Laboratory Two: Tensile Testing of Three “505” Specimens
Lab Group - 1st Mondays, Late:
Jesse Bertrand, Ryan Carmichael, Anne Krikorian, Noah Marks, Ann Murray
Report by Ryan Carmichael and Anne Krikorian
E6 Laboratory Report – Submitted 7 April 2008
Department of Engineering, Swarthmore College
Abstract:
We determined the elastic modulus, yield strength, tensile strength, modulus of toughnes,
elongation, reduction of area, as well as true stress and strain at rupture point for three “505”
specimens, one each of SAE 2011-T-3 aluminum, 1081 hot rolled steel, and PVC plastic. We
accomplished this by first placing our specimens one at a time into a universal testing machine
(UTM), which, under computer control, slowly increased the tension force on each specimen,
stretching each until failure. We then analyzed the data output from the computer controlling the
UTM to obtain the following results:
Elastic
Modulus
(103 ksi)
Yield
Stren
gth
(ksi)
Aluminum 9.2+0.1
46.0+
0.2
Steel
27.6+0.2
82.9+
0.4
PVC
0.402+0.002 5.478
+0.1
Tensile
Strength
(ksi)
Modulus of
Toughness
(in.)
55.9+0.1
8.945+0.1
Modulus
of
Resilience
(%)
89.89+0.1
91.2+0.2
14.429+0.1
82.43+0.1
7.111+0.05
1.910+0.08
22.14+0.8
1
Elongati
on in 2
in. (in.)
Reduction
of area
(%)
0.3120
+0.005
0.3615
+0.005
0.5505
+0.005
45.74+0.1
58.63+0.1
48.25+0.1
Purpose:
The purpose of this experiment is to extract data on the material properties of three “505”
specimens (SAE 2011-T-3 aluminum, 1081 hot rolled steel, and PVC plastic), using a
mechanically driven universal testing machine (UTM). These material properties include the
following: the elastic modulus, 0.2% offset yield strength, ultimate tensile strength, modulus of
rupture, modulus of resilience, as well as true strain and true stress at the point of rupture.
Theory:
Certain materials (those that are linear, homogeneous, elastic, and isotropic) can be
described by their material properties. These properties include the modulus of elasticity,
modulus of toughness, modulus of resilience, ultimate tensile strength, and yield strength. Once
established by experimental means, these properties are then applied to all instances of that
material undergoing the same type of stress, allowing one to design structural elements whose
behavior can be predicted. In practice, these qualities are affected by temperature and repeated
loading, and also by the purity of the material- flaws such as air bubbles, scratches, impurities,
and the like result in lower strength before yielding and can result in unpredictable breaking
points. As a result of such flaws (temperature can be adjusted for using mathematical formulas)
and because of natural variations in loading and uncertainties, in design a factor of safety is
introduced, which gives a margin of error, essentially, in which the material will not fail.
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However, the established properties of the material are relied on to determine what type of load
and under what situations that material is safe. Also, the properties allow comparison of
brittleness, toughness, and other such features.
In testing a material to determine its properties, a stress-strain graph becomes useful for
analysis, as is investigation into the mode of failure. Each mode of failure is related to a
significant material property: elastic failure to the elastic limit, yielding to yield strength, and
sudden fracture to ultimate strength2. When testing by applying an (tensile) axial load to a test
specimen, the necessary data for a stress-strain diagram can be acquired, and by testing a
material in tension to failure by sudden fracture, the conditions at which elastic failure and
yielding occur can also be determined (as they come under less stress than sudden fracture does).
The modulus of elasticity, or Young’s modulus, describes the direct, proportional
relationship between stress and strain that exists for stresses below the proportional limit.
Nominal yield strength is the stress at which a plastic deformation of 0.2% is achieved. Ultimate
tensile strength is the amount of stress that a sample under tension can withstand before failure
(here, sudden fracture). Percent elongation at failure simply gives us the final change in length of
a sample that has reached failure. Percent reduction in area gives the smallest cross-sectional
area of a failed specimen, presumably at the point of failure, and also is a quantitative measure of
necking.
3
The modulus of toughness documents the work done on a unit volume from the point
where stress is zero to the point of failure. The modulus of resilience displays the materials
ability to absorb energy without plastically deforming. Engineering stress is the load applied (in
this setup as measured by the UTM) divided by the original cross-sectional area. True stress is
the load applied divided by the cross-sectional area, taking the change in area that occurs with
deformation into account. Engineering strain is the deformation (in this setup as measured by the
UTM) divided by the original gauge length. True strain at the rupture point is the natural log of
the quantity final sample length divided by initial length, which is derived from taking each
instantaneous change in length into account.
