Details findings from 1018 Steel and PLA tensile and hardness testing. Provides detailed theory and experimental procedure. Skip to results for findings.

1. TENSILE AND HARDNESS TESTING
by
TOBY BARRONS
TECHNICAL REPORT FOR
MECHANICAL ENGINEERING 339/339L
CALIFORNIA STATE UNIVERSITY – MARITIME ACADEMY
12 JANUARY 2020
COPYRIGHT
BARRONS, 2020
GROUP MEMBERS:
FRANGINEAS, MCNARY

2. ii
Abstract
This report discusses the theory, procedure and results for tensile tests
conducted on 1018 cold finished steel and 3-D printed PLA thermoplastic
specimens. A Rockwell Hardness test for the 1018CF steel specimen was also
completed with the goal of comparing the predicted tensile strength from
hardness to measured tensile strength from tensile testing. The hardness test
was conducted using an automated hardness test machine. The tensile tests
were conducted using a SATEC universal test machine in accordance with
ASTM standards. From the tensile tests stress-strain plots were produced for
both materials. For the 1018CF steel material properties such as Ductility,
Tensile Strength, 0.2% Yield Strength, Young’s Modulus, Engineering/True
stress at fracture, and Toughness were determined. Similarly, for the PLA
specimen, the Young’s Modulus, Tensile Strength, Ductility, and Toughness were
calculated. Our 1018CF steel specimen exhibited typical ductile metal behavior
with unusually high strength and hardness. The PLA specimen was very brittle
which resulted in very low ductility and almost no plastic deformation.

3. iii
Table of Contents
Abstract .............................................................................................................................ii
Table of Contents...........................................................................................................iii
List of Tables................................................................................................................... v
List of Figures................................................................................................................ vi
List of Variables............................................................................................................ vii
Chapter 1: Introduction ................................................................................................ 8
Chapter 2: Theory .......................................................................................................... 9
2.1 Tensile Testing .................................................................................................9
2.1.1 Ductile Metals ...........................................................................................9
2.1.2 Thermoplastic .........................................................................................12
2.2 Hardness .........................................................................................................13
Chapter 3: Experimental Procedures .....................................................................15
3.1 Procedure for Hardness and Tensile Testing of Steel Specimen...........15
3.2 Procedure for Tensile Testing Thermoplastic Material.............................17
Chapter 4: Results and Discussion.........................................................................19
4.1 Comparison of 1018CF Steel and PLA Tensile Test Results .................23
Chapter 5: Conclusion................................................................................................24
Bibliography..................................................................................................................26
Appendices....................................................................................................................27
Appendix A ..................................................................................................................27
A.1 Stress-Strain Data Correction ..................................................................27
A.2 Young’s Modulus Calculation ...................................................................27
A.3 1018 CF Steel 0.2% Yield Calculation....................................................29
A.4 Tensile Strength and Engineering Stress at Fracture ..........................29
A.5 Ductility (% Elongation and % Area Reduction) Calculations .............30
A.6 True Stress at Fracture .............................................................................31
A.7 Toughness...................................................................................................31

4. iv
A.8 Hardness Curvature Correction ...............................................................32
A.9 Rockwell Hardness B Test Specifications..............................................33
A.10 Table for estimating Tensile Strength from Rockwell Hardness.........34
A.11 Uncertainty Calculations ...........................................................................35
Appendix B ..................................................................................................................37
B.1 1018CF Steel Manufacturer Specified Dimensions ..............................37

5. v
List of Tables
Table 2.1 Example Data from Tensile Test of 3-D Printed PLA. [6].......................13
Table 4.1 1018 CF Steel HRB Hardness Test Results............................................19
Table 4.2 1018 CF Steel HRB Predicted Tensile Strength. ....................................19
Table 4.3 1018 CF Steel Tensile Test Results..........................................................20
Table 4.4 3-D Printed PLA Tensile Test Results. .....................................................21
Table 5.1 Strain Correction Factors to Shift Stress-Strain to pass through origin.
...........................................................................................................................................27

