Laboratory Report
MatS 2002
Fall 2006
Group M2
Name of Experiment: Tensile Stress
Date of Experiment: September 11, 2006
Date Report Submitted: September 25, 2006
Group Members:
Jesse Kakstys
Tyler Bies
Kyle Sedam
Isaac Neitzell
James Grimm
Data and Analysis
Purpose
In this experiment, we aim to determine the mechanical properties of Aluminum
alloy 6061-T6, Carbon Steel 1018, and Lexan Polycarbonate. An Instron Universal
Testing machine Model 5500 will be used to gather data from which we can calculate
Young’s modulus, yield stress, tensile strength, and ductility for each specimen. The
computer-generated data required for these calculations include the applied force and the
elongation of the specimen. We will also need to measure the gauge length of each
specimen as well as the dimensions necessary to calculate the cross-sectional area.
Deviations
Prior to stretching our aluminum and steel samples in the Instron Testing
machine, we failed to measure the width and thickness of our specimens to determine the
cross-sectional area. Upon realizing this, we recorded these measurements off of
seemingly identical samples.
Stress-Strain Curves
Aluminum Alloy 6061-T6
Engineering Stress (MPa)
400
350
300
250
200
150
100
50
0
0.0
0.1
0.2
0.3
Engineering Strain
Engineering Stress (MPa)
Carbon Steel 1018
450
400
350
300
250
200
150
100
50
0
0
0.1
0.2
Engineering Strain
0.3
0.4
Polycarbonate (Lexan®)
Engineering Stress (MPa)
70
60
50
40
30
20
10
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Engineering Strain
Mechanical Properties
σ yield
(Mpa)
σ TS
(Mpa)
σ fracture
(Mpa)
Ductililty
(% elongation)
Ductility
(% reduction)
Young’s modulus
(Gpa)
Carbon Steel 1018
Aluminum Alloy 6061-T6
Polycarbonate (Lexan®)
355
272
43
414
348
58.8
414
348
55.5
31%
38%
88%
20%
30%
43%
380
180
1.39
*Sample calculations and a graph from which we established Young’s modulus can be
found in the Appendix.
Discussion
When comparing values for stress obtained by crosshead movement to those
calculated using the extensometer, the most notable difference is that the computer
generates a percent stress and strain. These values can be adjusted to fit our original
format so that stress is given in MPa. These adjusted figures for the Polycarbonate
sample are plotted in a graph below alongside our calculated stress-strain curve.
We can see from this graph that the figures are similar yet slightly different. The
two curves follow the same pattern, however the stress values measured by the crosshead
tend to be slightly higher than those of the extensometer. The graph from the crosshead
also seems more compact with a fracture occurring at a strain right around 0.8 as opposed
to the extensometer that places the fracture closer to 0.9.
These same trends can also be seen in the superimposed graphs for both the
Aluminum 6061-T6 and the Carbon Steel 1018, but with lower stress values coming from
the crosshead for carbon steel (see appendix). These small differences can be explained
by three factors. First, if the specimen slips at all, while in the grips of the testing
machine, it can alter the collected data. The same holds true if our sample extends in the
transition region rather than just the gauge region. The extensometer is used to prevent
these two issues. Lastly, the computer calculates the stress based on the force the
crosshead applies and the preset parameters for the cross-sectional area. If the data in the
computer program does not accurately represent the area of our sample, it will result in
stress values that are consistent with those based off of the extensometer only slightly
higher or lower.
Polycarbonate
70
Stress (MPa)
60
50
40
Crosshead
30
Extensometer
20
10
0
0
0.2
0.4
0.6
0.8
1
Strain
Sources of Error
The biggest source of error for this experiment is human error. To begin with,
measurements taken in the laboratory (especially smaller ones in mm) are only as
accurate as the human eye will allow them to be, despite the use of precise instruments
like the digital caliper used in this experiment. Also, the practice of sliding a ruler along a
graph in order to determine the 0.2% offset yield strength leaves plenty of room for
inaccuracies.
Secondly, it was difficult to determine precisely where to measure for our final
cross-sectional area. There was not a uniform area near the fracture due to necking and
jaggedness of the break.
The third problem we come across, regarding measuring imprecision, is that our
measurements did not come from the samples that were used in the experiment. It was
after we had already fractured our samples that the group realized that we had not taken
initial measurements of the cross-section. However, this fault should cause minimal
amounts of error since the samples we used to gather our dimensions were nearly
identical to those used in the experiment.
There were a few small surface scratches on our Carbon Steel sample. However,
they were not near the point of fracture and probably only affected our measurements
minimally.
