Tension Test - ME 220 MECHANICS OF MATERIALS LAB Tension...

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Unformatted text preview: ME 220 - MECHANICS OF MATERIALS LAB Tension Test Test: September 13th, 2007 Submitted: September 20th, 2007 Matthew Olsen Section 3 Summary The purpose of the tension test is to determine the strength and inelastic properties of A36 steel and cast iron, and to observe the deformation and fracture behavior of these materials under extreme, slow tensile load. The properties that will be measured or calculated include the stress, strain, true stress, true strain, modules of toughness, elasticity, and resilience, ductility, yield strength, and ultimate strength. The strength of a material can be measured as the maximum tensile load it can hold before fracture. A material that is more ductile can hold more before fracture due to the property of elasticity. The ductile material will stretch much like a spring, even past the point of recovery to withstand the load. A brittle load may not behave similarly. It may be more likely to simply crack rather than deform. To test a material's strength and measure its inelastic properties, a half inch "button-head" round bar will be placed in a tension machine, which will apply a slowly increasing axial load until the bar fractures. Two marks 2 inches apart are made on the bar, and the change in their distance is constantly measured throughout the test. A computer is setup to take data at intervals, recording the load and stretch length at each interval. From this data, all the above listed properties can be calculated, and the behavior of the material can be seen graphically. The following pages outline this information. When testing the A36 steel, the materials extreme ductility became apparent. The material stretched its length 35%, supporting a load of 14,350 pounds before fracturing. The cast iron did not deform any measureable amount, and held only 6,700 pounds. The fracture of the steel occurred only after stretching and necking, a visible process. The point of fracture demonstrated a perfect cup and cone fracture surface. The iron, however, simply cracked. When reassembled, the specimen looks identical to before the test. From