6. vi
List of Figures
Figure 2.1 Depiction of Tensile Test apparatus. [4]....................................................9
Figure 2.2 Example Engineering Stress-Strain diagram for ductile metal. [5]......11
Figure 2.3 Example Engineering Stress-Strain for 3-D Printed PLA. [6]...............13
Figure 3.1 This is the automated Rockwell Hardness test machine setup. ..........15
Figure 3.2 This is the gauge length indenter apparatus. .........................................16
Figure 3.3 This is the Universal Test Machine with sample inserted and
extensometer in place. ..................................................................................................17
Figure 4.1 1018 CF Steel Tensile Test Stress-Strain Plot.......................................21
Figure 4.2 3-D Printed PLA Tensile Test Stress-Strain Plot ...................................22
Figure 5.1 Linear Elastic Region of 1018CF Steel Stress-Strain Curve with Linear
Trend Line for Calculating Young’s Modulus.............................................................28
Figure 5.2 Linear Elastic Region of PLA Stress-Strain Curve with Linear Trend
Line for Calculating Young’s Modulus. .......................................................................28
Figure 5.3 This is the 1018CF Steel 0.2% Yield Graph. ..........................................29
Figure 5.4 Example of Raw Data printed to Excel from the data acquisition
system on the UTM and Extensometer. .....................................................................30
Figure 5.5 Curvature correction values for Rockwell hardness tests. ...................32
Figure 5.6 These are the HRB Test Specifications. .................................................33
Figure 5.7 Table used for estimating Tensile Strength from Rockwell Hardness
value.................................................................................................................................34
Figure 5.8 1018 CF Steel Tensile Strength and Modulus of Elasticity uncertainty
calculations......................................................................................................................35
Figure 5.9 3-D Printed PLA Modulus of Elasticity uncertainty calculations ..........36
Figure 5.10 1018CF Steel Tensile Test Specimen Dimensions .............................37

7. vii
List of Variables
𝐿 𝐹 Final Length (in)
𝐿 𝑂 Initial Length (in)
𝐴 𝐹 Final Cross-Sectional Area (in2)
𝐴 𝑂 Initial Cross-Sectional Area (in2)
𝐸 Young’s Modulus (psi)
𝜀 Strain (in/in)
𝜎 Stress (psi)
𝜔 𝐹 Force Measurement Uncertainty (psi)
𝜔 𝐸 Modulus of Elasticity Measurement Uncertainty (psi)
𝜔𝜀 Strain Measurement Uncertainty (in/in)
𝜔 𝑑,ℎ,𝑏 Diameter, Height, Base Measurement Uncertainty (in)

8. 8
Chapter 1: Introduction
The goal of this lab was to conduct tensile tests on 1018 cold finished steel and 3-D
printed PLA specimens to ultimately develop stress-strain curves and determine various
material properties. These properties could then be compared against values from
reference literature and material manufacturers to determine the validity of our results.
The material properties for PLA and 1018CF steel were also compared against each
other to develop insight into how individual material properties manifest into overall
material behavior. A secondary objective for this lab was to measure the hardness of
the steel specimen in order to compare a predicted tensile strength based the hardness
value to a measured tensile strength from the tensile test. By comparing these two
values we can determine the accuracy of tensile predictions based on material
hardness and better understand the benefits and limitation of this test method. Both,
tensile and hardness tests are widely used in industry and are fundamental to the field
of material science. Tensile tests yield valuable data that can be used to predict how
materials will behave under load. These predictions come from a variety of material
properties generated from tensile test data such as tensile strength, modulus of
elasticity, ductility, yield strength, fracture strength, and toughness. All these material
properties are explained in detail in the theory section of this report. This lab also served
to familiarize students with the procedure and equipment used for conducting tensile
and hardness tests in accordance with ASTM standards [1][2]. It was assumed that all
the tensile, hardness, and measurement test equipment were properly calibrated.
Assumed measurement uncertainties can be found in Appendix A.11.

9. 9
Chapter 2: Theory
2.1 Tensile Testing
The purpose of a tensile test is to gather information about a specimen’s material
properties. To conduct a tensile test, a gradually increasing tensile load is applied
uniaxially to a specimen until it fails. In an ideal test, the sample is elongated at a
constant rate so that there is no dynamic effect. Pictured below in Figure 2.1 is a
schematic depiction of tensile test apparatus [4].
Figure 2.1 Depiction of Tensile Test apparatus. [4]
In this example, the magnitude of the applied load is measured through the load cell
and the extensometer records the elongation of the specimen. The tensile test serves to
ultimately provide a Stress vs Strain diagram for the tested material. The Stress vs
Strain diagram is an extremely important tool in understanding material properties and
will be explained in detail later.
2.1.1 Ductile Metals
In the first part of this lab, the tensile strength of a ductile metal was tested. There are
two types of deformation, elastic and plastic. Elastic deformation is non-permanent and
can be recovered, like a rubber band bouncing back after it has been stretched. Plastic
deformation is permanent and non-recoverable distortion. Ductile metals are metals that
are capable of plastically deforming a measurable amount before rupture. For
reference, Shigley’s Mechanical Engineering Design [1] classifies the lower region for
ductility to be 5.0% elongation. It is important to note that Ductility can be measured as

