ME 220 University of Idahoo Strength and Inelastic Properties of A36 Steel Report

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ME 220 – Mechanics of Materials Laboratory TEST TITLE: Tension Test DATE OF TEST: 1/30/2018 DATE REPORT SUBMITTED: 2/6/2018 NAME: Jamal AL Dhahouri Abstract: In this experiment we were introduced to the test is a basic mechanical test you can perform on material. Tensile tests are simple, relatively inexpensive, and fully standardized. By pulling on something, we will be able to determine how a material reacts when forces being applied in tension. As the material is being pulled, we will find its strength along with how much it will elongate. The tests are conducted by placing the specimen into the test apparatus and then applying a force to the specimen by separating the testing machine crossheads. And by using our equations:σ = F / Ao ϵ = ΔL / Lo σT = F / Ao = (F / Ao) * ( Ao / A) = σ ( Ao / A) = σ (ΔL / L) = σ ( 1 + ϵ ). Where (F) is the forced applied, (Ao) is origin cross-section, (ΔL) is for the difference in length and Lo is the original length between the two marked points. Introduction/Experiment setup: During this lab, the tension test was used to determine the material properties of A36 steel and cast iron. We used “button head round bar” specimens to conduct the test. This is a basic test that provides very valuable information about the material being tested, including elastic modulus, strength, and ductility. Before we started the test, we put two reference marks (called gage points) on each specimen two inches apart. The initial gage length, L0, and initial diameter, D0, of each specimen was measured. After making sure the universal testing frame was properly calibrated, we placed the first sample in the machine. The extensometer was attached to measure the elongation of the specimen. The specimen was placed under a gradually higher load until it fractured, at which point the second material was tested. After fracture, the final gage length was measured between the two reference points as well as the final diameter at the point of fracture. The data from the tension test was then used to create a stress-strain curve of the A-36 steel. This graph can be used to determine the aforementioned material properties. RESULTS Load Cell Extensometer Load Displacement (Lbs) 9 8 9 10 10 71 159 360 1037 1865 1975 2119 2252 2409 (inches) 0.00005 0.00003 0.00006 0.00006 0.00005 0.00010 0.00017 0.00027 0.00077 0.00126 0.00134 0.00147 0.00160 0.00171 Engineering Stress Engineering Strain True Stress True Strain psi in/in 2.38089E-05 1.55897E-05 3.17378E-05 3.11795E-05 2.60648E-05 4.87569E-05 8.75747E-05 0.000133786 0.00038494 0.000633528 0.000672367 0.000738139 0.000803603 0.000859174 psi 46.92547102 38.78215324 43.92383151 47.41482865 48.76665795 351.4493716 791.740968 1790.66158 5157.137463 9277.529503 9823.771288 10544.23595 11206.45075 11988.10499 in/in Initial A36 Steel Cast Iron Final A36 Steel Cast Iron 46.9243538 38.78154865 43.92243751 47.41335033 48.76538689 351.4322369 791.6716376 1790.422048 5155.153038 9271.655654 9817.170544 10536.45858 11197.45244 11977.81396 Diameter Gauge length Maximum Load (inches) (inches) (Lb) 0.5062 1.989 12750 0.5049 1.9926 8500 0.3053 2.761 0.507 1993 2.38086E-05 1.55896E-05 3.17373E-05 3.1179E-05 2.60644E-05 4.87557E-05 8.75709E-05 0.000133777 0.000384866 0.000633327 0.000672141 0.000737867 0.00080328 0.000858806 SAMPLE CALCULATIONS (P) Max load: 14200 lbs (L) Gage length: L0 = 1.989 in Lf = 2.761 in (D) Neck Diameter: D0 = 0.5062 in Df = 0.3053 in (Lf – L0) Elongation: 2.761 in – 1.989 in = 0.772 in (A) Cross-sectional area: A0 = (π/4) D0² = (π/4)(0.5062 in)² = 