these results, it can be seen that A36 is a ductile material, and cast iron is a brittle one. Data and Calculations Following is an abridged table of the collected data, which the calculations and graphs are based upon: P(lb ) s 157 308 395 505 774 965 1294 1596 1834 2064 2242 2486 2740 3002 3545 3749 4033 4321 4611 4913 5218 5446 5758 6075 6381 6707 7030 7352 7591 7913 8237 8556 8876 9138 9456 9923 9439 9308 9087 9266 9277 9317 9235 9303 9469 9685 9801 9852 9899 9972 10016 10214 10427 10566 10657 10781 10805 10888 I-I0 (in ) 0.00005 0.00009 0.00014 0.00019 0.00028 0.00037 0.00046 0.00060 0.00069 0.00074 0.00079 0.00088 0.00097 0.00106 0.00120 0.00130 0.00139 0.00148 0.00157 0.00167 0.00176 0.00185 0.00194 0.00204 0.00217 0.00227 0.00236 0.00245 0.00250 0.00264 0.00273 0.00287 0.00301 0.00305 0.00319 0.00375 0.00532 0.00689 0.00745 0.00851 0.01087 0.04306 0.04302 0.04306 0.04320 0.04389 0.04510 0.04574 0.04648 0.04778 0.04852 0.05273 0.05708 0.05994 0.06073 0.06323 0.06415 0.06651 (lb / in ) s 2 7 9 1 7 7 .7 4 2 1 3 .4 8 5 3 3 9 1 6 .6 3 9 6 1 8 2 1 .4 4 5 2 1 1 3 4 .5 2 8 6 9 6 4 9 .5 7 7 9 7 3 6 3 .9 8 4 6 7 2 7 3 .7 3 9 5 6 1 9 2 .6 2 1 2 6 2 1 2 6 4 0 6 .2 4 1 1 9 2 1 4 .9 1 3 2 1 2 6 .8 1 6 7 8 3 2 .6 1 1 9 7 0 4 2 .2 5 1 6 0 1 7 3 .2 6 1 6 3 4 8 4 .8 5 2 0 5 9 0 5 .9 5 2 4 5 7 1 8 .4 2 2 9 2 7 2 3 .2 6 2 4 1 6 4 3 .0 1 2 9 7 7 5 4 .1 3 2 0 2 9 7 8 .0 1 2 6 2 5 8 3 .8 7 3 2 9 1 0 0 .6 4 3 7 4 8 1 3 .3 9 3 3 4 6 3 5 .4 3 3 9 7 1 4 5 .2 3 5 9 5 6 5 .9 7 3 7 6 5 7 4 .8 6 3 3 9 0 9 4 .6 3 4 9 1 1 0 6 .0 3 4 5 6 3 2 4 .4 3 4 1 0 1 4 4 .5 7 4 4 0 4 5 4 .0 1 4 0 5 6 7 2 .4 1 4 3 7 7 9 4 .2 8 4 9 8 2 6 3 .8 6 4 2 9 6 6 8 .0 4 4 1 8 5 8 .8 4 0 1 4 6 8 .1 4 1 3 2 6 3 .1 1 4 3 2 8 6 3 .3 1 4 9 5 9 5 2 .1 7 4 2 3 7 6 6 .0 3 4 0 6 9 7 8 .9 7 4 1 0 7 8 6 .3 9 4 7 1 5 8 4 .7 6 4 9 2 7 8 9 .0 5 4 2 5 8 9 2 .9 9 4 5 9 5 9 8 .8 6 4 8 6 4 9 0 .4 4 5 7 4 8 0 9 .0 2 5 8 1 2 1 5 .0 9 5 5 4 0 2 4 .1 9 5 9 4 1 2 9 .6 5 6 0 3 3 1 .7 3 5 7 2 2 3 3 .0 5 5 1 6 5 4 4 .8 5 (in in / ) 2 E 5 .3 -0 4 1 -0 .6 E 5 6 1 -0 .9 E 5 9 2 -0 .2 E 5 0 0 1 8 .0 0 3 0 0 1 4 .0 0 8 0 0 2 .0 0 3 0 0 3 .0 0 0 0 3 6 .0 0 4 0 0 3 9 .0 0 6 0 0 3 2 .0 0 9 0 0 4 8 .0 0 3 0 0 4 4 .0 0 8 0 0 5 .0 0 3 0 0 5 9 .0 0 9 0 0 6 5 .0 0 4 0 0 6 1 .0 0 9 0 0 7 7 .0 0 