10. 10
a reduction in a sample’s length (% Elongation) or as a reduction in its cross-sectional
area (% Area Reduction). Ductile metals typically begin to “neck” during a tensile test.
Necking is a reduction in local cross-sectional area where large amounts of strain have
localized. The equations for calculating these two types of ductility are shown below in
Equations 2.1 and 2.2 respectively.
% Elongation =
LF − LO
LO
× 100 2.1
% Area Reduction =
AF − AO
AO
× 100 2.2
Strain is a measure of how much a material deforms in the direction of an applied load.
Strain is a unitless number and is typically plotted along the x-axis in a Stress-Strain
curve. For ductile metals, strain values are typically very small fractions of the
specimen’s overall length. The strain produced in a tensile test is closely related to %
Elongation and is determined with Equation 2.3.
ε =
LF − LO
LO
2.3
Another important measurement for tensile testing is engineering stress. Engineering
stress is a measure of the internal forces experienced in a material under load.
Engineering stress is usually graphed along the y-axis in a Stress-Strain curve. The
equation for calculating engineering stress is displayed below in Equation 2.4.
σ =
F
AO
2.4
It is important to note here that there also exists a value known as True Stress. True
stress is the same as engineering stress except that it accounts for changes in stress
due to a reduction in a sample’s cross-sectional area from necking. Engineering stress
is more commonly used than true stress since metals can withstand large amounts of
stress before they begin to deform. Now the Stress-Strain Diagram can be introduced.
Shown below in Figure 2.2 is an example Stress-Strain diagram for a ductile metal [5].

11. 11
Figure 2.2 Example Engineering Stress-Strain diagram for ductile metal. [5]
This is a typical Stress-Strain diagram for a ductile metal with many of the key features
marked with blue dots. The first key feature, marked by the letter “A”, is the proportional
limit. This is the point at which the material exits the linear elastic region. This region is
defined by a linear relationship between stress and strain where only elastic
deformation has occurred. This relation is defined by Hooke’s law which is shown in
Equation 2.5
σ = Eε 2.5
In Equation 2.5, E is the materials Young’s Modulus or Modulus of Elasticity which is the
slope of the linear elastic region and a measure of a materials stiffness. Metals typically
have a high modulus of elasticity as it takes a large amount of stress to deform them.
The next area of note is marked with the letter “B”. Defined as the elastic limit, “B” is the
point at which the material begins to plastically deform. In materials such as ductile
metals there is often a slow transition from linear to non-linear behavior. In these
situations, it is advantageous to define an offset yield point. In Figure 2.2 the offset yield
point is labeled with the letter “y”. It is common practice to define this offset yield point
by creating a line parallel to the linear elastic region of the graph and offsetting it 0.002
in/in (0.2%) from the origin [1]. The yield strength is the stress corresponding to the
calculated yield point. Ductile metals typically exhibit lower yield strengths when
compared with slightly more brittle steel. This is because they are less resistance to
deformation. Another point of interest is “u”. This point is the ultimate or tensile strength.
It is the point of maximum engineering stress and is the point at which the specimen
begins to neck dramatically. Ductile metals are capable of plastically deforming before
rupture and it is the ultimate strength which defines this point where necking to begins.
Ductile metals usually exhibit tensile strengths much higher than their yield strength as
they are capable of plastically deforming a relatively large amount. Point “f” in figure 2.2
is the engineering failure strength. This is the stress value at which the material
ultimately fails. Its is expected that the engineering failure stress is lower that the tensile

12. 12
or ultimate strength. There also exists true failure strength which is typically much
higher than the ultimate strength as it takes necking into account. One more material
property that can be investigated from a stress-strain curve is toughness. Toughness is
total amount of energy that a specimen absorbs during a tensile test. It is the area under
the stress-strain curve and can be calculated from experimental data using a
trapezoidal approximation as shown in Equation.
Toughness = ∑
𝜎𝑘−1 + 𝜎𝑘
2
𝑛
𝑘=1
× (𝜀 𝑘 − 𝜀 𝑘−1) 2.6
Ductile metals usually exhibit higher toughness than brittle materials as they can
plastically deform for much longer which results in longer stress-strain curves and
ultimately more area under the curve.
2.1.2 Thermoplastic
In this lab the Thermoplastic tested was a 3-D printed Polylactic Acid (PLA) specimen.
3-D printing is an additive manufacturing process in which filament is heated and
extruded through a nozzle to be layered in a specific orientation to produce a three-
dimensional geometry. The process produces a brittle, but relatively strong final product
when compared to other thermoplastics. Since brittle plastics do not yield a large
amount before breaking there is no need to define a yield strength when testing these
materials. The main properties of interest when testing brittle plastics are the Young’s
Modulus, Tensile Strength, Toughness, and % Elongation. These properties are
determined in the same manner described in section 2.1.1. Shown below in Figure 2.3
and Table 2.1 is an example of stress-strain curve for a 3-D printed specimen as well as
the tensile test results.

