1st_assignment_solution - The University of Michigan...

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The University of Michigan - Dearborn Industrial and Manufacturing Systems Engineering Department IMSE 382: Manufacturing Processes I Assignment # 1 Mechanical Properties of Materials Solution 1. The following data were obtained during a tensile test of a standard specimen made of brass. D o = 12.50 mm, L o = 50.00 mm. Load and length readings are as follows: _ Load (N) Length (mm) Load (N) Length (mm) Load (N) Length (mm) 2,495 50.01 12,760 50.075 37,860 77.500 6,760 50.025 13,020 50.10 26,240 83.000 10,820 50.04 13,610 50.150 12,340 50.05 30,510 57.500 Ultimate Load = 42,090 N, and D f =6.25 mm, L f = 83.00. Determine the following: 1. Proof strength (using 0.2 % ) Load (N) Length (mm) A0 (mm^2) Eng Stress (MPa) Eng Strain True Stress (MPa) True Strain Comment 2,495 50.01 122.718438 20.33109328 0.0002 20.3351595 8.685E-05 6,760 50.025 122.718438 55.08544712 0.0005 55.11298985 0.00021709 10,820 50.04 122.718438 88.16931034 0.0008 88.23984579 0.0003473 12,340 50.05 122.718438 100.5553872 0.001 100.6559426 0.00043408 12,760 50.075 122.718438 103.9778558 0.0015 104.1338226 0.00065095 13,020 50.1 122.718438 106.0965269 0.002 106.3087199 0.00086772 13,610 50.15 122.718438 110.9042804 0.003 111.2369932 0.00130093 30,510 57.5 122.718438 248.6178982 0.15 285.9105829 0.06069784 42,090 122.718438 342.980247 Necking starts 37,860 77.5 122.718438 308.5110988 0.55 Unknown Unknown Unknown dia 26,240 83 122.718438 213.8228007 0.66 855.2912027 0.60205999 Use Df 1
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0 20 40 60 80 100 120 0 0.001 0.002 0.003 0.004 0.005 Engineering Strain Engineering Stress (MPa) From the above figure, proof strength 2245 111 MPa 2. Ultimate Tensile strength UTS = (Ultimate load)/A 0 = (42090)/122.72 = 343.0 MPa 3. Modulus of elasticity E = slope in the elastic region = (55.09 – 20.33) / (.0005 - .0002) = 115.9 GPa 4. Percentage elongation EL % = (Lf-L0)/Lo * 100 = (83 – 50)/50 *100 = 66 % 5. Modulus of toughness Toughness = area under the σ- ε curve 2245 2/3 * (UTS+YS) * EL = 2/3 * (343.0 + 111) * .66 = 199.8 MPa = 199.8 MJ / m 3 6. True stress true strain at ultimate load True Stress
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