0.39756855 in² Af = (π/4) Df² = (π/4)(0.3053 in)² = 0.239782059 in² (σ) Engineering stress: P/A0 = 12750/0.39756855= 32069.9 psi (ε) Engineering strain: (Elongation)/L0 = 0.85 in / 1.989 in = 0.4273504 in/in (σT) True Stress: σ(1+ ε) = 32069.9 psi (1+0.42735504) = 22468.1 psi (εT) True strain: ln(1 + ε) = ln(1 + 0.4273504) = 0.355819858 in/in GRAPHS MATERIAL PROPERTIES MODULUS OF ELASTICITY: 75043.6 psi E = σ/ε so the Modulus of Elasticity is the slope of the line of the first graph. After fitting a linear trend line to the graph, I found the slope to be 75043.6 . ELASTIC STRENGTH IN TENSION: Upper Yield Strength: 47790 ≈ 47,800 psi Lower Yield Strength: 47384 ≈ 47,400 psi Yield Strength for an offset of 0.2%*: 49168 ≈ 49,200 psi TENSILE STRENGTH (Su): 6950 psi The ultimate tensile strength can be seen as the highest engineering stress point reached on the second graph. DUCTILITY: (1) Percentage elongation in two inches at fracture: 39% % elongation= (LF/L0)-1*100%= (2.761/1.989)-1*100%= 38.8% (2) Percentage reduction in area at fraction: 39.7% % rduction= (1- Af/A0)*100%= (1-0.239782059/0.39756855)*100%= 39.7% MODULUS OF RESILIENCE: 8.414psi e= (σ y^2)/2E= (22468.1^2)/2(30,000,000)= 8.414psi MODULUS OF TOUGHNESS: 1648.6 psi (2/3)(Su)(εf) = (2/3)(6950psi)( 0.355819858 psi) = 1648.6 psi STRAIN HARDENING COEFFICIENT “m” AND σ0: m=0.2215, σ0=22468.1 psi The power relationship seen in the last graph is σT=22468.1εT0.2215. Thus the strain hardening coefficient m is 0.2215 and σ0 is 22468.1psi. DISCUSSION 1) It doesn’t make sense to calculate true stress and true strain using the equations given in the lab notes after the maximum load is reached because at that point necking has began taking place. Once the material begins necking the volume of the sample at the point of necking becomes inconsistent and therefore true stress and true strain calculations become inaccurate. 2) Elastic strain is strain that takes place in a material that is reversible. When a material undergoes elastic strain it will fully recover as soon as the load is removed. On the other hand, plastic strain causes a permanent change in the material that is irreversible even after the load has been completely removed. When a material’s 0.2% offset yield strength is σ0 , it’s modulus of elasticity is E, and the stress reaching σ0 is equal to σ0 /E, the plastic strain is equal to 0.002. The total strain is equal to ε(elastic) + ε(plastic). Similarly, total strain is also equal to σ0 /E + 0.002. 3) The ductile material (in this case, A-36 steel) deformed gradually, and at higher levels of loading began necking. The steel specimen deformed in length far more than the cast iron, which did not deform before fracture. The fracture surface of the cast iron was a cleaner, and less rough cut when compared with the fracture of the steel. The fracture of the steel exhibited a plastic strain and the necking before fracture caused a cup-and-cone type of fracture. 4) Taking the original diameter of a tensile specimen as D0, and the new diameter D takes place at a load that occurs in the plastic range, the true strain can be shown by: True Strain = ln(L/L0) = (A0/A) = ln[([(π/4 D0 ²)/ (π/4 D ²)] = ln(D0²/D²) Conclusion: The tension test allows for the examination of both elastic and inelastic properties of the two materials. The tension test is important in understanding how material properties are determined as well as understanding how a brittle material fractures versus a ductile material. Understanding this difference will allow an engineer to choose the best possible material for a variety of applications. stress_strain NO Load readings Load Cell Extensometer 0.007568 -0.002069 load