13. 13
Figure 2.3 Example Engineering Stress-Strain for 3-D Printed PLA. [6]
Table 2.1 Example Data from Tensile Test of 3-D Printed PLA. [6]
Looking at the engineering stress-strain curve it is easy to see that the majority of the
curve is in the linear elastic region and there is very little plastic deformation. This is
typical of a brittle material and is what we should expect with our 3-D printed specimen.
The 45-degree roster orientation will be most comparable to our data as that was the
print orientation used in our experiment.
2.2 Hardness
Hardness is a material characteristic and is defined as a materials resistance to
deformation or abrasion. Hardness tests are widely used in industry as they are easy to
conduct and are minimally non-destructive. The most common measure of hardness is
Indentation Hardness. Indentation Hardness is a measure of a materials ability to resist
localized permanent plastic deformation. Indentation Hardness values are obtained by
applying a known load, to a material, through an indenter of known geometry and then
subsequently measuring the permanent depth of indentation in the material. For many
common grades of steel, recognized correlations between hardness data and other
material properties have been developed through experimentation. These relationships
enable engineers and scientists to gather valuable information about a material through

14. 14
a simple hardness test. One of the most valuable relationship is the established
correlation between steel tensile strength and Rockwell hardness. Rockwell hardness is
an indentation hardness scale. Conversion tables for relating Rockwell hardness to
tensile strength as well as other features of the Rockwell Hardness test can be found in
Appendices A.8, A.9 and A.10.

15. 15
Chapter 3: Experimental Procedures
3.1 Procedure for Hardness and Tensile Testing of Steel Specimen
1018 Cold finished steel was used in this part of the experiment. The sample was
provided by The Laboratory Devices Company and was manufactured to tension test
specimen dimensions specified in ASTM E8 [1]. These specified dimensions are located
in Appendix B.1 for reference. A Rockwell Hardness B test was completed prior to
tensile testing. The purpose of the hardness test was to generate an estimate for the
sample’s tensile strength for later comparison to the actual tensile test results. A total of
five hardness measurements were taken at various points along the ½“ diameter shaft
of the test section on the sample. The measurements were taken using a BUEHLER
automated Rockwell test machine. For operating instructions on this device, see the
equipment manual [9]. Basic test specifications for Rockwell B Hardness tests can be
found in Appendix A.9. The hardness test setup is pictured below in Figure 3.1.
Figure 3.1 This is the automated Rockwell Hardness test machine setup.
After five measurements were recorded, they were averaged and corrected by a factor
of +2 to account for the curvature of the sample’s reduced section. More information on
standards for rounding correction factors can be found in Appendix A.8. After the
hardness test was completed, the pre-stretched sample’s test section diameter was
measured with digital calipers. The diameter reading was assumed to have an
uncertainty of 0.0005in with a confidence of 95%. This uncertainty was determined
based on the resolution of the digital micrometer used to take the diameter
measurement. The shaft was then visually inspected to ensure that the sample’s test

16. 16
section was uniform and free of any major imperfections. Two small indentations were
prescribed 2” apart on the test section. These indentations formed the initial gauge
length which served as a reference for measuring the samples elongation after the
tensile test. The apparatus used to prescribe the 2” gauge length on the test section is
shown below in Figure 3.2.
Figure 3.2 This is the gauge length indenter apparatus.
The next step was to begin the setup for the Tensile test. The test was conducted
following the guidelines described in ASTM E8 [1]. To conduct the test, the sample was
placed inside of a SATEC, Universal Test Machine. The top of the sample was placed
into the upper jaws of the UTM until the sample’s grip section was even with the end of
the jaws. The upper jaws were hand-tightened until snug. Then, the lower portion the
UTM was raised until the table was level with the top of the lower grip section of the
sample. The lower jaws were then hand-tightened until sung. An extensometer was
then fitted approximated in line with the prescribed gauge length on the test section of
the sample. Both the extensometer and the UTM were connected to DAQ system which
recorded the stress, strain, elongation, load, position, and time. Before beginning the
test, a small amount of pre-tension was manually applied, through the hydraulic system,
in order to remove any slack present in the jaws. Next, an extensometer was fitted to
the test section of the sample approximately in line with the gauge length that was
previously inscribed on the sample. The extensometer was connected to a DAQ system
on a nearby computer to accurately measure the strain during the beginning of the
tensile test. The UTM with the sample inserted and extensometer attached is pictured
below for reference in Figure 3.3.

17. 17
Figure 3.3 This is the Universal Test Machine with sample inserted and extensometer in place.
The tensile test was then conducted quasi-statically at a position rate of 0.1 in/min.
During the test, the extensometer was removed at a pre-determined strain of 0.07 in/in
in order to prevent inaccurate readings and potential damage that could incur on the
extensometer during sample failure. After the extensometer was removed, the
remainder of the test’s strain measurements were recorded by the UTM’s internal
position sensor. Once the tensile test was completed the sample was removed and the
elongation of the gauge length as well as final test section diameter were measured
using digital calipers.
3.2 Procedure for Tensile Testing Thermoplastic Material
For this portion of the experiment a 3-D printed PLA sample was tested. The sample
was printed on a FlashForge Creator 3 Pro. 1.75mm Hatchbox PLA was utilized for the
print. The print was conducted with an infill setting of 100%, layer height of 0.2mm,
nozzle temperature of 215°C, and bed temperature of 60°C. The layers were printed in
alternating 45-degree angles. The sample had a rectangular cross-section. The test
section was measured with digital calipers and had a width of 0.500in and a height of
0.246in. The tensile test was conducted in accordance with ASTM-D638 [2] test
methods. Prior to the test, the width and height of the sample’s rectangular cross
section were measured using digital calipers. A gauge length of 2” and 3” were also
prescribed on the test section before the tensile test. The overall length of the sample
was also measured during this time. The same Universal Test Machine and

