Lab 2 Report.pdf - 50 Results The resulting data from the...

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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.
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