While to truly establish material properties many trials would be required, the testing of
specimens that we performed allows us to determine estimates of a number of material
properties. These material properties are summarized in the following handout (Everbach)
4
E6 Mechanics
Spring 2008
Tensile Testing Backgrounder
TYPICAL STRESS - STRAIN CHARACTERISTIC
Ultimate Tensile Strength
Yield
Strength
STRESS - LBF/IN^2
Proportional
Limit
Point of
Rupture
Slope =
Elastic Modulus
.002
Elongation at Failure
STRAIN - IN./IN.
Figure 1
Mechanical Property Definitions
Engineering Stress
- Load divided by Initial cross-sectional Area (normally 0.200 in^2)
Engineering Strain
- Elongation divided by Initial Length (normally 2.000 inches)
Proportional Limit
- Stress above which strain is not proportional to stress
Elastic Limit
- Stress above which strain does not return to zero on release of stress
Yield (Proof) Strength - Stress at which strain remaining on release of stress equals 0.2%
(Ultimate) Tensile Strength - Greatest tensile Stress borne by specimen
Modulus of Elasticity (Young's Mod.) - Slope of stress-strain plot below Proportional Limit
Elongation at Rupture (Failure) - elongation in 2 inches, as a %
Reduction in Area
- (1 - Final Area/Initial Area) * 100 (a %)
Modulus of Resilience - Area beneath stress-strain curve up to Elastic Limit
Modulus of Rupture (Toughness)- Area beneath stress-strain curve up to point of Rupture
5
Procedure:
In this lab, we first selected three “505” specimens (SAE 2011-T-3 aluminum, 1081 hot
rolled steel, and PVC plastic) to undergo tension in the UTM. We hammered two small indents
into each specimen, two inches apart. These designated gauge length and to facilitate the
measurement of final length, while being shallow enough to not compromise the sample’s
integrity. We then measured the distance between the two indents with a caliper to get a more
accurate measurement of the gauge length, and also measured the initial diameter of the sample.
Next, we screwed our first specimen into the mechanically driven UTM and let the computer
steadily increase the tension. The UTM “operates by rotation of two long power-screws, thereby
moving a cross member attached to the upper end of the test specimen. A calibrated load cell
measures the applied force in pounds, and the computer software controlling the UTM can
specify either the displacement or the applied load” (Everbach1). The computer software then
steadily increased the force exerted on the sample by the UTM, along with displacement (change
in length), until the specimen failed. We then removed the specimen from the UTM, fit the two
pieces together and measured the final gauge length and the final diameter with the caliper. We
repeated this process for the other two specimens. Finally, we analyzed the data collected by the
computer controlling the UTM to determine several material properties of the three specimens.
Our analyses relied on both Matlab and Kaleidagraph, using the techniques delineated below.
6
We found the modulus of elasticity by performing a linear fit on a selected linear portion
of each graph.
The 0.2% yield strength was determined by plotting a line y=mx+b, where m was the
modulus of elasticity and b was an offset of 0.002 (or 0.2%).
Ultimate tensile strength simply required that we find the highest recorded load applied.
Percent elongation at failure was determined by fitting the two pieces of the specimen
together and measuring the distance between the indents placed earlier in the procedure, while
percent reduction of area was found by measuring the smallest diameter of the sample after
failure and using it to calculate the cross-sectional area.
The modulus of toughness we found by taking the area under the curve of the stressstrain graph from the origin to the point of failure, and the modulus of resilience used the same
method, but from origin to the elastic limit (both via Kaleidagraph Macros:Calculus.eqn).
Engineering stress and strain were found by dividing load by cross-sectional area and
change in length by initial length, respectively. True strain and true stress take the change in
dimension of the specimen into account, in stress using the final cross-sectional area in
calculations and in strain using a formula derived from the integration of change in strain.
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Results:
This table lists experimental values first, followed by established values where applicable.
Units
Aluminum
Steel
PVC
Elastic Modulus
Established Value
103 ksi
9.2 + 0.1
27.6 + 0.2
29.7
Yield Strength
Established Value
Ultimate Tensile Strength
Established Value
Elongation in 2 in.