18. 18
extensometer used in Section 3.1 were utilized for this portion of the experiment. The
sample was loaded into the UTM in same manner as the steel sample described in the
previous section. The tensile test was conducted at a position rate of 0.1 in/min with a
pre-determined extensometer removal at a strain of 0.03 in/in. All the experiments strain
data was recorded through the extensometer as the sample failed with the
extensometer still attached. After the tensile test was completed the sample’s final
gauge and overall length were measured using digital calipers.

19. 19
Chapter 4: Results and Discussion
Table 4.1 below displays the results from the automated Rockwell Hardness test
machine. The table used to determine the curvature correction factor can be found in
Appendix A.8.
Table 4.1 1018 CF Steel HRB Hardness Test Results.
1018 CF Steel HRB Hardness Test Results
Unadjusted Radius of Curvature Corrected
92.5 94.5
92.7 94.7
91.7 93.7
92.4 94.4
92.6 94.6
Average = 92.4 Average = 94.6
Our average corrected Rockwell hardness value of 94.6 is very high for 1018CF steel. A
flat 1018 CF steel specimen is typically expected to have a Rockwell B hardness of 71
[8]. Our value of 94.6 is more in line with what would be expected from a higher carbon
content or tempered steel. It is possible that our sample contained more than the
specified 0.18% Carbon, but more experimentation would be needed to determine that.
It is also possible that there was some bias present in the automated HRB test machine.
Table 4.2 shows the predicted tensile strength from the corrected average HRB. The
table used to determine this value can be found in Appendix A.10.
Table 4.2 1018 CF Steel HRB Predicted Tensile Strength.
1018 CF Steel Predicted Tensile Strength from HRB Hardness
98,000 PSI
As with the HRB value, this predicted tensile strength is also higher than the
manufacturers specified tensile strength of 82,000psi [7]. This makes sense as the
predicted tensile strength is directedly related to the measured hardness value, so if the
hardness value is high the predicted tensile strength will also be high.

20. 20
Table 4.3 displays the results from the 1018CF Steel Tensile Test.
Table 4.3 1018 CF Steel Tensile Test Results.
1018 CF Steel Tensile Test Results
Ductility
(FromCaliperMeasurement) 18.1%
Ductility
(FromStrainData) 15.89%
% AreaReduction 57.6%
0.2% YieldStress(PSI) 87,909
Tensile Strength(PSI) 92806.7 ± 333
EngineeringFracture Stress(PSI) 61,848.0
True Fracture Stress(PSI) 146,013.0
Toughness(in‫﮲‬ lbf‫﮲‬ in-3
) 13,125.7
Young's Modulus (PSI) 30250868 ± 749920
Details for the calculations of these values can be found in Appendix A.1-7 as well as
A.11. The % Elongations as measured with calipers was higher than the % Elongation
from the experimental strain values. This could be due to human error in measurement
and the fact that the strain values were offset based on a linear trend line fit.
Calculations as well as an explanation for why this correction was necessary can be
found in Appendix A.1. The 15.89% ductility from the strain measurements fits well with
expected material database values of 15% [8]. However, the % Area reduction of 57.6%
was larger than expected values of 40% [8]. This could be due to a local imperfection
such as a void or crack that allowed stress to concentrate right before fracture.
However, all the ductility values still classify our sample as a ductile metal. The
calculated 0.2% yield stress was much higher than the expected values of 70000psi [7]
for 1018 CF Steel. This higher yield stress is consistent with our hardness values and is
another indicator of the possibility of a higher carbon %. The measured tensile strength
of 92806.7 ± 333 was also larger than the manufacturer stated 82,000psi [7]. The tensile
strength was also much larger than the 0.2% yield which indicates a relatively large
plastic deformation range. This is another reinforcement that our specimen was quite
ductile. The engineering stress at fracture was lower than the tensile strength as
expected which is an indicator of a reduction in cross-sectional area. The Young’s
Modulus was consistent with expectations of (~29,000,000psi [8]). This means that our
sample had a typical resistance to elastic deformation, but a higher than usual
resistance to plastic deformation with a large plastic deformation range. Overall, it
seems as if our sample behaved more like a higher carbon content, tempered steel,
rather than cold finished 1018.

