 174.6
6061-T6 1.600 60.03
Polycarbonate 0.3793 63.73
PMMA 0.3091 2.475

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The true fracture strength provides the actual value of the stress encountered by the
sample during the tensile test, just before fracture. The true fracture strength is the
greatest stress that the material can handle after yielding. The percent elongation and the
percent reduction in area provide information about the ductility of a material, and how
much it can be stretched before failure. The calculations of these properties are outlined
in Appendix D. The averages of all three values for each of the four materials are shown
in Table 4.
Table 4: The average true fracture strength, percent reduction of area, and the percent elongation
for all four materials.
Sample
Material
True Fracture
Strength, ̃ (MPa)
Percent Reduction of
Area, %RA
Percent Elongation,
%EL
A-36 Steel 1047 64.79% 33.47%
6061-T6 571.8 54.02% 17.30%
Polycarbonate 94.11 44.88% 82.20%
PMMA 67.29 0.2609% 0.7333%
C.3 True Stress and True Strain
One sample of aluminum was used to find the true stress and the true strain encountered
during a tensile test, and to compare both to the engineering stress and the engineering
strain. The engineering stress and strain does not account for the change in cross sectional
area, and only accounts for the axial strain in the sample. The true stress and strain
account for the change in cross sectional area, and therefore the true stress is higher than
the engineering stress. The true strain is also greater than the engineering strain due to
strains in the transverse direction along the gage of the sample. Figure 7 shows the true
stress versus the true strain, along with the engineering stress and the engineering strain
for the same sample. The second sample of aluminum was used in this analysis, as
defined by Appendix E.

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Figure 7: The True Stress versus the True Strain, along with the Engineering Stress and Strain
for a sample of 6061-T6 Aluminum.
The true stress at the point of maximum load (where the ultimate tensile strength occurs)
for the 6061-T6 aluminum sample had a value of 404.9 MPa, compared to a maximum
tensile strength of 376.6 MPa. The true strain at this point had a value of 0.0723 m/m,
compared to an engineering strain of 0.0750 m/m. The maximum true stress at fracture
was 561.5 MPa, with a strain of 0.765 m/m. At fracture, the engineering stress was 261.3
MPa, with a strain of 0.182 m/m.
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
Stress(MPa)
Strain (m/m)
True Stress and Strain
Engineering Stress and Strain

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C.4 The Ramberg-Osgood Model
The behavior of the true stress due to the true plastic strain can be accurately modeled
using the Ramberg-Osgood equation. This equation models the stress-strain curve as a
power hardening model, after yielding. The resulting equation, as derived in Appendix F,
gives rise to Figure 8, where it is plotted against the true stress and strain values derived
from the experiment.
Figure 8: The plot of the true stress versus the true plastic strain for both the experimental values
and the calculated values obtained from the Ramberg-Osgood model.
The value of the true stress and strain obtained from the Ramberg-Osgood model at three
defined points is compared against the experimental values in Table 5, showing the
increasing accuracy of the model as plastic strain increases.
Table 5: The true stresses calculated using the Ramberg-Osgood model, compared to the
experimental true stress.
True Plastic Strain
(m/m)
Calculated Stress
(MPa)
Experimental Stress
(MPa) Percent Error
0.001 300.5 360.1 19.84%
0.01 353.9 364.1 2.886%
0.05 396.7 396.8 0.01496%
0
50
100
150
200
250
300
350
400
450
0 0.02 0.04 0.06 0.08
TrueStress(MPa)
True Plastic Strain (m/m)
Calculated
Experimental