slope ext slope 8662062 243.3301072 Load Cell Extensometer Voltage Voltage (Volts) (Volts) 0.007577 -0.002068 0.007780 -0.002065 0.007912 -0.002064 0.008208 -0.002059 0.008638 -0.002056 0.008610 -0.002056 0.008686 -0.002054 0.008781 -0.002054 0.008839 -0.002053 0.008890 -0.002052 0.008952 -0.002051 0.009014 -0.002051 0.009069 -0.002050 0.009134 -0.002049 0.009199 -0.002048 0.009255 -0.002047 0.009321 -0.002047 0.009388 -0.002045 0.009445 -0.002045 0.009513 -0.002044 0.009580 -0.002043 0.009640 -0.002042 0.009708 -0.002042 0.009776 -0.002041 0.009835 -0.002039 0.009904 -0.002039 0.009976 -0.002038 0.010038 -0.002037 0.010111 -0.002036 0.010185 -0.002035 0.010249 -0.002034 0.010328 -0.002033 0.010408 -0.002032 0.010476 -0.002032 0.010558 -0.002030 0.010644 -0.002028 0.010717 -0.002028 0.010806 -0.002026 0.010896 -0.002025 0.010974 -0.002024 0.011067 -0.002022 Initial Excitation 5.458496 A36 Steel Cast Iron Final A36 Steel Cast Iron Excitation Voltage (Volts) 5.458505 5.458452 5.458485 5.458534 5.458512 5.458516 5.458541 5.458507 5.458508 5.458464 5.458483 5.458456 5.458539 5.458539 5.458477 5.458488 5.458476 5.458537 5.458556 5.458559 5.458507 5.458559 5.458561 5.458558 5.458559 5.458476 5.458532 5.458487 5.458498 5.458548 5.458516 5.458539 5.458486 5.458480 5.458500 5.458537 5.458555 5.458545 5.458550 5.458512 5.458477 Load Cell Load (Lbs) 15 337 547 1016 1699 1654 1774 1926 2017 2098 2196 2295 2382 2486 2589 2678 2782 2888 2979 3088 3194 3289 3397 3505 3598 3708 3822 3920 4036 4153 4256 4380 4507 4616 4746 4881 4998 5138 5282 5406 5553 Page 1 Extensometer Displacement (inches) 0.00002 0.00016 0.00024 0.00043 0.00056 0.00060 0.00066 0.00069 0.00071 0.00075 0.00081 0.00082 0.00083 0.00090 0.00093 0.00097 0.00098 0.00105 0.00106 0.00112 0.00115 0.00120 0.00122 0.00126 0.00132 0.00133 0.00138 0.00144 0.00145 0.00152 0.00154 0.00158 0.00166 0.00167 0.00175 0.00181 0.00185 0.00191 0.00196 0.00199 0.00208 stress_strain 0.011162 0.011244 0.011340 0.011437 0.011521 0.011620 0.011719 0.011805 0.011906 0.012009 0.012099 0.012201 0.012304 0.012394 0.012498 0.012602 0.012692 0.012796 0.012900 0.012988 0.013093 0.013198 0.013286 0.013391 0.013495 0.013584 0.013687 0.013789 0.013877 0.013980 0.014080 0.014169 0.014267 0.014361 0.014098 0.013958 0.013931 0.013929 0.013924 0.013941 0.013953 0.013957 0.013983 0.014000 0.014011 0.013995 0.014059 0.014076 0.014070 0.013929 0.013931 0.014153 -0.002021 -0.002020 -0.002019 -0.002017 -0.002017 -0.002015 -0.002014 -0.002013 -0.002011 -0.002010 -0.002008 -0.002007 -0.002006 -0.002005 -0.002004 -0.002002 -0.002001 -0.001999 -0.001998 -0.001997 -0.001995 -0.001994 -0.001993 -0.001991 -0.001990 -0.001989 -0.001988 -0.001986 -0.001985 -0.001984 -0.001983 -0.001981 -0.001980 -0.001979 -0.001983 -0.001985 -0.001984 -0.001983 -0.001982 -0.001981 -0.001979 -0.001979 -0.001979 -0.001978 -0.001978 -0.001972 -0.001952 -0.001852 -0.001673 -0.001432 -0.001170 -0.000974 5.458503 5.458473 5.458493 5.458555 5.458578 5.458570 5.458571 5.458541 5.458549 5.458568 5.458500 5.458505 5.458511 5.458574 5.458559 5.458570 5.458517 5.458507 5.458467 5.458560 5.458548 5.458573 5.458516 5.458476 5.458510 5.458593 5.458564 5.458549 5.458482 5.458500 5.458501 5.458490 5.458542 5.458507 5.458561 5.458569 5.458554 5.458573 5.458561 5.458568 5.458520 5.458612 5.458599 5.458564 5.458541 5.458526 5.458525 5.458546 5.458592 5.458609 5.458574 5.458512 5703 5833 5986 6141 6273 6430 6587 6724 6885 7049 7191 7353 7517 7659 7824 7990 8132 8296 8463 8602 8768 8935 9074 9241 9406 9547 9711 9873 10013 10176 10334 10476 10632 10780 10363 10140 10098 10094 10088 10114 10133 10139 10181 10208 10225 10199 10301 10328 10318 10094 10098 10450 Page 2 0.00212 