Question

In: Mechanical Engineering

The data file contains displacement (in mm)-load (in N) data for a mechanical test that was...

The data file contains displacement (in mm)-load (in N) data for a mechanical test that was conducted on an unknown metal. The initial length and diameter of the specimen are also given.

a. (5 pts.) Using the data and a computer program (such as Excel), create an engineering stress-engineering strain graph with proper labels. The stress axis should be in the units of MPa. You do not need to show your spreadsheet or software code used to make the graph. Just provide the resultant graph.

b. (3 pts. each) Using the resultant stress-strain graph determine the following: 1. Young’s modulus 2. 0.2% offset yield strength 3. Ultimate tensile strength 4. Strain at fracture 5. Plastic strain after fracture

DATA:

Starting Length: 45 mm
Starting Diameter: 4.5 mm

Displacement	Load
(mm)	(N)
0	0
0.00381	7.60425
0.01136	11.62058
0.02002	11.50859
0.02897	33.09734
0.03793	57.60998
0.04678	80.50632
0.05549	129.06431
0.0641	189.98748
0.07265	236.10657
0.08112	294.54054
0.08955	376.3719
0.09795	452.95712
0.10634	524.02308
0.1147	590.90229
0.12305	590.90229
0.13139	681.9556
0.13975	769.05638
0.14808	844.02785
0.15641	914.92804
0.16474	1013.60097
0.17309	1100.03585
0.18143	1175.01337
0.18976	1212.42693
0.19809	1249.42046
0.20642	1342.2973
0.21476	1435.33153
0.2231	1512.78847
0.23142	1597.03009
0.23976	1688.1146
0.24809	1780.8429
0.25641	1835.63656
0.26475	1865.63819
0.27309	1939.82595
0.28143	2041.12497
0.28976	2139.00022
0.29808	2215.27717
0.30643	2294.47964
0.31476	2392.71671
0.32308	2460.84132
0.33143	2491.41105
0.33976	2579.03151
0.3481	2656.36481
0.35642	2754.75672
0.36475	2857.68067
0.37309	2934.79091
0.38143	3014.14798
0.38976	3085.83397
0.39809	3115.05073
0.40643	3210.80931
0.41475	3291.99783
0.42309	3374.03477
0.43142	3473.05369
0.43976	3570.88121
0.44809	3649.65945
0.45641	3714.74773
0.46475	3723.96712
0.47309	3827.87758
0.48142	3920.71065
0.48976	3998.61624
0.49809	4072.91576
0.50643	4169.56842
0.51476	4258.46968
0.52309	4328.78314
0.53142	4332.09492
0.53976	4392.7026
0.5481	4490.65492
0.55642	4574.81435
0.56474	4635.82762
0.57309	4701.41089
0.58142	4783.0618
0.58975	4864.17534
0.5981	4924.53761
0.60642	4952.59883
0.61476	4992.41613
0.62309	5065.56081
0.63142	5144.18166
0.63976	5206.31066
0.6481	5258.32409
0.65641	5345.19786
0.66475	5418.6848
0.67309	5473.05867
0.68143	5533.98766
0.68976	5593.6412
0.69809	5612.32027
0.70643	5683.70335
0.71476	5739.82624
0.72308	5790.18192
0.73141	5865.71218
0.73975	5938.99516
0.74808	5986.2081
0.75641	6040.23645
0.76474	6116.43633
0.77308	6186.98634
0.78141	6206.46589
0.78141	6239.50781
0.78975	6295.9888
0.79808	6366.13835
0.80642	6439.34915
0.81475	6486.84893
0.82309	6540.69753
0.83142	6615.6406
0.83975	6684.9119
0.84259	6738.55701
0.84808	6790.99048
0.85641	6843.61532
0.86474	6868.54543
0.87308	6938.96506
0.88143	6988.10304
0.88976	7045.70767
0.89808	7116.68376
0.90434	7188.33739
0.90642	7239.34593
0.91475	7289.30579
0.92308	7370.99163
0.93142	7433.80981
0.93975	7459.2568
0.94809	7488.78112
0.95641	7547.09262
0.96249	7612.02537
0.96474	7682.93301
0.97309	7727.95035
0.98142	7780.15982
0.98975	7854.76901
0.99809	7924.39003
1.00642	7967.13214
1.01475	8020.92254
1.01958	8088.9957
1.02309	8091.09118
1.03141	8151.73052
1.03975	8207.40592
1.04809	8247.65023
1.05642	8316.47497
1.06475	8388.57517
1.07309	8427.04531
1.08016	8474.49712
1.08142	8540.54932
1.08975	8609.39268
1.09808	8653.98254
1.10642	8695.35934
1.11476	8718.74671
1.12309	8764.17197
1.13142	8823.87348
1.13975	8865.01279