21. 21
The stress-strain diagram developed from the 1018CF steel tensile test is shown in
Figure 4.1. This shape of the stress-strain curve was consistent with what was outlined
in theory section 2.1.1. Only a small portion of the curve is elastic. There is no definite
yield point, only a single peak stress value, and a long tail end until failure. This stress-
strain curve indicates a sample capable of absorbing a large amount of energy which is
a typical material property of ductile metals. It also shows a large plastic deformation
range as most of the strain occurred after the peak tensile strength.
Figure 4.1 1018 CF Steel Tensile Test Stress-Strain Plot.
Table 4.4 below displays the results from the PLA tensile test. The calculations for these
results are described in Appendix A.1-7 as well as A.11.
Table 4.4 3-D Printed PLA Tensile Test Results.
PLA Tensile Test Results
Ductility
(FromStrainData) 1.96%
Tensile Strength(PSI) 5,818.7
Toughness(in‫﮲‬ lbf‫﮲‬ in-3
) 64.5
Young's Modulus(PSI) 363957 ± 1417
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600
Stress(PSI)
Strain (in/in)
1018CF Steel Tensile Test Stress-Strain Plot

22. 22
As expected, the 3-D printed PLA exhibited material properties consistent with a brittle
plastic. The 1.96% Elongation was consistent with the expected result of 2.50% [6]
obtained from a similar tensile test conducted at South Dakota State University. Our
tensile strength of 5,818.7 PSI was lower than the reference value of 9286.7 PSI [6].
This discrepancy is most likely due to difference in the PLA filament and print settings.
The specimen used in the South Dakota State University PLA tensile test [6] was
printed at with a 15°C greater nozzle temperature and 5°C greater bed temperature with
single rather than alternating 45° raster orientation and an unspecified filament brand.
The modulus of elasticity was also lower than the expected value of 522136 PSI [6].
Again, this discrepancy is also likely due to differences in specimen printing properties.
Figure 4.2 below shows the stress-strain graph generated from the PLA tensile test
data. This plot is typical of a very brittle material. The majority of the curve is linear
elastic illustrating that there was very little plastic deformation. There is no clear yield
point nor is it possible to apply the 0.2% yield method. The peak stress value is located
where fracture occurs, indicating little to no reduction in cross sectional area and
therefore very low ductility. It is clear that the PLA was not able to absorb much energy
as the stress-strain curve has a gentle slope, is almost entirely linearly elastic, and
fractures at a relatively low strain.
Figure 4.2 3-D Printed PLA Tensile Test Stress-Strain Plot
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
0.0000 0.0025 0.0050 0.0075 0.0100 0.0125 0.0150 0.0175 0.0200
Stress(PSI)
Strain (in/in)
PLA Tensile Test Stress-Strain Plot

23. 23
4.1 Comparison of 1018CF Steel and PLA Tensile Test Results
The 1018CF exhibited over seven times greater ductility than the 3-D printed PLA
specimen. The steel also had a much larger tensile strength and modulus of elasticity.
These three material properties together enabled the steel sample to absorb a huge
amount of energy when compared to the PLA specimen. This is evident in the materials
toughness values. One advantageous behavior for the PLA was that it was linearly
elastic for the majority of the tensile test. This means that it may be possible to
continuously load 3-D printed PLA parts to a high percentage of their ultimate tensile
strength and not damage the part. This could be a valuable material behavior and is not
possible for steel as permanent deformation occurs well before the ultimate tensile
strength.

24. 24
Chapter 5: Conclusion
Our 1018 cold finished steel sample exhibited a higher hardness, ductility, modulus of
elasticity, yield stress and tensile strength than specified by the manufacturer[7] and the
literature[8]. This leads to the conclusion that there must have been some error
introduced into the experiment. Possible sources of error could include equipment
calibration, a higher carbon content than specified, and tempered treatment instead of
cold finishing. It is also possible that our sample was simply at the upper limits for the
1018CF steel specifications as all the manufacturer and literature values referenced are
averages. The predicted tensile strength (98000 psi) from hardness testing provided a
reasonable estimate of actual tensile strength (92806.7 psi) but should not be solely
relied upon when the tensile strength must be known to high degree of certainty. It is
also a point of concern that the predicted hardness was an overestimate of the actual
value as underestimating tensile strength is typically a safer design practice as it leads
to higher factors of safety. From a practicality perspective the hardness predicted tensile
strength is an attractive measurement method because it is a non-destructive test and is
therefore less expensive and easier to conduct that a tensile test. It should also be
noted that Hardness tests cannot account for any internal material imperfections that
may affect tensile strength as the test only indents the outer surface of the material. The
3-D printed PLA sample had a ductility value (1.96%) similar to those found in literature
(2.50%) [6]. However, the tensile strength and young’s modulus results were lower than
comparable values found in literature [6]. I believe these discrepancies are justifiable as
different PLA filaments and printer settings were used in the reference literature which
would have affect over material performance during tensile testing.