3 0 0 7 3 .0 0 8 0 0 8 .0 0 3 0 0 8 6 .0 0 7 0 0 9 2 .0 0 2 0 0 9 8 .0 0 6 0 0 0 4 .0 1 1 0 0 0 3 .0 1 8 0 0 1 9 .0 1 2 0 0 1 5 .0 1 7 0 0 2 1 .0 1 2 0 0 2 4 .0 1 4 0 0 3 3 .0 1 1 0 0 3 9 .0 1 5 0 0 4 9 .0 1 2 0 0 4 8 .0 1 9 0 0 5 1 .0 1 2 0 0 5 .0 1 9 0 0 8 6 .0 1 6 0 0 6 .0 2 5 0 0 4 3 .0 3 3 0 0 7 .0 3 1 0 0 2 .0 4 4 0 0 4 5 .0 5 1 0 2 4 2 .0 1 5 0 2 4 9 .0 1 2 0 2 4 2 .0 1 5 0 2 5 2 .0 1 2 0 2 8 7 .0 1 6 0 2 4 6 .0 2 6 0 2 7 8 .0 2 8 0 2 1 7 .0 3 5 0 2 8 2 .0 3 0 0 2 1 1 .0 4 7 0 2 2 8 .0 6 6 0 2 4 4 .0 8 3 0 2 8 2 .0 9 6 0 3 2 4 .0 0 5 0 3 4 9 .0 1 9 0 3 9 .0 1 6 0 3 1 4 .0 3 3 (lb / in ) s 2 T 7 9 3 6 5 7 .7 2 8 1 3 .5 9 1 5 3 0 6 1 6 .7 9 4 9 6 4 7 2 1 .6 5 6 5 2 4 6 3 4 .1 4 1 8 7 2 4 4 0 .4 2 8 0 6 6 3 .4 1 8 4 8 6 3 7 3 .1 0 6 9 8 4 2 9 2 .8 5 7 1 5 1 2 1 2 0 2 7 0 7 .0 8 1 1 4 8 1 5 .2 8 1 3 8 2 4 2 6 .2 2 1 6 4 7 8 3 3 .2 4 1 9 5 1 4 3 .1 6 1 6 0 7 2 7 4 .7 8 1 6 5 7 8 8 5 .8 3 2 0 9 5 1 0 6 .8 9 2 5 1 1 4 1 0 .3 4 2 9 0 4 2 5 .2 2 2 4 1 2 4 5 .3 7 2 9 9 9 3 5 6 .8 2 2 1 7 5 2 7 0 .0 2 2 6 0 6 9 8 6 .5 6 3 2 0 4 4 0 4 .2 1 3 7 8 5 4 1 6 .7 6 3 3 2 2 3 9 .1 2 3 9 8 8 4 4 9 .2 9 3 6 4 0 6 6 0 .6 4 3 7 3 2 9 7 9 .8 2 3 4 1 8 1 9 0 .2 4 4 0 6 9 6 1 1 .6 8 4 6 7 1 9 2 0 .2 4 4 2 6 2 9 4 0 .6 6 4 5 9 4 8 5 0 .1 4 4 1 0 2 4 7 0 .2 6 4 4 9 7 7 9 3 .3 9 4 0 3 0 5 7 6 .2 5 4 4 7 8 5 6 4 .9 5 4 3 6 3 7 5 5 .4 8 4 2 6 1 6 6 7 .5 0 4 3 2 2 7 6 8 .9 4 4 3 6 0 2 7 2 .3 4 4 9 9 2 8 6 0 .3 6 4 2 5 0 5 7 5 .5 9 4 1 0 8 9 8 0 .3 1 4 2 3 9 9 1 .4 1 4 8 6 0 2 9 3 .8 2 5 1 8 2 1 0 0 .5 8 5 3 5 2 2 0 6 .9 1 5 7 0 0 2 0 7 .2 8 5 0 0 1 1 1 1 .3 3 5 1 8 2 6 2 2 .3 9 5 3 5 4 1 3 2 .3 6 5 1 3 9 1 4 1 .1 7 5 5 7 1 6 4 9 .9 0 5 2 9 1 6 5 9 .4 1 5 4 9 8 6 5 4 .2 5 5 9 0 7 6 5 4 .9 1 (in in / ) T 2 E 5 .3 -0 4 1 -0 .6 E 5 6 1 -0 .9 E 5 9 2 -0 .2 E 5 0 0 1 8 .0 0 3 0 0 1 4 .0 0 8 0 0 2 .0 0 3 0 0 2 9 .0 0 9 0 0 3 6 .0 0 4 0 0 3 9 .0 0 6 0 0 3 2 .0 0 9 0 0 4 8 .0 0 3 0 0 4 4 .0 0 8 0 0 5 .0 0 3 0 0 5 9 .0 0 9 0 0 6 5 .0 0 4 0 0 6 1 .0 0 9 0 0 7 7 .0 0 3 0 0 7 3 .0 0 8 0 0 8 9 .0 0 2 0 0 8 5 .0 0 7 0 0 9 1 .0 0 2 0 0 9 7 .0 0 6 0 0 0 3 .0 1 1 0 0 0 2 .0 1 8 0 0 1 8 .0 1 2 0 0 1 4 .0 1 7 0 0 2 .0 1 2 0 0 2 3 .0 1 4 0 0 3 3 .0 1 1 0 0 3 9 .0 1 5 0 0 4 8 .0 1 2 0 0 4 7 .0 1 9 0 0 5 .0 1 2 0 0 5 9 .0 1 8 0 0 8 5 .0 1 6 0 0 6 6 .0 2 4 