# The linear region of the stress-strain curves

We originally started out with eight samples of 5052 dogbone shaped aluminum. Five of the samples had to be excluded from analysis because of experimental conditions. These five samples were unable to stay in place because of the Instron grips. To combat this, we placed a piece of sandpaper on the bottom grip to increase the friction. We also switched the round grips for a set of grips that could be tightened with a wrench instead of vice grips. Since we had to change our grips in the middle of testing, the data may not be consistent.

The load over time graphs appear relatively similar. This shows that the metal is consistent. In the graphs, the curves were not perfectly smooth, there is an occasional noise that appears. This was due to the dogbone aluminum pieces slipping out of the Instron grips.

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The maximum load had an average of 122.308 pounds with a standard deviation of 2.81094 pounds. The high standard deviation most likely stems from having to switch the Instron grips during the experimental testing.

The ultimate strength was calculated by dividing the maximum load by the cross sectional area prior to testing. The average ultimate strength was 30627.8 pounds per square inch. The 95% confidence interval was calculated to be (30626.4 to 30629.4 psi). The literature value for ultimate strength2 was found to be 33,000 psi. Since the literature value does not fall within our confidence interval, our experimental value is significantly different. This most likely stems from imprecise measurements of cross sectional area or inconsistencies in the Instron grips throughout the testing.

The Young’s modulus was calculated by finding the stress and strain of the elastic regions and calculating the slope. The slope can be used for the Young’s modulus because we are only investigating the linear region of the stress-strain curves. Our average Young’s modulus was calculated to be 329477 pounds per square inch. The 95% confidence interval was calculated to be (310822, 348131). The Young’s modulus of Aluminum 5052 was reported to be 10,200 pounds per square inch based off of our literature value1. This value is significantly different from the literature value. This could stem from incorrect substitution in our calculations. When calculating stress we used the force divided by the original cross sectional area, it may have been better to use the final cross sectional area.

The average cross sectional area for a 50 pound breakaway force was calculated to be 0.00230107 square inches. This is probably relatively small given our average Young’s modulus was so high compared to the literature value. The cross sectional area does make sense with our data because it is less than the original cross sectional area and greater than the cross sectional area after breaking.

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