0.00217 0.00223 0.00230 0.00233 0.00239 0.00245 0.00252 0.00257 0.00262 0.00271 0.00275 0.00280 0.00287 0.00291 0.00297 0.00305 0.00313 0.00318 0.00322 0.00330 0.00334 0.00338 0.00347 0.00351 0.00355 0.00363 0.00369 0.00374 0.00381 0.00384 0.00390 0.00395 0.00400 0.00382 0.00376 0.00377 0.00383 0.00387 0.00393 0.00401 0.00401 0.00402 0.00405 0.00406 0.00430 0.00522 0.00969 0.01766 0.02838 0.04009 0.04880 stress_strain 0.014088 0.014121 0.014331 0.014496 0.014632 0.014729 0.014817 0.014928 0.015032 0.015113 0.015189 0.015154 0.015256 0.015328 0.015415 0.015485 0.015562 0.015632 0.015688 0.015750 0.015811 0.015859 0.015911 0.015961 0.016003 0.016047 0.016089 0.016123 0.016162 0.016196 0.016226 0.016257 0.016285 0.016311 0.016337 0.016362 0.016382 0.016405 0.016424 0.016441 0.016457 0.016474 0.016488 0.016502 0.016514 0.016525 0.016535 0.016545 0.016554 0.016561 0.016567 0.016572 -0.000918 -0.000904 -0.000863 -0.000764 -0.000659 -0.000568 -0.000497 -0.000401 -0.000298 -0.000211 -0.000115 -0.000073 -0.000017 0.000052 0.000157 0.000254 0.000367 0.000480 0.000576 0.000690 0.000803 0.000901 0.001016 0.001131 0.001230 0.001346 0.001465 0.001568 0.001687 0.001808 0.001913 0.002036 0.002160 0.002268 0.002394 0.002521 0.002631 0.002760 0.002891 0.003003 0.003137 0.003271 0.003387 0.003523 0.003661 0.003779 0.003919 0.004060 0.004182 0.004326 0.004472 0.004599 5.458592 5.458602 5.458555 5.458553 5.458549 5.458602 5.458530 5.458508 5.458526 5.458506 5.458555 5.458544 5.458561 5.458521 5.458598 5.458556 5.458589 5.458530 5.458558 5.458514 5.458519 5.458527 5.458527 5.458548 5.458531 5.458554 5.458600 5.458540 5.458541 5.458583 5.458587 5.458574 5.458610 5.458553 5.458537 5.458524 5.458546 5.458541 5.458593 5.458588 5.458594 5.458550 5.458539 5.458539 5.458512 5.458587 5.458554 5.458556 5.458541 5.458498 5.458550 5.458571 10347 10399 10733 10995 11211 11364 11503 11680 11845 11974 12093 12039 12200 12316 12453 12565 12685 12798 12886 12985 13081 13158 13239 13319 13386 13456 13523 13576 13638 13693 13740 13789 13833 13874 13916 13956 13987 14024 14054 14080 14107 14134 14155 14177 14198 14215 14231 14246 14260 14272 14281 14288 Page 3 0.05130 0.05195 0.05377 0.05818 0.06287 0.06689 0.07007 0.07437 0.07893 0.08283 0.08711 0.08898 0.09148 0.09453 0.09923 0.10354 0.10859 0.11361 0.11789 0.12297 0.12801 0.13237 0.13750 0.14264 0.14707 0.15224 0.15753 0.16211 0.16745 0.17282 0.17752 0.18299 0.18852 0.19335 0.19897 0.20461 0.20951 0.21527 0.22110 0.22611 0.23206 0.23803 0.24322 0.24929 0.25541 0.26069 0.26692 0.27322 0.27865 0.28508 0.29156 0.29726 stress_strain 0.016578 0.016583 0.016586 0.016589 0.016592 0.016594 0.016595 0.016595 0.016593 0.016595 0.016593 0.016592 0.016587 0.016583 0.016579 0.016574 0.016569 0.016562 0.016554 0.016542 0.016532 0.016515 0.016494 0.016470 0.016436 0.016389 0.016335 0.016258 0.016165 0.016073 0.015951 0.015813 0.015680 0.015506 0.015310 0.015126 0.014885 0.014613 0.014348 0.013998 0.004749 0.004900 0.005030 0.005184 0.005341 0.005478 0.005638 0.005802 0.005946 0.006115 0.006288 0.006439 0.006620 0.006806 0.006969 0.007164 0.007366 0.007545 0.007761 0.007986 0.008188 0.008431 0.008686 0.008916 0.009193 0.009481 0.009734 0.010036 0.010342 0.010609 0.010921 0.011238 0.011510 0.011831 0.012155 0.012438 0.012770 0.013108 0.013404 0.013756 5.458522 5.458544 5.458608 5.458558 5.458554 5.458579 5.458555 5.458511 5.458574 5.458568 5.458593 5.458569 5.458546 5.458550 5.458522 5.458505 5.458555 5.458505 5.458519 5.458502 5.458497 5.458508 5.458559 5.458521 5.458569 5.458580 5.458520 5.458590 5.458539 5.458600 5.458512 5.458539 5.458520 5.458522 5.458511 5.458506 5.458561 5.458532 5.458512 5.458505 14298 14306 14311 14317 14320 