1.14	8907.96166
1.14808	8975.17428
1.15641	9032.69462
1.16475	9071.61459
1.17309	9116.02844
1.18143	9179.37793
1.18975	9232.64213
1.19809	9271.36373
1.20642	9309.68206
1.20867	9353.93199
1.21477	9371.04877
1.22309	9422.49224
1.23141	9456.01147
1.23975	9478.51222
1.24808	9534.31241
1.25642	9579.88016
1.26476	9593.71403
1.27308	9618.12492
1.28142	9652.22903
1.28642	9675.42548
1.28976	9684.97712
1.29808	9684.06349
1.30642	9702.05292
1.31476	9716.4046
1.32308	9712.21831
1.33142	9708.62154
1.33975	9730.25244
1.34809	9745.46
1.35642	9736.68881
1.36475	9733.18424
1.37009	9751.42233
1.37309	9766.22943
1.38143	9758.84777
1.38976	9755.2361
1.39809	9780.73385
1.40643	9789.64567
1.41475	9782.84515
1.42308	9772.59781
1.4314	9794.28645
1.43974	9806.33125
1.44807	9797.49672
1.45274	9795.4385
1.45641	9813.41023
1.46474	9823.46945
1.47307	9816.54786
1.48141	9811.10986
1.48975	9829.22222
1.49808	9842.10521
1.50642	9836.49492
1.51475	9826.79892
1.52307	9843.86913
1.53141	9856.42988
1.53749	9844.41582
1.53974	9840.74548
1.5481	9856.80614
1.55642	9868.48585
1.56473	9858.90254
1.57308	9854.50204
1.58142	9870.85886
1.58974	9882.90738
1.59808	9877.61561
1.60641	9869.20856
1.61474	9889.05691
1.62308	9900.37713
1.6255	9889.65016
1.63141	9884.26432
1.63975	9905.88963
1.64809	9913.50878
1.6564	9907.3993
1.66475	9900.34547
1.67309	9921.08136
1.68141	9931.75805
1.68975	9923.78686
1.69807	9915.8166
1.70641	9934.46447
1.71476	9943.04381
1.71717	9938.18045
1.72307	9931.23837
1.73142	9951.6809
1.73975	9964.21184
1.74808	9956.06557
1.75642	9947.27947
1.76474	9966.97042
1.77308	9976.42055
1.78141	9957.01831
1.78974	9973.82868
1.79808	9965.90592
1.80641	9981.65831
1.81474	9989.0111
1.81975	9981.65365
1.82308	9978.55049
1.83142	9996.67868
1.83976	10007.54721
1.84808	9998.69406
1.8564	9991.63184
1.86475	10010.99404
1.87308	10023.29122
1.88142	10014.39337
1.88975	10011.98497
1.89807	10024.01114
1.90642	10034.66547
1.91476	10034.1728
1.92309	10023.55572
1.93142	10038.80892
1.93975	10053.63278
1.94808	10042.70371
1.95642	10044.74517
1.96475	10055.77669
1.97309	10064.2154
1.98142	10060.27684
1.98974	10050.07979
1.99808	10067.15186
2.00642	10080.26581
2.01474	10071.93327
2.02309	10067.91182
2.03142	10089.91338
2.03975	10096.10854
2.04809	10088.28171
2.0564	10082.85023
2.06474	10100.0797
2.07309	10106.72562
2.08142	10096.72694
2.08976	10091.4631
2.09808	10109.13495
2.10642	10120.93853
2.11476	10119.13177
2.12309	10107.97638
2.13141	10127.43264
2.13976	10133.8001
2.14808	10124.16743
2.15642	10122.91014
2.16474	10144.46281
2.17308	10152.59977
2.18142	10143.70099
2.18974	10135.52211
2.19809	10155.91249
2.20643	10172.90913
2.21475	10162.29205
2.22309	10145.32708
2.23141	10169.84228
2.23976	10174.50914
2.24809	10168.50304
2.25643	10162.52395
2.26475	10181.94109
2.27309	10192.50415
2.28141	10184.80957
2.28976	10178.04164
2.29808	10198.34913
2.30642	10206.99739
2.31476	10199.51794
2.32308	10189.58725
2.33142	10210.91826
2.33975	10218.0643
2.34809	10215.47522
2.35642	10206.80647
2.36474	10223.12976
2.37308	10233.9508
2.38142	10221.75048
2.38975	10217.60982
2.39809	10235.35896
2.40643	10250.3188
2.41475	10236.4039
2.42309	10229.3985
2.43141	10246.98466
2.43725	10263.00527
2.43975	10251.02939
2.4481	10245.2198
2.45643	10260.53913
2.46474	10272.46378
2.47308	10261.64368
2.48142	10255.02943
2.48975	10268.42557
2.49809	10279.9125
2.50643	10272.00185
2.51476	10263.50632
2.52308	10282.64314
2.53143	10295.33334
2.53976	10284.18727
2.54809	10275.57254
2.55642	10288.41455
2.56474	10302.44213
2.57309	10296.78248
2.58143	10287.47484
2.58974	10305.06566
2.5981	10311.63055
2.60642	10304.44074