Lastly, there are various types of these alloys with different mechanical
properties. It is difficult to hold our experimental values to standard accepted values
without knowing precisely how the alloy was processed. We were able to positively
identify the Aluminum alloy, however it is not evident whether the Carbon steel is cold
drawn or hot rolled, etc. For comparison purposes within this report, we chose the
variations of Carbon Steel 1018 and Lexan that seemed most common.
Based on the chart of standard mechanical properties below, the yield stresses that
we extrapolated from our graphs are very precise. We were also able to calculate the
tensile strength for each material fairly accurately based on Force readings from the
Instron Testing machine and the cross-sectional areas we had measured.
The calculated percent elongation is close but slightly inaccurate. This is most
likely due to the fact that it is difficult to determine, strictly from the data sets, the exact
point at which the fracture occurs. The percent reduction is also somewhat off, probably
because of small inaccuracies when measuring the cross-sectional area at the point of
fracture.
As far as the figures we determined for Young’s modulus, we are in the vicinity
of the standard data, but fairly inaccurate. Excel charts were used to establish these
figures. The disagreement with the standard statistics shows the limitations of some
computer programs.
Standard Mechanical Properties
(All data in the following chart was obtained from MatWeb.
http://www.matweb.com)
σ yield
(Mpa)
σ TS
(Mpa)
Ductililty
(% elongation)
Ductility
(% reduction)
Young’s modulus
(Gpa)
Carbon Steel 1018
Aluminum Alloy 6061-T6
Polycarbonate (Lexan®)
370
276
not available
440
310
57.2
15%
12%
110%
40%
17%
not available
205
69
2.03
True Stress-True Strain Curves
Carbon Steel 1018
True Stress (MPa)
600
500
400
300
200
100
0
0
0.05
0.1
0.15
True Strain
0.2
0.25
0.3
True Stress (MPa)
Aluminum Alloy 6061-T6
450
400
350
300
250
200
150
100
50
0
0
0.05
0.1
0.15
0.2
0.25
True Strain
Polycarbonate (Lexan®)
True Stress (MPa)
120
100
80
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
True Strain
n and K
Strain Hardening
Component (n)
Strength
coefficient (K)
Carbon Steel 1018
Aluminum 6061-T6
1.2
1.1
5.0
4.4
1
Using Excel, we can make a scatter plot of log(σT) vs. log(εT). We can then use an
integrated Excel function to plot a trendline for our graph. Excel will also produce the
equation of the trendline for us. From this equation, the slope of the line will equal the
strain hardening component and the x-intercept will represent the strength coefficient.
The graphs are shown on the next page with the trendlines highlighted in red.
Carbon Steel 1018
y = 1.1596x + 4.9276
3
2.5
Log σ T
2
1.5
1
0.5
0
-5
-4
-3
-2
-1
0
Log εT
Aluminum Alloy 6061-T6
y = 1.0889x + 4.4032
3
2.5
Log σ T
2
1.5
1
0.5
0
-5
-4
-3
-2
Log εT
-1
0
Design Problem
In order to support a load of 2000N, without causing permanent deformation, it is
critical that we examine the yield stress of the materials we are considering. As a
standard, we want our structural components to stay within 2/3 of the yield stress for the
material we are working with, to ensure the safety of our structure. After computing this
boundary, we are able to determine the size of the components we need to use based on
their cross-sectional area. In this instance, we are using a cylindrical rod. Therefore, our
area will be π*r2.
These computations were made and put in a table below. From this table, it is
clear that the best material to use in this situation is the Carbon Steel 1018. Because of its
high yield stress, we are able to minimize the size of the Carbon Steel 1018 cylindrical
rod. Since we are able to conserve on materials, our final product will be more compact
and cheaper to produce.
237
8.44
Aluminum Alloy
6061-T6
181
11.0
Polycarbonate
(Lexan®)
28.7
69.7
1.64
1.88
4.71
Carbon Steel 1018
2
/3 σy (MPa)
Area (mm2)
Minimum radius
(mm)
Conclusion
Based on data generated from a computer and Instron Universal Testing machine
as well as dimensions collected from a digital caliper, we were able to successfully
calculate the yield stress and tensile strength of Carbon Steel 1018, Aluminum alloy
6061-T6, and the polycarbonate Lexan ®. Despite quite a few sources of error, we were
also able to determine percent elongation and percent reduction values of ductility for all
three materials with some degree of accuracy. Our only shortcoming, in what was a
successful experiment, was in calculating Young’s modulus. The important thing learned
in this lab is how a material can be tested in order to determine its mechanical properties,
which in turn have vast amounts of practical value when deciding on a material to use for
a particular project.