14323 14325 14325 14323 14325 14322 14320 14313 14306 14300 14292 14285 14273 14260 14241 14225 14199 14165 14128 14073 13998 13913 13790 13644 13496 13304 13085 12873 12597 12287 11994 11613 11181 10760 10204 Page 4 0.30392 0.31066 0.31647 0.32332 0.33033 0.33641 0.34358 0.35088 0.35728 0.36483 0.37252 0.37927 0.38734 0.39562 0.40289 0.41159 0.42057 0.42858 0.43819 0.44821 0.45722 0.46808 0.47943 0.48968 0.50202 0.51488 0.52617 0.53960 0.55325 0.56513 0.57909 0.59321 0.60534 0.61964 0.63408 0.64668 0.66148 0.67655 0.68977 0.70545 stress_strain Page 5 stress_strain Page 6 stress_strain Page 7 stress_strain Page 8 stress_strain Page 9 stress_strain Page 10 stress_strain Page 11 stress_strain Page 12 stress_strain Page 13 stress_strain Page 14 stress_strain Page 15 stress_strain Page 16 stress_strain Page 17 stress_strain Page 18 stress_strain Page 19 stress_strain Page 20 stress_strain Page 21 stress_strain Page 22 stress_strain #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 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Page 38 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! stress_strain #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Page 39 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! stress_strain Diameter Gauge length (inches) (inches) 0.5056 2.0086 0.3133 Maximum Load (Lb) 13750 2.749 Copy of Data Sheet Page 40 ME220 – Mechanics of Materials Laboratory TEST TITLE: Tension Test NAME: (refer to lab manual pp. 7-19) (submit your report in WORD) 1. Summary (1/12) (The summary should be succinct (limited to one page), but contain the following four pieces of information, namely, the purpose of the experiment; experimental methods; results; and conclusion.) 2. Calculations (6/12) 1. Tabulate the test results according to the following format P, l − l0 , σ , ε , σ T , ε T , where: P: the current load l : the current gage length l − l0 : elongation σ : engineering stress ε : engineering strain σ T : true stress ε T : true strain Note: 1. True stresses and true strains need only to be calculated to maximum load. 2. You only need to print out 10 rows of data, but you should of course use all the data to make the plots described in step 3. 2. Show a few sample calculations 3. Make the following graphs a. The σ-ε curve up to ε ≈ 0.3%(0.003) . 2 b. Both the whole σ-ε curve and σ T − ε T curve on the same graph using linear coordinates c. σ T vs ε T in the plastic region, i.e. excluding the elastic part of the data. 4. Determine the following material properties: a. Modulus of Elasticity (use linear curve fitting of the data in figure 3(a) to determine the slope) b. Elastic strength in tension (1) upper yield strength (from 3a.) (2) lower yield strength (from 3a.) (3) yield strength for an offset of 0.2% (from 3a.) c. Tensile strength (ultimate) (from 3b.) d. Ductility (1) percentage elongation in two inches at fracture (2) percentage reduction in area at fracture e. Modulus of resilience (from 3a.) f. Modulus of toughness (from 3b.) 5. Use EXCEL to fit the curve obtained in (3c) by σ T = σ 0 ε T m and obtain the strain hardening coefficient m and σ0 for the data in the plastic region. 3. Questions (4/12) 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? 2. Define elastic strain and plastic strain. Suppose a material’s 0.2% offset yield strength is σ0 and the modulus of elasticity is E. When the stress reaches σ0, what are the 3 elastic strain, plastic strain, and total strain in terms of σ0 and E. 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. 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. 4. Conclusion (1/12) 4
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Explanation & Answer

