1
Results
The resulting data from the compression tests
for Cast Iron, 1045 Steel (Normalized), 6061
Aluminum, and PMMA is used to construct
graphs showing the relationship between
engineering stress and engineering strain.
These graphs are then used to determine the
following
mechanical
properties:
the
modulus of elasticity (E), yield strength (
s
!
),
and ultimate strength (
s
"
). Fitting a linear
trendline to the data points corresponding to
the linear elastic region will give the modulus
of elasticity, which is the slope of the best fit
line, seen in Figure 1 for 6061 Aluminum.
Figure 1:
Best fit line of elastic region to obtain
the modulus of elasticity for 6061 Aluminum.
Once Young’s modulus (E) is obtained, the
yield strength is determined by using a 0.2%
offset yield line with the equation
y = Ex + C
(1)
where the constant C is found by using the
initial point (0.2, 0). This line is graphed onto
the stress-strain curves for each specimen,
and the intersection of the offset line and the
curve is defined to be the yield strength. This
process is demonstrated in Figure 2, showing
the yield strength of . As for the ultimate
strength of 6061 Al, the Instron machine
stopped before the material failed, ending the
test when it reaches its maximum load;
therefore, the ultimate yield strength cannot
be determined by simply looking at the
stress-strain plot (Figure 3).
Figure 2:
Stress as a function of strain for 6061
Aluminum in the linear elastic region.
Figure 3:
Tensile and compressive stress-strain
plot of 6061 Al.
The ultimate strength can be determined by
analyzing the plot of stress as a function of
strain, which is shown in Figure 4. Note that
the compressive stress vs. strain curves are
negative due to negative loads being applied
while tensile stress-strain curves are positive.
The modulus of elasticity and yield strength
are
obtained
using
the
same
methods
aforementioned. Similar to 6061 Aluminum,
Cast Iron and 1045 Steel did not reach
ultimate strength. The stress vs. strain curves
of each material are presented in Figures 4-9.
Because the extensometer was omitted from
the testing of PMMA, stress is plotted as a
function of position, or extension, rather than
the
strain
(“Lab
2:
Compression
and
Hardness Tests”).
y = 643.54x - 3.9536
R
²
= 0.9966
-300
-250
-200
-150
-100
-50
0
-0.46
-0.36
-0.26
-0.16
-0.06
Stress (MPa)
Strain (%)
-350
-300
-250
-200
-150
-100
-50
0
50
-2
-1.5
-1
-0.5
0
0.5
Stress (MPa)
Strain (%)
y = 643.54x + 128.708
-475
-375
-275
-175
-75
25
125
225
325
-15
-5
5
15
25
Stress (MPa)
Strain (%)
s
!

2
Figure 4:
Stress vs. position curve of PMMA.
However, when finding the yield strength
using the 0.2% offset line, stress is analyzed
with respect to strain instead of position
(Figure 5).
Figure 5:
Stress-strain curve of PMMA in
elastic region.
Figure 6:
Stress vs. strain of Cast Iron.
Figure 7:
Elastic region of stress-strain curve of
Cast Iron.
Figure 8 shows the true stress-strain curve
imposed on the engineering stress-strain
curve of 1045 Steel. The true stress (
s
#
) and
true strain (
e
#
) are calculated using the
following equations:
s
#
=
s
(1 +
e
)
(2)
e
#
= ln (1 +
e
)
(3)
where
s
is the engineering stress and
e
is the
engineering strain.