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D. Discussion
The test results were consistent for each of the materials, as evident in Figures 3-6, where
each of the three stress-strain curves were approximately overlapping. An interesting
observation can be made from the PMMA graph, where sample one suddenly loses stress
as it is stretched. This sample may have fractured partially across the cross section before
complete failure, or a void could have caused a sudden release of stress. All of the other
samples exhibited consistent behavior.
From the ultimate tensile strength data in Table 1, it is clear that the A-36 hot rolled steel
was the strongest material, followed by aluminum, PMMA, and polycarbonate,
respectively. All of the standard deviations were low, not exceeding 2.606 MPa,
suggesting that the data was consistent and that the testing procedure was valid and
repeatable. The true fracture strength, shown in Table 4, gives a better view of the true
stress at fracture. The A-36 steel had the highest true fracture strength, followed by the
aluminum, polycarbonate, and PMMA.
Although the A-36 hot rolled steel had a much higher modulus of elasticity (209300
MPa, compared to 69460MPa for the 6061-T6 aluminum), and a higher ultimate tensile
strength, the yield strength is about the same as the 6061-T6. The higher ultimate stress is
due to work hardening as the material is plastically deformed. The introduction of
dislocations reduces their motion, and hardens the material. The 6061-T6 is a tempered
and aged alloy that is already precipitation hardened. It will not work harden as much as
the A-36 steel, resulting in a lower ultimate tensile strength. The standard deviations for
the yield strength and modulus of elasticity are also small compared to the average
values, proving the consistency of the data.
The modulus of resilience and the modulus of toughness are important values in
determining the energy that a material can absorb before yielding and before fracture.
The modulus of resilience is the area under the engineering stress-strain curve up until the
yield, and corresponds to the energy per unit volume that a material can absorb before it
yields. The 6061-T6 aluminum had the highest modulus of resilience, followed by A-36

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steel, polycarbonate, and PMMA. The aluminum had the highest resilience due to the
high yield strength, and the low modulus of elasticity (compared to the A-36 steel), as
shown in Table 3. The low modulus of elasticity ensured that the aluminum was strained
more before yielding, allowing it to absorb more energy.
The modulus of toughness was the highest for the A-36 steel due to the high ultimate
tensile strength, and the ductility of the steel. The polycarbonate had a higher modulus of
toughness than the 6061-T6 aluminum due to its high ductility, even though it had a
lower yield and ultimate tensile strength. The acrylic had the lowest modulus of
toughness due to its brittle nature.
The percent reduction of area and the percent elongation are indicators of the ductility of
a material. All of these values are located in Table 4. A more ductile material will have a
greater percent elongation, and the material will neck down further, resulting in a greater
reduction of area. The A-36 steel samples had the greatest reduction of area due to the
large amount of necking just before fracture. The polycarbonate had the highest percent
elongation due to the straightening of the polymer chains. The polymer chains did not
neck down after they were straightened, which resulted in a smaller percent reduction of
area compared to the steel and aluminum samples. The aluminum did not elongate as far
as the steel due to the alloying of the material and the precipitation hardening that was
used to improve other properties. The PMMA had the lowest percent reduction of area
and the lowest percent elongation, indicating that it is a brittle material.
The true stress and true strain take into account the changing area of the cross section as
it is being elongated, and the strains that accompany the changing area. Accounting for
these two effects results in a final true stress that is much higher than the engineering
fracture stress and a greater amount of strain. As shown in Figure 7, the true stress
reaches a maximum at the point of fracture. At this point, the area is much smaller, so the
specimen cannot withstand a large load, which causes the engineering stress-strain curve
to drop off after necking. There is no ultimate tensile stress in the true stress-strain curve

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as with the engineering stress-strain curve, and the true stress is always increasing up
until fracture.
The Ramberg-Osgood model proved to be excellent at determining the true stress at
higher values of true plastic strain, but had higher error at low values of true plastic
strain, especially near the yield strain, where plastic strain is essentially zero. Table 5
shows that near the ultimate tensile strain, the error is very small, but near the yield
strain, the error is rather high at 19.84%. The aluminum samples did not exhibit the
power hardening behavior that is typical of the Ramberg-Osgood model. The engineering
stress-strain curve was flat after yielding, and not curved like the model shows in Figure
8. Since the model was fitted to the data between three times the yield strain, and the
ultimate tensile strain, it does not fit the sample well at low values of true plastic strain.
This error could be alleviated by fitting multiple models to the curve, or by choosing a
different model that better fits the shape of the engineering stress-strain curve.