Here you go!

Objective
The aim of this experiment was to determine the strength and inelastic properties of a
material and to observe the deformation and fracture of material under load.

Introduction and Procedure
This experiment uses a button head round bar specimen of A36 Steel alloy and a Tensile
test machine. Before experiment two reference marks called gage points are created on the
specimen. Initial gage length as well as diameter is measured. As load is applied to the specimen,
changes in gage length is noted to calculate elongation for load. This data is obtained till point of
failure. Schematic diagram of the tensile test setup is shown below:

Data is analyzed to find stress, strain, True stress, true strain and many more important
characteristic values. Stress is defined as:

Where A0 is the initial cross-sectional area. Strain is defined as:

It can be noted that cross sectional areas and gage lengths are continuously changing as applied
load value increases, and thus stress and strain calculated by above formula needs a correction
factor to be as close to actual value as it can. True stress and True strain values are used to
correct the situation. True Stress and True strain are also calculated by using these equations:

Graphs for the data are plotted and various other important values like modulus of elasticity,
ductility. Upper yield strength, lower yield strength, ultimate tensile strength and so on are
calculated for the specimen.

Calculations

1) Results for first few load values

Extensometer
Load Cell Load

Displacement

Engineering

Engineering

True Stress

(Lbs)

(inch)

Stress (psi)

Strain

(psi)

True Strain

15

0.00002

75.02419

1.09637E-05

75.02501

1.09636E-05

337

0.00016

1680.481

8.15624E-05

1680.618

8.15591E-05

547

0.00024

2722.49

0.00011756

2722.81

0.000117553

1016

0.00043

5061.403

0.000212348

5062.477

0.000212325

1699

0.00056

8460.238

0.000278996

8462.598

0.000278957

1654

0.00060

8236.97

0.000298415

8239.428

0.000298371

1774

0.00066

8836.513

0.000327088

8839.403

0.000327034

1926

0.00069

9593.212

0.000341449

9596.487

0.000341391

2017

0.00071

10046.36

0.000352124

10049.9

0.000352062

2098

0.00075

10451.11

0.000372945

10455.01

0.000372875

2196

0.00081

10939.88

0.000401352

10944.27

0.000401271

2) Sample calculations

(P) Max load: 13750 lbs
(L) Gage length:

L0 = 2.0086 in

Lf = 2.749 in

(D) Neck Diameter:

D0 = 0.5056 in

Df = 0.3133 in

(Lf – L0) Elongation: 2.749 in – 2.0086 in = 0.7407 in
(A) Cross-sectional area: A0 = (π/4) D0² = (π/4)(0.5056 in)² = 0.2007724 in²
Af = (π/4) Df² = (π/4)(0.3133 in)² = 0.077092241 in²
(σ) Engineering stress: P/A0 = 13750/0.2007724 = 68485.5 psi
(ε) Engineering strain: (Elongation)/L0 = 0.7407 in / 2.0086 in = 0.3687643
(σT) True Stress: σ(1+ ε) = 68485.5 psi (1+0.3687643) = 93740.51 psi
(εT) True strain: ln(1 + ε) = ln(1 + 0.3687643) = 0.31390836

3) Graphs (from excel data)

Stress Vs Strain till Strain is 0.3%
60000

50000

Stress

40000

y = 1E+07x + 957.87

30000

20000

10000

0
0.00000 0.00050 0.00100 0.00150 0.00200 0.00250 0.00300 0.00350 0.00400 0.00450 0.00500

Strain

Stress Vs Strain
100000
90000
80000
70000

Stress

60000

50000

Engineering Stress Vs Strain

40000

True Stress Vs Strain

30000
20000
10000
0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Strain

True Stress Vs True Strain in plastic region
100000
90000

80000

y = 98172x0.1165

70000

Stress

60000
50000
40000
30000
20000
10000
0
0

0.05

0.1

0.15

0.2

Strain

4) Material properties obtained from above graphs:
a) Modulus of elasticity = 10^7 psi

0.25

0.3

0.35

b) Upper yield strength 53693 psi, lower yield strength 50468 psi, yield strength for an offset of
0.2% = 50801 psi
c) Tensile strength (ultimate) = 71348 psi
d) Ductility: Percentage elongation in two inches at fracture = 36.88%, Percentage reduction in
area at fracture = 61.60%
e) Modulus of resilience = 0.5*σy*εy = 76.38241 psi
f) Modulus of toughness = (2/3)*Su*εf = 21476.00236 psi
5) Strain hardening coefficient = m = 0.1165 and σ0 = 98172 psi

Questions and Discussion
1) Necking begins after maximum load has been achieved. The formula written in lab notes
uses the fact that volume remains consistent as necking does not occur.