Established Value
Modulus of Toughness
Modulus of Resilience
Reduction of area
True Stress at Rupture
True Strain at Rupture
Engin. Stress at Rupture
Engin. Strain at Rupture
ksi
0.402 + 0.002
0.000230.470
5.48 + 0.1
2.47-7.54
7.11 + 0.05
0.580-8.56
0.5505 + 0.005
0.06-12
1.91 + 0.08
22.14 + 0.8
48.25 + 0.1
7.181 + 0.3
0.243 + 0.005
3.732 + 0.1
0.33650 + 0.003
10.2
psi
ksi
in
%
in/in
ksi
in/in
ksi
in/in
46.0 + 0.2
43.0
55.9 + 0.1
55.0
0.3120 + 0.005
0.30
8.9 + 0.1
89.89 + 0.1
45.74 + 0.1
82.5 + 0.5
0.145 + 0.005
44.753 + 0.1
0.1734 + 0.003
82.9 + 0.4
39.9
91.2 + 0.2
68.9
0.3615 + 0.005
0.76
14.4 + 0.1
82.43 + 0.1
58.63 + 0.1
147.2 + 0.5
0.166 + 0.005
60.766 + 0.1
0.17690 + 0.003
Note: all established values listed are from matweb.com Values listed are from “Aluminum
2011-T3,” “AISI 1018 Steel, Hot rolled,” and “Overview of Materials for PVC, Molded.”
8
Discussion:
Qualitatively, the visible effects of the tensile loading on the specimens relate to the
stress-strain diagrams from our testing. Aluminum and steel were very similar, displaying very
little elongation through the proportional area of the graph. Then, at yield strength, the
elongation (strain) on each became visible. Necking occurred as the stress-strain curve became
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non-linear; the specimens formed regions on the specimen where the diameter was noticeably
smaller, and then fractured at those thinner points (documentation of this can be found in
appendix E). Neither specimen displayed the classic ‘cup and cone’ fracture, where one side of
the fractured region displays a prominent bulge, and the other a matching indent. However, both
the aluminum and steel specimens displayed what we termed a ‘half cup and cone,’ as each side
of the fracture displayed on approximately half of the cross-sectional area a cone-like bulge, with
the opposite half showing raised “walls” like a cup. The PVC elongated more noticeably before
reaching the yield strength, and as the test continued we observed necking similar to in the
metallic samples, followed by an increase in the length of the necked section. This was a result
of the PVC stiffening after undergoing strain, and therefore becoming more impervious to strain
than the regions directly below and above the stiffened section. This may have been the cause of
the departure from a smooth curve that occurs slightly above the 0.1 in./in. strain value. At break,
there was a significant length of PVC that had lightened from the material stretching and
stiffening, with the fracture occurring at a location between the section with the smaller crosssectional area (which was stiffest and strongest) and the more elastic, thicker region. The PVC
sample lacked a distinctively classifiable break pattern, perhaps due to more elasticity at the
break than with the metals. When investigating this, we determined that while the exterior of the
specimen fit roughly back together, the interior areas did not, leaving a gap. Also interesting is
10
that all of the specimens fractured at a point about 40% of the way from an end. This may have
occurred from an uneven fit in the UTM or from flaws in the samples.
Quantitatively, we had varying success in experimentally determining material property
values that came near established values. This is due in part the possibility of the data from the
UTM being inaccurate due to the time interval between data collection points, and also comes
from the specific sources of error for each value, with potential sources and (where applicable)
methods of determining area are addressed below. (For the properties that lack a specific
explanation of our determination of error method, we simply estimated it by examining the
nearby data points and applying the change between nearby points as a measure of variance to
account for gaps between data points. Others additionally included factors added to the error to
account for human estimation.)
For the modulus of elasticity, we determined error through Kaleidagraph’s quality of fit
analysis, as shown in the “Determination of Elastic Modulus” graphs of appendices B, C, and D.
Additional error in the PVC calculation also came from the nonlinear nature of what should have
been the linear section of the stress-strain graph.
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In the nominal yield strength, error was propagated from our modulus of elasticity value
and also came from the distance between data points. This is shown in the “Yield Strength
Determination” graphs of appendices B, C, and D.
Our ultimate tensile strength error likely came from the distance between the data points:
the value may have peaked in between recorded points, meaning that the real value may be
larger.
Error in percent elongation at failure came from any decrease in length that may have
occurred when the tension was released, from failure to fit the pieces together as they were when
they broke, and from error in measurements.
