metals vs. plastics. results to given.
**tensile strength-max force withstood. and tensile elongation..
Sample Calculations
All values (stress, strain, and modulus of elasticity) were obtained from data studio software.\
Stress:
𝜎=
𝐹𝑜𝑟𝑐𝑒 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎
𝑃
=
𝐶𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐴𝑟𝑒𝑎
𝑙∙𝑤
𝑃
𝜎 = 𝑙∙𝑤 = ??
The cross sectional area for all plastic samples was 2.482 mm2.
There were two brass samples, one with 0.303 mm2 cross-section and the other with 0.506 mm2
cross-section. The cross sectional for all other metals specimens was 0.303 mm2.
Strain:
𝜀 =
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐿𝑒𝑛𝑔𝑡ℎ
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐿𝑒𝑛𝑔𝑡ℎ
=
∆𝑙
𝑙𝑜
Modulus of Elasticity:
𝑆𝑡𝑟𝑒𝑠𝑠
𝐸 = 𝑆𝑡𝑟𝑎𝑖𝑛 =
𝜎
𝜀
In this case the modulus of elasticity is the slope of the linear regression of the linear region of
the stress-strain curve.
Discussion
Table 1 displays the expected Modulus of Elasticity of the plastic samples. The Modulus of
Elasticity for each experimental value differs from the expected by at least half. For example, the
modulus of elasticity for the white plastic was expected to be about 1900MPa, but the result
obtained from the experiment was 458±9.6MPa. The black plastic was expected to have a
Modulus of elasticity of 2900MPa. The experimental value for this was 936±7.6MPa. This trend
is repeated for the orange and blue plastic samples. One of the reasons for such large deviation is
because the force was measured at the sensor?? rather than along the line where the force was
actually applied. Another reason could be because when placed between the clamps, the samples
may have slightly slipped which would affect the results. All the plastic samples in this
experiment broke except for the white plastic, even though the orange plastic had a higher tensile
elongation. Figure 1 displays the stress-strain curve for the black plastic. The linear portion of
the stress strain curve, known as the modulus of elasticity, displays a slope of 931.68 MPa. This
value can be compared to the known value for this sample which is 2900 MPa. These values are
quite different which shows that there was some error in the experiment. However, as informed
by the laboratory instructor, the range for modulus of elasticity is very large.
Table 2 displays the expected modulus of elasticity of metal samples. Just like the plastic
samples, the modulus of elasticity for the metal samples differs from the expected by at least half
the value. If the thick brass was taken as an example, the experimental value was
63600±2100MPa while the expected value was 117000MPa. The reasons for this error are the
same as the ones stated above. The same pattern occurs in the other metal samples. The thick and
thin brass was expected to have the same modulus of elasticity. The thin brass had a modulus of
71400±2000MPa. The percent difference between the thin and thick brass is 11.6% which is a
reasonably small and indicates that the values are similar to each other.
Comparing the plastic and metal samples, it can be observed that the metal samples have a much
higher modulus of elasticity. The metal sample values are higher than the plastic samples by at
least 50 times.
given a range?!
Conclusion
The objective of the experiment was…
The modulus of elasticity, obtained from the slope of the linear region of the stress-strain graph,
is a property that can be used to characterize materials.
Eight specimens of various plastics and metals, nine samples with two brass thicknesses,
underwent the stress-strain tensile test performed using the Pasco stress strain apparatus.
DataStudio software collected the data and produced a stress vs. strain graph for each sample.
From prior knowledge, the modulus of elasticity is the slope of the linear region of a stress strain
graph. Via DataStudio, each modulus of elasticity was found by applying a linear curve fit to the
selected data for each sample.
In general the tensile strength and modulus of elasticity of metals are larger than those of the
plastics. The thick and thin brass samples have a comparable modulus of elasticity value, as
expected. Overall, however, the modulus of elasticity for each sample was less than half of the
expected values provided in the Pasco stress strain apparatus instructions manual. List values?
The tensile strengths were…. comparable to the expected values??
The percent error of the experimental value from the expected or theoretical value??
Possible errors that contributed to the large deviation in the experimental and expected modulus
of elasticity values include sample slipping while the tensile for was being applied, measurement
uncertainties within the Pasco stress strain apparatus, the age of the sample….??
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Reference
Pasco Stress Strain Apparatus Manual. 2012.