On July 21, 2010, I went into the Materials Science and Engineering Lab with Dan Satko, a post-graduate student who also works within Drexel's Mechanics of Microstructures Group. There I was able to observe Dan perform a compression test on a titanium cylinder. Pictures from throughout the course of the experiment can be found below.
^{2}. At the end of the experiment, the cylinder's new length measured 5.587 mm with a cross-sectional area of 25.589 mm^{2}. My plan was to create a mathematical model that described the displacement of the cylinder in relation to the force applied to the cylinder, while simultaneously correcting for any errors/adjustments within the compression device. In effect, what I created after graphing this model was a common materials engineering analytical tool known as a "stress-strain" curve, where stress measured the force in Newtons applied against the cross-sectional area of the cylinder, and strain measured the percentage of change in length as the cylinder was continuously compressed. 1. To prove that the graph of my stress-strain curve displayed the known Young's Modulus for the element of titanium (which is approximately 110 GPa). 2. To prove that the the "unload modulus" of my graph was identical to the Young's Modulus due to elastic recovery after any plastic deformation may have occurred. 3. To prove that the final strain measurements in my curve corresponded with the logarithmic formula for the true strain of the original and final lengths of the cylinder. |

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