Error in percent reduction in area is introduced in measurements and in potential change
in cross-sectional area as tension was released, along with our assumption of a perfectly circular
cross section at break.
Error in our value for the modulus of resilience also comes from numerical integration,
and from equating the elastic and proportional limits. Error in the PVC calculation also came
from the nonlinear nature of what should have been the linear section of the stress-strain graph.
The elastic limits are shown in the “Determination of Elastic Limit” graphs of appendices B, C,
and D. In the modulus of toughness, error comes from numerical integration as performed in
Kaleidagraph. (Our interpolation method, which may have been responsible for the error from
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numerical integration, was that built into a Kaleidagraph Macros function termed calculus.eqn.
While many methods for interpolation exist, such as first-order (linear), spline, and cubic
interpolation, the advanced, nonlinear methods should have nearly equivalent results considering
the large number of data points provided.)
In engineering stress and strain, error comes into play from potential inaccuracy in the
UTM’s recorded data points and from the gaps between those points.
In true stress and strain, error is propagated: from machine-recorded values of stress and
strain and from our value of percent reduction in area.
Also important to note as a source of error is the ‘stacking’ behavior of our data: their
exist in some regions of the stress-strain graphs up to six stress values for a single strain value.
This comes from the gradual application of stress and the comparatively slower process of
change in strain- it may take long enough for a sample to stretch appreciably that the UTM will
record the increasing values of stress as for a single strain value, but may potentially alter the line
of best fit found or other analyses of the data. The stacking particularly affected the
determination of the elastic limit of the steel specimen.
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Conclusion:
Our testing of aluminum, steel, and PVC “505” to sudden fracture under tensile stress had
varyingly accurate results. While it is hard to determine the accuracy of the material properties
we found for the PVC sample as we are unsure of the specific variety of PVC it may have been,
we can see that the experimental values are within the ranges possible for PVC plastic. Our
experimental values for aluminum came near the established values for the modulus of elasticity,
yield strength, ultimate strength, and elongation (although generally not close enough to be
within uncertainty), while our values for steel were much farther from established values. The
far-ranging values found for steel may have been the result of inaccurate data or flaws in the
sample or some other cause, but the error is not accounted for by normal variance in data.
References:
Everbach1:
Everbach, Carr. “Tensile Testing and Numerical Integration.” Swarthmore College, 2008
Everbach2:
Everbach, Carr. “Tensile Testing Backgrounder.” Swarthmore College, 2008.
Riley:
Riley, William et al. Statics and Mechanics of Materials: an Integrated Approach. John
Wiley and Sons, Inc., 2002
Matweb:
“Material Property Data.” <www.matweb.com> Retrieved 5 April 2008.
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List of Appendices:
A……………………………………………. Diagram of a Universal Testing Machine
B……………………………………………. Aluminum Graphs
C……………………………………………. Steel Graphs
D……………………………………………. PVC Graphs
E…………………………………………….. Photos of Specimens
F…………………………………………….. Gauge Length Data
G……………………………………………. Lab Handout
H……………………………………………. Computer Printouts from the Testing
15
Appendix A:
http://nees.berkeley.edu/Facilities/4Mlb-test-machine.shtml
16
Appendix B:
17
18
Appendix C:
19
20
Appendix D:
21
22
Appendix E:
Fitted Together Specimens After Fracture
In descending order: PVC, Aluminum, and Steel
23
Half-Cup Half-Cone Fracture Pattern
Aluminum Specimen
Irregular Fracture Pattern
PVC Specimen
24
Appendix F:
Lab Data
Alum
Before
After
Change
% Change
Gauge Length
2.0000 in
2.3120 in
0.3120 in
15.60%
Gauge Diameter
0.5050 in
0.3720 in
-0.1330 in
-26.33%
Cross Sec. Area
0.2003 in2
0.1087 in2
-0.0916 in2
-45.74%
Steel
Before
After
Change
% Change
2.0060 in
2.3675 in
0.3615 in
18.02%
0.5045 in
0.3245 in
-0.1800 in
35.68%
0.1999 in2
0.0827 in2
-0.1172 in2
-58.63%
PVC
Before
After
Change
% Change
1.9940 in
2.5445 in
0.5505 in
27.61%
0.5060 in
0.3640 in
0.1420 in
28.06%
0.2011 in2
0.1041 in2
-0.0971 in2
-48.25%
25
Appendix G:
E-6 Mechanics
Laboratory #2
Spring 2008
Tensile Testing and Numerical Integration.