0 0 4 7 .0 3 2 0 0 7 3 .0 3 0 0 0 2 1 .0 4 3 0 0 4 .0 5 0 2 2 5 .0 1 2 0 2 2 3 .0 1 0 0 2 2 5 .0 1 2 0 2 2 3 .0 1 9 0 2 6 1 .0 1 3 0 2 2 8 .0 2 1 0 2 5 3 .0 2 3 0 2 8 3 .0 2 9 0 2 5 3 .0 3 2 0 2 8 3 .0 3 8 0 2 9 9 .0 5 2 0 2 0 7 .0 8 3 0 2 4 5 .0 9 2 0 2 8 5 .0 9 0 0 3 0 3 .0 1 1 0 3 4 .0 1 6 0 3 5 7 .0 2 9 lo () g T 2 9 9 6 .8 1 4 3 8 6 7 .1 5 8 3 9 7 9 .2 3 4 3 0 1 1 .4 0 3 3 8 1 6 .5 5 3 3 8 2 3 .6 1 8 3 0 7 2 .8 8 8 3 9 7 9 .8 9 1 3 6 2 2 .9 0 7 4 1 5 2 .0 1 7 4 4 4 2 .0 7 4 4 9 3 7 .0 2 0 4 3 6 2 .1 4 3 4 7 2 9 .1 4 0 4 4 5 8 .2 6 1 4 7 8 6 .2 0 1 4 0 5 4 .3 2 4 4 3 4 5 .3 2 6 4 6 7 7 .3 0 8 4 8 3 2 .3 8 0 4 1 4 .4 4 7 4 3 0 2 .4 3 8 4 5 2 5 .4 7 8 4 8 5 5 .4 0 8 4 0 .5 2 4 2 6 4 .5 3 4 4 4 0 7 .5 4 4 4 6 5 6 .5 3 3 4 7 4 1 .5 7 2 4 9 5 .5 5 1 4 1 9 1 .6 2 6 4 2 4 3 .6 9 8 4 4 4 7 .6 5 8 4 5 0 9 .6 8 9 4 7 0 3 .6 3 2 4 9 0 3 .6 4 7 4 7 6 2 .6 2 8 4 6 9 7 .6 6 6 4 5 6 9 .6 6 3 4 6 3 1 .6 5 6 4 6 3 8 .6 6 5 4 7 1 3 .6 5 0 4 7 2 9 .6 1 5 4 7 4 2 .6 4 5 4 8 1 9 .6 2 4 4 9 0 4 .6 2 8 4 9 5 .6 7 5 4 9 9 2 .6 9 1 4 0 1 7 .7 2 3 4 0 6 9 .7 5 0 4 0 6 8 .7 7 5 4 1 0 4 .7 7 7 4 2 9 4 .7 6 3 4 3 3 3 .7 3 0 4 3 1 6 .7 7 7 4 4 7 1 .7 2 2 4 4 8 6 .7 3 9 4 4 7 .7 7 3 lo ( ) g T -4 3 4 .6 7 9 -4 3 4 .3 6 6 -4 6 3 .1 0 8 -4 3 4 .0 5 4 -3 5 3 .8 9 6 -3 3 4 .7 4 3 -3 3 5 .6 7 3 -3 2 6 .5 3 -3 6 4 .4 1 7 -3 3 4 .4 3 4 -3 0 1 .4 7 2 -3 5 8 .3 8 2 -3 1 3 .3 5 7 -3 7 8 .2 5 7 -3 2 6 .2 2 4 -3 9 4 .1 0 6 -3 6 5 .1 0 1 -3 3 4 .1 2 9 -3 0 1 .1 6 7 -3 8 3 .0 1 6 -3 5 8 .0 7 9 -3 3 6 .0 5 2 -3 1 4 .0 4 4 -2 9 2 .9 4 5 -2 6 6 .9 5 2 -2 4 5 .9 7 3 -2 3 1 .9 0 7 -2 1 4 .9 3 7 -2 0 3 .9 5 6 -2 8 8 .8 1 9 -2 6 9 .8 6 2 -2 4 4 .8 5 -2 2 8 .8 4 9 -2 1 2 .8 8 7 -2 9 9 .7 8 8 -2 2 4 .7 9 -2 7 3 .5 7 6 -2 6 0 .4 5 4 -2 3 4 .4 1 6 -2 7 5 .3 3 8 -2 6 5 .2 7 9 -1 7 1 .6 3 5 -1 7 6 .6 3 1 -1 7 1 .6 3 5 -1 7 7 .6 1 6 -1 6 9 .6 4 2 -1 5 3 .6 3 -1 4 1 .6 7 9 -1 4 3 .6 0 -1 2 5 .6 8 -1 2 9 .6 1 -1 8 2 .5 6 2 -1 5 2 .5 2 7 -1 3 2 .5 1 8 -1 2 7 .5 5 1 -1 0 4 .5 8 6 -1 0 2 .5 2 5 -1 8 8 .4 6 2 P(lb ) s 10936 10969 11019 11871 11925 11960 12012 12059 12857 12894 12937 12977 13016 13047 13972 13986 13995 14005 14016 14026 14035 14042 14050 14103 14110 14113 14117 14120 14146 14146 14144 14144 14138 14138 14134 14132 14127 14126 14124 14120 14117 14110 