2) Elastic strain is the strain in a material which is not in plastic region and material will
fully recover as soon as load is removed. Plastic strain is permanent in nature and will
not recover even if the load is removed. When a material’s 0.2% offset yield strength is
σ0 , it’s modulus of elasticity is E and the stress reaching σ0 is equal to σ0 /E, the plastic
strain is equal to 0.002. The total strain is equal to ε(elastic) + ε(plastic) and total strain
is also equal to σ0 /E + 0.002.

3) A36 Steel specimen behaved like a ductile material, which was expected given its
properties. Percentage elongation in the specimen came out to be 36.88% which is
significant ductility. Deformation was clearly observed along with necking. Cup-and cone type fracture occured. Cast iron, however, behaved very differently. Significant
deformation was not observed and fracture was sudden without necking. Ductility could
not be calculated, leading to the result that it behaved like brittle material.

4) True strain can be calculated as follows:
εT = ln(L/L0) = ln(A0/A) = ln[([(π/4 D0 ²)/(π/4 D²)] = ln(D0²/D²)

Conclusion
In conclusion, the experiment was a success. Data was collected for A36 Steel alloy
specimen using the Tensile testing machine. Values for ultimate tensile stress, fracture stress,
percent elongation, percent reduction in area, elastic modulus, modulus of toughness and so on
were calculated. The difference of fracture of brittle and ductile material was observed.
Understanding these differences and properties will allow an Engineer to choose the best
possible alternative for many applications.


stress_strain
NO Load readings
Load Cell Extensometer
0.007568
-0.002069
load slope
ext slope
8662062 243.3301072

Load Cell Extensometer
Voltage
0.007577
0.007780
0.007912
0.008208
0.008638
0.008610
0.008686
0.008781
0.008839
0.008890
0.008952
0.009014
0.009069
0.009134
0.009199
0.009255
0.009321
0.009388
0.009445
0.009513
0.009580
0.009640
0.009708
0.009776
0.009835
0.009904
0.009976
0.010038
0.010111
0.010185
0.010249
0.010328
0.010408
0.010476
0.010558
0.010644
0.010717
0.010806
0.010896
0.010974

Voltage
-0.002068
-0.002065
-0.002064
-0.002059
-0.002056
-0.002056
-0.002054
-0.002054
-0.002053
-0.002052
-0.002051
-0.002051
-0.002050
-0.002049
-0.002048
-0.002047
-0.002047
-0.002045
-0.002045
-0.002044
-0.002043
-0.002042
-0.002042
-0.002041
-0.002039
-0.002039
-0.002038
-0.002037
-0.002036
-0.002035
-0.002034
-0.002033
-0.002032
-0.002032
-0.002030
-0.002028
-0.002028
-0.002026
-0.002025
-0.002024

Initial
Excitation
5.458496

A36 Steel
Cast Iron
Final
A36 Steel
Cast Iron

Excitation
Voltage
5.458505
5.458452
5.458485
5.458534
5.458512
5.458516
5.458541
5.458507
5.458508
5.458464
5.458483
5.458456
5.458539
5.458539
5.458477
5.458488
5.458476
5.458537
5.458556
5.458559
5.458507
5.458559
5.458561
5.458558
5.458559
5.458476
5.458532
5.458487
5.458498
5.458548
5.458516
5.458539
5.458486
5.458480
5.458500
5.458537
5.458555
5.458545
5.458550
5.458512

Load Cell Load
(Lbs)
15
337
547
1016
1699
1654
1774
1926
2017
2098
2196
2295
2382
2486
2589
2678
2782
2888
2979
3088
3194
3289
3397
3505
3598
3708
3822
3920
4036
4153
4256
4380
4507
4616
4746
4881
4998
5138
5282
5406

...


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