An exercise in materials characterization and numerical methods using MATLAB.
Introduction
This lab involves destructive testing of standard tensile specimens using a mechanically driven
universal testing machine (UTM). The mechanically driven UTM operates by rotation of two long powerscrews, thereby moving a cross member attached to the upper end of the test specimen. A calibrated load
cell measures the applied force in pounds, and the computer software controlling the UTM can specify
either the displacement or the applied load. You will observe this machine’s testing specimens under
both elastic and post-yield (plastic) conditions, and extract data on the material properties of the
specimens from the test results.
Lab Tasks
Conduct and observe tensile tests of at least three “505” specimens, using the UTM; two of the
specimens should be metals and one plastic. Record the basic structure and functional operation of the
UTM, details of specimen geometry and its behavior under test. Diameter readings should be taken at
several points along the specimen before and after yielding.
ASCII data files consisting of six comma-delimited columns will be produced by the computer
attached to the testing machine. Column 1 represents load in pounds (and so may be translated into
Engineering stress using initial cross-sectional area); Column 2 represents strain in inches per inch
(assuming 2.0 inch gauge length); Columns 3 and 4 may be discarded, while Column 5 lists length
increase in inches times two. Column 6 represents elapsed time in minutes. These files should be labeled
descriptively, such as PVC1ME.csv (for PVC plastic tested by the 1ME group), and transferred to
Blackboard for later Matlab analysis.
Notes about Processing File Data
Each data file has a ten-line header describing the measurement that must be removed before
MATLAB can read and process the numeric data. It is best to groom your data file first using Matlab’s
editor, Excel™, or another program (such as Word) to remove any leading or trailing data that is garbage.
Save As using (comma-delimited) Text format.
Because your raw data is in Pounds and Inches, whereas intermediate and final values are to be in
units of stress (psi or MPa) and strain (in./in.) respectively, you will need to cast the data in the
26
appropriate form prior to manipulation by MATLAB. If the data are in comma-delimited text format, the
Matlab command rawdata = csvread(‘PVC1ME.csv’) will produce a matrix variable rawdata with the six
columns described above. Variables may be created ho hold column data, for instance:
psi = rawdata(:,1)/0.2003; % engineering stress in lbf/in^2
inperin = rawdata(:,2); % engineering strain in inches per inch
(Raw data files may be as long as 600 lines, and therefore should NOT be printed at any time.)
Items to be Included in Lab Reports - Reports may be authored by a maximum of three people, with all
group members and any other collaborators listed.
1.
Sketch (hand sketches on your final printout are OK) and describe observed changes in geometry or
behavior of the test specimens corresponding to significant features of the test curves.
2.
Determine the Elastic Modulus E, 0.2% offset Yield Strength, ultimate Tensile Strength and
Percent Elongation at failure for at least one metal and one plastic specimen. Once you have found the
Elastic Modulus, you can use [DL0 - (F/A0 E) - 0.002 > 0] to indicate nominal yielding (stress at 0.2%
strain). From initial and final diameter measurements, determine final Percent Reduction in Area. For
least-squares linear fitting, use the Matlab polyfit command (and polyval for plotting the best-fit lines on
top of the data).
3.
Using load and displacement data taken from the computer-logged data file, determine the Modulus
of Rupture and the Modulus of Resilience for both the metal and plastic specimens by numerical
integration using first-order (linear), spline, and cubic interpolation of the data. Present and briefly
compare the results obtained by the different interpolation methods. For one of the methods (your
choice), compare the calculation integration time for tolerances of 1.0e-4 (the default), 1.0e-6, and 1.0e-8.
What does that comparison say about tradeoffs of time versus precision?
4. Using the measurements of the final load and cross-section, estimate true strain and true stress at the
point of rupture.
5. Begin your Results/Discussion section with a Table of Results for Elastic Modulus, Yield Strength,
Tensile Strength, Modulus of Rupture, Modulus of Resilience, Elongation in 2 inches and Reduction in
Area of all specimens. Include the same table in your Abstract. Plot data curves for all three samples on
the same graph of Engineering Stress vs. Engineering Strain.
Report
Reports should follow the format handed out earlier, with .m files in the Appendix and emailed to
Prof. Everbach. In your report, do not include printouts of the data! The graphs you will include in your
report will be enough.
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