14103 14099 14021 14010 13996 13981 13967 13525 13451 13396 13310 13218 13120 13012 12930 12810 11361 11134 10943 I-I0(in ) 0.06836 0.06915 0.07003 0.09288 0.09468 0.09598 0.09773 0.09949 0.13562 0.13751 0.13945 0.14172 0.14385 0.14560 0.25291 0.25619 0.25841 0.26151 0.26480 0.26790 0.27123 0.27386 0.27719 0.30296 0.30642 0.30994 0.31253 0.31600 0.36877 0.37146 0.37488 0.37881 0.39393 0.39800 0.40152 0.40568 0.40985 0.41281 0.41702 0.42091 0.42530 0.42956 0.43400 0.43737 0.48773 0.49287 0.49823 0.50379 0.50944 0.58386 0.59097 0.59630 0.60352 0.61078 0.61809 0.62544 0.63090 0.63830 0.70494 0.71289 0.71924 (lb / in ) (in in (lb / in ) s 2 s 2 / ) T 53 1 4 8 .8 0 3 0 7 5 2 3 6 .0 4 5 6 3 .8 55 5 8 0 3 48 54 4 4 4 4 .3 .0 4 4 6 2 .3 57 6 2 0 3 85 57 8 2 4 9 .6 .0 4 8 6 0 .2 50 4 9 0 4 29 67 5 4 9 3 .1 .0 6 6 1 6 .6 53 2 6 0 4 18 60 9 3 9 0 .7 .0 7 6 2 9 .9 54 6 3 0 4 83 63 9 5 9 7 .0 .0 7 1 2 1 .7 57 5 4 0 4 68 66 4 9 9 3 .9 .0 8 8 2 4 .3 59 9 6 0 4 54 69 2 1 9 6 .8 .0 9 6 2 4 .2 69 7 2 0 6 5 62 7 7 3 3 .8 .0 7 6 8 5 .4 61 8 4 0 6 54 65 0 9 4 1 .5 .0 8 0 8 1 .8 63 5 3 0 6 41 68 4 8 4 3 .1 .0 9 7 8 0 .5 65 4 9 4 3 .3 0 76 60 0 4 .0 0 9 9 .5 67 4 9 0 7 6 4 2 .9 .0 1 6 6 3 3 9 6 .2 68 0 3 0 7 56 65 7 3 4 8 .9 .0 2 3 9 8 .1 64 1 4 0 2 93 72 5 1 9 8 .2 .1 5 9 8 3 .4 65 0 5 0 2 69 74 7 3 9 5 .5 .1 7 2 8 2 .2 65 3 7 0 2 75 75 3 5 9 9 .8 .1 8 3 8 5 .0 66 5 5 0 3 29 77 9 4 9 4 .8 .1 0 7 8 1 .2 66 7 3 0 3 95 78 2 2 9 9 .8 .1 1 1 8 9 .0 67 9 1 0 3 49 70 8 3 9 4 .8 .1 3 5 9 5 .5 67 3 3 0 3 18 72 3 2 9 9 .1 .1 5 1 9 2 .4 68 7 8 0 3 41 73 4 7 9 2 .7 .1 6 3 9 5 .4 68 1 9 7 .1 0 3 0 7 5 9 1 .1 8 9 9 1 .6 71 1 1 0 5 94 87 5 9 0 3 .0 .1 0 2 0 1 .4 71 5 6 0 5 63 88 6 3 0 6 .6 .1 2 5 0 7 .6 71 2 9 0 5 44 80 9 1 0 8 .9 .1 4 0 1 1 .5 72 0 2 0 5 64 81 0 9 0 0 .3 .1 5 9 1 3 .0 72 7 4 0 5 42 82 1 7 0 1 .6 .1 7 2 1 7 .4 73 7 9 0 8 73 82 1 7 0 4 .5 .1 3 1 3 7 .3 73 7 9 0 8 0 83 5 9 0 4 .5 .1 5 5 3 6 .3 73 8 3 0 8 75 84 5 5 0 3 .9 .1 6 5 3 7 .0 73 8 3 0 8 73 86 2 2 0 3 .9 .1 8 1 3 1 .8 73 4 8 0 9 28 81 1 5 0 0 .2 .1 6 4 4 0 .3 73 4 8 0 9 26 8 23 0 0 .2 .1 8 7 4 4 .9 72 6 5 0 0 07 83 6 2 0 8 .9 .2 0 2 4 4 .2 72 8 9 0 0 11 84 1 7 0 7 .2 .2 2 0 4 8 .5 72 2 0 5 .3 0 0 1 4 8 5 6 1 .2 4 7 4 9 .0 72 4 6 0 0 63 86 1 4 0 4 .9 .2 5 5 4 9 .0 72 6 0 