25. 25

26. 26
Bibliography
[1] ASTM International. (2008). ASTM E 8/E 8M - 08: Standard Test Methods for
Tension Testing of Metallic Materials. In Annual book of ASTM standards 2008.
West Conshohocken, PA: American Society for Testing and Materials.
[2] ASTM International. (2008). ASTM D 638 – 02a: Standard Test Methods for Tensile
Properties of Plastics. In Annual book of ASTM standards 2008. West
Conshohocken, PA: American Society for Testing and Materials
[3] Budynas, Richard, and J.Keith Nisbett. Shigley's Mechanical Engineering Design.
10th ed., McGraw-Hill Education, 2015.
[4] Callister, William D., and David G. Rethwisch. Fundamentals of Materials Science
and Engineering: an Integrated Approach. John Wiley & Sons, Inc., 2019.
[5] “Stress-Strain Diagram.” Engineeringarchives.com, Engineering Archives, n.d.
Web. 22 Jan. 2020.
[6] Letcher, Todd & Waytashek, Megan. (2014). Material Property Testing of 3D-
Printed Specimen in PLA on an Entry-Level 3D Printer. ASME International
Mechanical Engineering Congress and Exposition, Proceedings (IMECE). 2.
10.1115/IMECE2014-39379.
[7] "Material List." Laboratorydevicesco.com. Laboratory Devices Company, n.d. Web.
06 Jan. 2017.
[8] “AISI 1018 Steel, Cold Drawn”, MatWeb.com. MatWeb Material Property Data. n.d.
Web. 21 Jan. 2020.
[9] BUEHLER MACROMET 3100 TWIN TYPE, BUEHLER Ltd. Lake Bluff, IL, United
States, 05 Aug. 2000. Web. 25 Jan. 2020. Available:
https://www.mse.iastate.edu/files/2011/07/Manual-for-BUEHLER-Hardness-
Tester.pdf
[10] "Test Specimens." Laboratorydevicesco.com. Laboratory Devices Company, n.d.
Web. 06 Jan. 2017

27. 27
Appendices
Appendix A
This appendix contains all the necessary calculations and literature for this experiments
results.
A.1 Stress-Strain Data Correction
Due to deformation in the Universal Test Machine’s jaws there was error in the data
collected during the initial loading in both tensile tests. Therefore, it was deemed
necessary to remove the inaccurate initial data and then correct all plot to pass through
origin. The correction factors are shown below in Table 5.1. These same correction
factors were applied in the 0.2% yield calculations, elongation calculations, toughness
calculations and the final stress-strain graphs.
Table 5.1 Strain Correction Factors to Shift Stress-Strain to pass through origin.
Strain Correction Factors Due to Error in Initial Data
1018 CF Steel Shifted Left by 0.000513 in/in
PLA Shifted Right by 0.000293 in/in
A.2 Young’s Modulus Calculation
As stated in Theory section 2.1.1 of this report the Young’s Modulus can be defined as
the slope of the linear elastic region of a stress-strain graph. To determine the Young’s
Modulus for the 1018CF Steel and PLA the linear elastic regions of the stress-strain
curves needed to be determined. To find these regions a linear trend line was fitted the
experimental data in excel. Portions of data were then subsequently thrown out until the
highest R2 correlation was achieved. The slope of the resulting linear trend line is the
materials Young’s Modulus. These plots are shown in Figure 5.1 and Figure 5.2.

28. 28
Figure 5.1 Linear Elastic Region of 1018CF Steel Stress-Strain Curve with Linear Trend Line for
Calculating Young’s Modulus.
Figure 5.2 Linear Elastic Region of PLA Stress-Strain Curve with Linear Trend Line for Calculating
Young’s Modulus.
y = 30,250,868x - 0
R² = 1
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
0.00000 0.00025 0.00050 0.00075 0.00100 0.00125 0.00150
Stress(PSI)
Strain (in/in)
Trend Line Fit of Linear Elastic Portion of 1018CF Steel
Stress-Strain Curve
y = 363,958x + 0
R² = 1
0
500
1000
1500
2000
2500
3000
3500
0.00000 0.00200 0.00400 0.00600 0.00800 0.01000
Stress(PSI)
Stress (in/in)
Trend Line Fit of Linear Elastic Portion of PLA Stress-
Strain Curve

29. 29
A.3 1018 CF Steel 0.2% Yield Calculation
As previously stated in Theory section 2.1.1 of this report, for ductile metals that do not
exhibit a clear yield point it is often necessary to define a 0.2% yield. For this
experiment the graph shown below in was used to determine the 0.2% yield strength for
the 1018 CF Steel specimen. The graph was created by offsetting the trend line fit from
the linear elastic region to the right by 0.002in/in.
Figure 5.3 This is the 1018CF Steel 0.2% Yield Graph.
A.4 Tensile Strength and Engineering Stress at Fracture
The reported Tensile Strength for both the 1018CF Steel and the PLA was the
maximum engineering stress value present in that specimen’s experimental data. The
reported engineering stresses at fracture for both tensile tests were also determined
from the experimental data. No calculations were necessary to determine these values
as the UTM’s data acquisition system used in this lab automatically calculated stress
values and printed them to an excel file. However, the equation the program used to
calculate these stress values can be found in Equation 2.4 in the theory of this report.
y = 30,250,868.35x - 60,501.74
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
110000
0.00000 0.00100 0.00200 0.00300 0.00400 0.00500 0.00600 0.00700 0.00800
Stress(PSI)
Strain (in/in)
1018CF Steel 0.2% Yield Line
Experimental
Stress/Strain Data
0.2% Yield Line