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Appendix A: Calculating the Engineering Stress and Strain
Each material was tested three times, and the Engineering stress was plotted against the
engineering strain. To calculate the engineering stress and strain, the Instron machine
used extensometers up until necking, which measured the strain induced on the sample.
Past necking, the Instron machine obtained strain data from the position of the crosshead.
The load cell on the moving crosshead measured the vertical load applied to the sample.
The diameter of the gage on the sample was measured using calipers, and from there the
area was calculated using Equation A.1. The engineering stress is a function of the force
applied and the original cross-sectional area of the gage of the sample. Using Equation
A.2, the engineering stress was calculated. P denotes the tensile force applied to the
specimen.
(Equation A.1)
(Equation A.2)
Appendix B: Determining the Modulus of Elasticity and the Yield Stress
The modulus of elasticity and the yield stress was calculated for all three samples of both
the aluminum and the steel. To find the modulus of elasticity, a small portion of the
stress-strain curve was plotted to only include the linear region around zero strain. The
slope of the graph at this point is the modulus of elasticity for that material. Excel was
used to plot this portion of the stress-strain curve, and a trend line was added to best fit
the data. Using the modulus of elasticity, the yield stress was also found. A line was
plotted with the modulus of elasticity as the slope, but it was offset 0.002 mm/mm of
strain. The value of the stress where the two lines cross is the corresponding yield stress.
This method is the standard 0.2% offset method used to find the yield stress. The average
of each value was calculated, along with the standard deviation, using Equation B.1 and
Equation B.2, respectively.
̅ ∑ (Equation B.1)
√ ∑ ̅ (Equation B.2)

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The ultimate tensile strength was found by determining the maximum load, and using
Equation A.2 to solve for the maximum engineering stress encountered. The standard
deviation was also calculated for the ultimate tensile strength, using Equation B.2.
Appendix C: Determining the Modulus of Resilience and the Modulus
of Toughness
The modulus of resilience is defined as the area under the engineering stress-strain curve
up until yielding. It is the maximum energy per unit volume that the sample can absorb
elastically. This energy can be recovered by relaxing the stress. Both Equation C.1 and
Equation C.2 can be used to calculate the modulus of resilience.
(Equation C.1)
(Equation C.2)
The modulus of toughness is defined as the area under the entire stress-strain curve up
until fracture. It is the maximum energy per unit volume that the sample can absorb
before it fails completely due to fracture. Unlike the modulus of resilience, most of the
energy cannot be recovered by relaxing the stress. The plastic deformation of the material
is permanent. The modulus of toughness cannot be calculated using an equation due to
the variety of shapes encountered in the stress-strain curves. To find the modulus of
toughness for the four materials, one of the three samples was chosen from each material
(All of the data was taken from Sample 1 of each material). The data was loaded into
MATLAB using XLSREAD, and the area under the curve was evaluated using the
TRAPZ command. The cumulative integral from zero strain up until the fracture strain
was recorded as the modulus of toughness. The modulus of resilience was also calculated
using MATLAB, but the integral was only carried out to the value of the yield strain.