3 .3 0 0 7 8 8 7 7 .2 7 5 4 2 .8 72 8 7 0 0 65 89 2 6 0 1 .9 .2 9 8 4 4 .8 72 1 4 0 1 84 80 5 7 0 0 .6 .2 1 7 5 7 .5 71 6 9 0 1 94 81 2 2 0 6 .9 .2 3 9 5 8 .3 71 2 3 0 1 26 82 5 9 0 3 .3 .2 6 0 5 9 .3 71 3 8 0 1 84 83 0 5 0 1 .6 .2 7 8 5 9 .3 67 3 2 0 4 97 9 2 .8 .2 2 7 66 1 4 0 4 55 9 7 .8 .2 5 3 66 2 3 0 4 27 9 0 .5 .2 8 0 65 5 8 0 5 97 9 2 .8 .2 0 7 64 6 7 0 5 78 9 5 .5 .2 3 8 62 6 0 9 83 75 .2 0 6 68 0 6 0 9 46 6 9 .8 .2 4 0 66 4 9 0 9 02 6 1 .8 .2 7 6 61 0 7 0 0 66 6 9 .3 .3 0 5 67 1 9 0 0 24 5 3 .1 .3 4 7 62 6 3 0 0 95 5 4 .0 .3 7 1 67 8 8 0 1 59 4 0 .8 .3 1 7 63 1 9 0 1 28 4 0 .6 .3 4 9 67 3 3 0 .9 0 1 9 4 .3 7 8 54 4 6 0 5 12 6 9 .6 .3 1 8 53 8 1 0 5 15 5 6 .4 .3 5 4 54 6 5 0 5 38 4 1 .4 .3 8 0 (in in / ) T 0 349 .0 3 8 0 388 .0 3 6 0 321 .0 4 9 0 421 .0 5 3 0 409 .0 6 8 0 475 .0 6 0 0 45 .0 7 4 0 435 .0 8 7 0 636 .0 5 7 0 629 .0 6 5 0 614 .0 7 6 0 62 .0 8 2 0 629 .0 9 0 0 706 .0 0 2 0 165 .1 8 6 0 217 .1 0 1 0 208 .1 1 9 0 244 .1 2 6 0 291 .1 3 1 0 224 .1 5 7 0 276 .1 6 3 0 283 .1 7 9 0 232 .1 9 5 0 456 .1 0 6 0 406 .1 2 6 0 454 .1 3 8 0 471 .1 4 0 0 415 .1 6 9 0 666 .1 8 5 0 675 .1 9 8 0 722 .1 1 2 0 781 .1 2 7 0 71 .1 9 9 0 884 .1 0 8 0 834 .1 2 4 0 80 .1 4 7 0 874 .1 5 9 0 801 .1 7 2 0 879 .1 8 5 0 93 .1 0 6 0 918 .1 2 6 0 996 .1 3 1 0 976 .1 5 3 0 915 .1 7 1 lo () g T 4 4 98 .7 9 9 4 5 46 .7 1 6 4 5 66 .7 3 4 4 9 77 .7 0 4 4 9 01 .7 3 9 4 9 66 .7 4 2 4 9 82 .7 6 8 4 9 92 .7 8 4 4 3 1 .8 4 5 4 3 7 .8 5 6 4 3 67 .8 7 1 4 3 49 .8 9 1 4 4 19 .8 1 2 4 4 59 .8 2 2 4 9 43 .8 3 0 4 9 47 .8 4 6 4 9 13 .8 5 6 4 9 01 .8 6 8 4 9 03 .8 7 3 4 9 99 .8 7 4 4 9 84 .8 8 5 4 9 51 .8 9 7 4 0 44 .9 0 7 4 0 97 .9 6 5 4 0 83 .9 7 2 4 0 5 .9 8 9 4 0 12 .9 9 8 4 0 98 .9 9 3 4 2 46 .9 0 9 4 2 96 .9 0 8 4 2 57 .9 1 5 4 2 23 .9 2 7 4 2 83 .9 4 0 4 2 58 .9 5 3 4 2 06 .9 6 6 4 2 72 .9 6 6 4 2 3 .9 7 5 4 2 87 .9 7 3 4 2 59 .9 8 3 4 2 17 .9 9 2 4 2 85 .9 9 0 4 3 39 .9 0 4 4 3 96 .9 0 2 4 3 49 .9 1 0 lo ( ) g T -1 7 0 .4 5 9 -1 7 2 .4 0 2 -1 6 8 .4 4 2 -1 4 5 .3 4 7 -1 3 4 .3 6 -1 3 6 .3 0 4 -1 2 9 .3 2 4 -1 1 3 .3 5 8 -1 8 5 .1 4 8 -1 7 7 .1 8 5 -1 7 8 .1 2 6 -1 6 0 .1 6 9 -1 5 8 .1 9 4 -1 5 7 .1 4 4 -0 2 6 .9 5 8 -0 2 3 .9 0 9 -0 1 8 .9 6 6 -0 1 9 .9 1 9 -0 0 8 .9 6 9 -0 0 1 .9 2 4 -0 9 1 .8 7 -0 9 1 .8 3 5 -0 8 2 .8 8 3 -0 