30. 30
For tensile strength, a simple column maximum function on the stress data column was
used in excel to locate the highest stress value. The engineering stress at fracture was
determined by selecting the stress value corresponding with the maximum corrected
strain value before rupture. Some example data from the data acquisition system is
shown below in Figure 5.4 for reference.
Figure 5.4 Example of Raw Data printed to Excel from the data acquisition system on the UTM and
Extensometer.
A.5 Ductility (% Elongation and % Area Reduction) Calculations
Equation 5.1 is the calculated % elongation ductility from caliper measurements.
Equation 5.2 is the % elongation ductility for the 1018CF Steel calculated from the
maximum corrected extensometer strain measurement. Equation 5.3 is the %
elongation ductility for the PLA calculated from the maximum corrected extensometer
strain measurement. Equation 5.4 is the % area reduction ductility for 1018CF Steel.
(%EL)Ductility1018 =
LF − LO
LO
× 100 =
2.3625 − 2.000
2.000
× 100 = 18.1% 5.1
(%EL)Ductility1018 = εmax × 100 = 0.15839802 × 100 = 15.89% 5.2
(%EL)DuctilityPLA = εmax × 100 = 0.01960445 × 100 = 1.96% 5.3
(%AR)Ducitlity1018 =
AF − AO
AO
× 100 = 57.6% 5.4

31. 31
A.6 True Stress at Fracture
Equation 0.5 is the true fracture stress for the 1018CF Steel Specimen.
𝜎𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒 =
𝐹𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒
𝐴 𝐹
=
12412.9
𝜋0.3292
3
= 146013.0 PSI
5.5
A.7 Toughness
Toughness was calculated in the same manner for both PLA and 1018CF Steel.
Equation 0.6 was used to calculate the theoretical area under the curve during the initial
loading in which inaccurate data was removed. It is an integration of the equation for the
linear trend line fit from the linear elastic region of each materials stress-strain plot.
Equation 0.7 is a trapezoidal area approximation and was used to determine the
remaining area under the stress-strain curve. The results from Equations 0.6 and 0.7
where then added together to yield a final toughness value for each material.
Toughness = ∫ 𝐸𝜀
𝜀2
𝜀1
dε =
𝐸
2
𝜀2
|
𝜀2
𝜀1
=
𝐸
2
(𝜀2 − 𝜀1)2
5.6
Toughness = ∑
𝜎𝑘−1 + 𝜎𝑘
2
𝑛
𝑘=1
× (𝜀 𝑘 − 𝜀 𝑘−1) 5.7

32. 32
A.8 Hardness Curvature Correction
Pictured below in Figure 5.5 are the cylindrical correction values for rounded hardness
test specimens. This correction is necessary as hardness values are will normally be
lowered if the test surface is curved as it is easier to penetrate curved surfaces and the
Rockwell Hardness test values are designed for flat surfaces. This table is in
accordance with ASTM E18-61. The chosen correction value is highlighted in yellow.
Figure 5.5 Curvature correction values for Rockwell hardness tests.

33. 33
A.9 Rockwell Hardness B Test Specifications
Pictured below in Figure 5.6 are the HRB penetrator dimensions and geometry as well
as the specified test force. The chart was retrieved off the BUEHLER, model number
1800-5202, automated hardness test machine located in the Lab Building, Room 118.
Figure 5.6 These are the HRB Test Specifications.

34. 34
A.10 Table for estimating Tensile Strength from Rockwell Hardness
The Table show below in Figure 5.7 was provided by our lab instructor and used to
predict the Tensile Strength of the 1018CF Steel specimen from its Rockwell B
Hardness value.
Figure 5.7 Table used for estimating Tensile Strength from Rockwell Hardness value.

35. 35
A.11 Uncertainty Calculations
Figure 5.8 shows the calculations for 1018 CF Steel Tensile Strength and Modulus of
Elasticity uncertainties with a confidence of 95%.
Figure 5.8 1018 CF Steel Tensile Strength and Modulus of Elasticity uncertainty calculations.

36. 36
Figure 5.9 show the calculations for the uncertainty in the PLA’s Modulus of Elasticity
with a confidence level of 95%.
Figure 5.9 3-D Printed PLA Modulus of Elasticity uncertainty calculations

37. 37
Table below shows the assumed measurement uncertainties for this experiment. These
values were provided by our lab instructor.
𝜔 𝐹 Uncertainty of 0.30% of the force reading
𝜔𝜀 Uncertainty of 0.00001 in/in
𝜔 𝑑,ℎ,𝑏 Uncertainty of 0.0005in
Appendix B
B.1 1018CF Steel Manufacturer Specified Dimensions
Figure 5.10 1018CF Steel Tensile Test Specimen Dimensions