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Appendix D: Determining the True Fracture Strength, Percent
Reduction in Area, and Percent Elongation
The true fracture strength provides the actual stress at fracture. The engineering stress
does not account for the reduction in area due to necking. Equation D.1 provides the true
stress at fracture. The diameter of the gage of the specimen was measured after fracture
using calipers, and the area of the cross section was calculated using equation A.1. and
represent the load and the area at fracture, respectively.
̃ (Equation D.1)
The percent reduction in area and the percent elongation provide useful information about
the ductility of the material. A more ductile material typically has a higher percent
elongation up until fracture, and the reduction in area is greater as the material necks
down before fracture. A brittle material will not elongate much past the yield strain, and
the percent reduction of area is lower than for a ductile material. Equation D.2 is used to
calculate the percent reduction in area. is the area at fracture, and is the area of the
cross section before testing, both taken from caliper measurements before and after the
tensile test.
( ) (Equation D.2)
Equation D.3 is used to calculate the true length of the specimen just before fracture. The
length measured after fracture is less than the length before due to the elastic recovery
when the stress is relieved when the material fractures. is the length of the gage post
fracture, and is the engineering stress at fracture. The length after fracture was
measured by placing the two halves of the specimen back together, and measuring the
length of the gage. Equation D.4 is then used to calculate the percent elongation of the
material.
(Equation D.3)
( ) (Equation D.4)

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Appendix E: Determining the True Stress and the True Strain
The true stress and true strain was calculated for one sample of aluminum, in this case for
the second sample. The engineering stress and strain does not account for the reduction in
area as the sample is pulled apart, nor does it account for strains besides the axial
direction. The true stress and true strain show the actual stress and strain encountered
during the tensile test. The true stress can be calculated at any point using Equation E.1,
but since the instantaneous area was not known for this test, other methods had to be
incorporated. ̃ denotes the true stress. The tensile force is denoted by P, and the
instantaneous area is shown by A.
̃ (Equation E.1)
For strains below two times the yield strain, the true stress is well approximated by the
engineering stress, shown by Equation E.2. Between two times the yield strain and
necking (the strain at the ultimate tensile stress), the true stress is approximated by
Equation E.3. is the engineering stress, and is the engineering strain.
̃ (Equation E.2)
̃ (Equation E.3)
The true strain was calculated using Equation E.4, up until necking. From necking until
fracture, there was not enough information to fully define the true stress or true strain.
The final true stress was calculated using the final area and the tensile force right before
fracture, as shown in Equation E.5. The true strain at fracture was calculated using
Equation E.6. A final point was plotted, and a straight line was drawn from necking to
fracture. is the tensile force at fracture.
̃ (Equation E.4)
̃ (Equation E.5)
̃ ( ) (Equation E.6)

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Appendix F: The Ramberg-Osgood Equation for Plastic Deformation
After the true stress and true strain were calculated, the true plastic strain was calculated
using Equation F.1. This resulted in the elastic strain being taken out, leaving only the
permanent plastic strain. The true elastic strain was calculated using Equation F.2.
̃ ̃ ̃ (Equation F.1)
̃
̃
(Equation F.2)
A plot was made of the logarithm of the true stress versus the logarithm of the true plastic
strain. The plot only concerned the region between three times the yield strain, and the
strain corresponding to the ultimate tensile stress. This resulted in a straight line that was
fit with a best fit model of the curve, yielding a linear equation, as shown in Figure F.1.
Figure F.1: The plot of the logarithm of the true stress versus the logarithm of the true plastic
strain
Excel was used to create the linear equation, and the slope and y intercept were used to
create a model of the true stress encountered, using the true plastic strain, according to
Equation F.3.
̃ ̃ (Equation F.3)
y = 0.0710100522x + 2.6908893716
2.58
2.585
2.59
2.595
2.6
2.605
2.61
2.615
2.62
-2 -1.5 -1 -0.5 0 Log(TrueStress)
Log(True Plastic Strain)

20
Using logarithm identities, the slope of the equation (0.07101) became n in Equation F.3,
and 10 raised to the power of the y intercept (2.6909) became H (490.8) in Equation F.3.
The resulting equation is shown as Equation F.4.
̃ ̃ (Equation F.4)
Equation F.4 was used to create a plot of the true stress versus the true strain to compare
it to the experimental plot of the true stress versus the true strain, as shown in Figure 8.
The equation was also used to calculate the true stress at set values of true plastic strain
of 0.001, 0.01, and 0.05. The calculated values of the true stress were compared to the
true stress values obtained from the experiment in Table 5 using percent error.

Tensile testing-laboratory

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