Rafael Torres Rodriguez
MECH 15 Lab
Section 27680
Lab #3 (Tensile Test)
Abstract
In this lab we explore the change in metal properties subjected to different annealing conditions.
In this experiment it was found that as the temperature of annealing increases so does the average
grain size of the specimen. As the grain size increases the yield strength of the specimen
decreases. We found that this causes the ductility of the specimen to increase. The increase in
grain size was found by using the Hall-Petch equation and the activation energy (135kJ/mol) that
was found from the Arrhenius plot of the specimen. The decrease in yield strength was found by
creating a yield strength versus 1/√d plot. Lastly, the ductility increase was found by comparing
the two engineering stress vs engineering strain plots of the annealed and unannealed specimens.
Introduction
The purpose of this lab is to analyze and explain stress versus strain curves of the copper
alloy when it is subjected to different conditions. In our lab we will be using data given to us
since we can not do it in person. From this data we will analyze the problems that come up when
we try to measure this type of data. In an ideal test, to obtain the data we would attach the alloy
to an extensometer or stain gauge. If we were in person for this lab we would not be able to use
this type of device, instead we would use a coarser displacement measurement to obtain the data.
After analyzing this data we will analyze the grain size of several copper alloys. We will relate
this data to the stress vs strain curves we observed in the first half of the lab. To determine the
grain size of the alloys one has to do measurements on their micrographs. In this lab we will use
the intercept technique to determine the grain size. It has to be noted that it is hard to identify the
grain boundaries so this may affect our analysis.
Approach
Testing Apparatus And Procedure Details:
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Machine Manufacturer: Instron
➢
Model Number:3369
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Load Cell Capacity:50 KN
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Displacement Rate: 10mm/min
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Specimen Dimensions: (Thickness = 0.124 inches)
Annealing Conditions:
The specimens that were used in this lab were annealed at temperatures ranging from
450°C to 750°C. These specimens were annealed in these temperatures for 0.5 hours to 64
hours. During annealing the specimens were exposed to oxygen and nitrogen from the air. This
means that the specimens were most likely contaminated by oxygen and possibly nitrogen. This
is noticed by a dark reaction layer on the annealed specimens. For the purposes of this
experiment it is assumed that this layer is thin enough to have negligible impact on the test
results.
Method Of Grain Size Determination:
To determine the grain size of our specimens we use the linear intercept technique. With
this technique we started by tracing the grain boundaries on the micrographs of the specimen that
was provided to us. We then drew 10-15 lines that are equidistant from each other on the
micrograph. After that, we counted how many times each line intersected a grain boundary. For
the final step we determined the total length of the lines we drew by using the distance scale that
was on the micrograph. To find the average grain size we divided the total length of the lines we
found by the total number of grain boundaries intersected. This calculation gave us the average
grain size boundary.
Results and Discussion
The data from the annealed engineering stress vs engineering strain plot was obtained by
using mechanical testing machines to obtain the coarser displacement measurement. There are
discrepancies with this method of measurement because it measures the displacement of the
specimen and the load train. For our experiment we assumed that the displacement measurement
was for our specimen. The machine works by attaching the specimen by its two ends to the two
grips of the machine. When the set up is ready the machine applies tensile stress by displacing
the grips apart from each other at a constant rate. Using this machine for testing can create some
discrepancies on the plastic deformation of the specimen. When the specimen is being loaded on
the machine some plastic deformation is applied to it by several factors, for example when the
grips are attached to the specimen they create plastic deformation as the teeths grapp onto the
specimen. Another cause of discrepancy is that when the test is being performed some slippage
may be possible. For our experiment these discrepancies will be not taken into account as trying
to fix them since it is outside of the purpose of this lab.
From the engineering stress vs engineering strain plot it was found that Young’s Modulus
is equal to 18579.83 ksi. This value does not agree with the reported value in Appendix V
because in this experiment we relied on the coarser displacement measurement. This means that
the displacement reflected both the displacements in the specimen and along the rest of the load
train of the machine. Because of this the initial slope of the graph does not relate to the Young’s
modulus. This is what created a difference between our Young’s modulus and the one provided
by the vendor.
From the engineering stress vs engineering strain plot we can see that after annealing the
ductility of the specimen increased. This is noticed by annealed data taking slightly more strain
before the specimen fractures. From the plot we can also see that the toughness of the specimen
decreased after annealing. This is noticed by the greater area under the unannealed curve
compared to the area under the annealed curve.
Specimen’s Grain Boundaries (Annealed at 550°C for 32 hours)
Average Grain Size determined = 38.27 μm
The activation energy was determined to be 135 kJ/mol which is about 32.27 kcal/mol. The
activation energy for bulk diffusion in Cu is 43.9 kcal/mol. The activation energy associated with
grain boundary diffusion should be close to half of the bulk diffusion value. The activation
energy found from the plot is close to half of the activation energy for bulk diffusion.
Yield Strength vs Grain Size
Yield Strength (MPa)
Grain Size (μm)
62.69
12.698
57.75
18.78
59.28
33.446
55.22
64.67
46
21.17
43
38.74
47.63
75.579
42.55
150.186
35.9
35.72
35.19
69.37
33
137.686
36.09
274.84
From the yield strength versus 1/√d plot we can see a trend that as grain size increases the
yield strength decreases. Looking at the Hall-Petch equation, we can see that since grain size is
on the denominator of the independent variable, as the grain size increases the value of the
independent variable decreases. On yield strength versus 1/√d plot we can see that as the
independent variable decreases so does the yield strength as well.
Conclusion
In this experiment we found that the annealing conditions of our specimens causes
changes in the grain size, yield strength, and ductility. We found that as the temperature of
annealing increases the average grain size increases as well. The increase in grain size causes a
decrease in the yield strength. This causes the ductility of the specimen to increase as the yield
strength decreases. From these results we can determine that annealing of the specimen caused
an increase in ductility that allows us to work with the specimen more easily.
References
● MECH_15L_exercise_3_tensile_test.pdf
● MECH_15L_appendix_vii.pdf
● MECH_15L_appendix_v.pdf