5 1 .8 2 2 -0 4 5 .8 7 1 -0 4 8 .8 2 9 -0 3 5 .8 9 3 -0 3 0 .8 5 7 -0 7 .7 3 -0 7 1 .7 0 -0 6 4 .7 6 4 -0 6 2 .7 2 8 -0 4 6 .7 6 9 -0 4 6 .7 2 -0 3 1 .7 9 1 -0 3 0 .7 5 2 -0 3 9 .7 0 7 -0 2 1 .7 8 1 -0 2 0 .7 4 9 -0 2 4 .7 0 2 -0 1 3 .7 6 2 -0 1 3 .7 2 9 -0 0 3 .7 8 3 -0 0 2 .7 5 8 To calculate the stress, divide the axial load by the cross sectional area as follows: =PA=10943 lbs40.506 in254416.45 lbin2 To calculate strain, divide the stretch by the original length, as follows: =L=.71924 in2.007333 in=0.358308 inin To calculate the true stress, a simplified equation exists as follows: T=1+=54381.8 lbs 1+0.034057 inin =56233.86 lbin2 To calculate true strain, another simplified equation becomes useful, as shown below: T=ln1+=ln1+ 0.034057 inin =0.33489 inin Following this page are three graphs. The first is a graph of the elastic region for the stress-strain relationship. Included with this graph is a linear trend line which gives Young's Modulus as the slope. The second graph is the complete stress-strain graph including true stress and strain. The final graph is the true stress true strain relationship shown on a log-log scale. The data measured of A36 steel during the tension test give us a Young's Modulus of Elasticity of 29613447.94. The upper yield strength is approximately 49347.3 pounds per square inch, and the lower yield strength is approximately 45188.8 pounds per square inch. The 0.2% offset yield strength is 46938.8 pounds per square inch. The ultimate tensile strength of the A36 is 70348.9 pounds per square inch. The cast iron maxed out at 6700 pounds, a tensile strength of 33230.71 pounds per square inch. Ductility can be measured as a percentage of elongation or of diameter reduction. The A36 stretched in gauge length from 2.007333 inches to 2.714 inches, a 35.2% increase. The diameter shrunk from 0.506 inches to 0.33 inches, a 34.8% reduction. The cast iron, however, did not have a change in diameter, and its length changed from 1.992 inches to 1.997 inches, a 0.3% increase. This increase may even be zero, because the change is so small as to be within the margin of error. The Modulus of Resilience can be calculated as follows: uR=12PLPL=1249347.3 lbin20.001866 inin=46.04 lbin2 The Modulus of Toughness can be approximated as follows: uT=23FULT=230.366 inin70348.9 lbin2=17165.3 lbin2 The strain hardening coefficient is 0.31, and the 0 is 12.3. Questions 1. Why does it not make much sense to calculate true stress and true strain using the equations given in the lab notes after the maximum load is reached? After you reach your ultimate stress, the necking of the material begins, and the stress no longer increases. At this point, only the strain is increasing. 2. Define elastic strain and plastic strain. Suppose a material's 0.2% offset yield strength is 0, and the Modulus of Elasticity is E. When the stress reaches 0, what are the elastic strain, plastic strain, and total strain in terms of 0 and E? Elastic strain is the strain that is recovered if the load is removed. This behavior is much like a spring. Plastic strain is the permanent deformation, measured as the strain that is not recovered when the load is removed. In terms of 0 and E, The elastic strain will be the strain recovered along the slope E from stress 0 to zero. The plastic strain is the strain remaining once the stress is zero. The total strain is the sum of the elastic and plastic strains. 3. In general, A36 can be categorized as a ductile material, and cast iron as a brittle material. Based on the results of the tensile tests, discuss the differences between the ductile and brittle materials in terms of the overall deformation and fracture behavior. During the test, the A36 behaved much like predicted. The deformation could be seen, the stretch and the necking watched. Its fracture was expected at the time. The deformation was significant, with a measured ductility of 35%. The cast iron, on the other hand, was very unexpected. No deformation could be witnessed visually, no necking occurred, and it fractured very suddenly away from the expected point of failure. No measureable ductility could be measured or calculated. 4. Suppose the original diameter of a tensile specimen is D0. When the load reaches a certain value in the plastic range, the new diameter is measured to be D. Write the true strain in terms of D and D0. The true strain can be written as follows: T=ln1+D0-DD ...
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