2.61476	10299.88471
2.6231	10318.40965
2.63142	10329.07143
2.63976	10318.90418
2.64809	10315.15747
2.65641	10329.32196
2.66476	10339.18746
2.67309	10331.02628
2.68142	10320.44645
2.68976	10338.8885
2.69809	10348.35633
2.70641	10344.66084
2.71476	10332.16901
2.72309	10351.412
2.73142	10363.06284
2.73976	10353.2197
2.74809	10345.37517
2.75642	10364.25866
2.76474	10373.61939
2.77309	10365.42747
2.78143	10359.65886
2.78977	10376.13861
2.79808	10385.67629
2.80642	10376.90509
2.81476	10370.31692
2.8231	10387.72985
2.83142	10393.82443
2.83973	10384.74869
2.84805	10376.90789
2.85639	10401.66896
2.86473	10404.47317
2.87307	10399.25963
2.88141	10395.1972
2.88975	10408.16214
2.89808	10419.36222
2.90642	10407.5009
2.91475	10398.51084
2.92306	10422.80812
2.93138	10429.50619
2.93972	10420.41741
2.94806	10410.95238
2.9564	10429.90852
2.96474	10438.21033
2.97308	10428.21165
2.98142	10422.24374
2.98976	10437.83873
2.99806	10449.86863
3.00638	10441.74284
3.01472	10438.15538
3.02306	10448.84324
3.0314	10456.99324
3.03974	10449.05838
3.04808	10439.93142
3.05642	10460.34414
3.06476	10469.20847
3.0731	10461.51109
3.08141	10455.82257
3.08971	10471.33747
3.09805	10479.60576
3.10639	10465.84919
3.11473	10456.2724
3.12307	10480.64418
3.13141	10486.39417
3.13975	10477.60434
3.14809	10470.29719
3.15643	10487.63748
3.16473	10496.26339
3.17305	10484.99066
3.18139	10478.22181
3.18973	10495.01915
3.19807	10504.15728
3.20641	10494.30482
3.21475	10491.36929
3.22309	10508.44975
3.23141	10517.30849
3.23971	10511.78388
3.24805	10495.37584
3.25639	10520.56719
3.26473	10526.94768
3.27307	10513.54781
3.28141	10509.58876
3.28975	10520.48057
3.29808	10536.3261
3.30642	10524.11087
3.31476	10516.5327
3.32309	10531.69928
3.33139	10540.63998
3.33972	10528.68646
3.34809	10531.83246
3.35641	10545.42419
3.36471	10552.89246
3.37305	10540.87747
3.38143	10533.20151
3.38974	10548.04493
3.39806	10560.8711
3.40643	10549.67847
3.41475	10542.80903
3.42305	10562.35656
3.43138	10569.21761
3.43972	10557.03498
3.44806	10552.59258
3.4564	10570.62764
3.46474	10575.92966
3.47308	10562.93957
3.48142	10556.38772
3.48976	10577.26145
3.4981	10583.38024
3.50641	10571.99296
3.51471	10567.3261
3.52305	10583.74345
3.53139	10590.32883
3.53973	10579.93434
3.54807	10572.80414
3.55641	10588.306
3.56474	10597.6807
3.57305	10597.6807
3.5814	10588.18866
3.58976	10576.91686
3.59806	10596.37126
3.60638	10607.03211
3.61472	10591.6243
3.62306	10580.84797
3.6314	10608.31826
3.63974	10614.54602
3.64808	10603.58062
3.65642	10594.61106
3.66476	10608.98602
3.67309	10618.23871
3.68139	10604.41602
3.68973	10597.46649
3.69807	10621.49089
3.70641	10622.27972
3.71475	10611.05542
3.72309	10604.15711
3.73143	10622.72768
3.73977	10632.86699
3.74809	10622.30952
3.75639	10609.77578
3.76472	10628.40223
3.77306	10638.59463
3.7814	10628.94054
3.78974	10613.81865
3.79808	10637.12314
3.80642	10645.0934
3.81475	10628.94333
3.82309	10622.06365
3.83143	10641.56834
3.83977	10640.94249
3.84808	10629.55894
3.85638	10624.432
3.86473	10642.04704
3.8731	10649.38772
3.88141	10637.69124
3.88972	10631.37595
3.89806	10647.66105
3.9064	10649.3542
3.91474	10642.17277
3.92308	10632.28119
3.93142	10649.045
3.93976	10654.32373
3.94808	10641.22841
3.95639	10635.92546
3.96472	10658.08162
3.97306	10655.33888
3.9814	10646.04707
3.98973	10635.83232
3.99807	10654.84434
4.00641	10664.89518
4.01475	10648.97422
4.02309	10644.74322
4.03143	10660.81878
4.03973	10665.55362
4.04806	10652.22081
4.0564	10645.72111
4.06473	10662.18782
4.07307	10666.8463
4.08141	10654.43736
4.08975	10643.6722
4.09809	10661.82368
4.10643	10667.52896
4.11476	10658.47278
4.12307	10644.35486
4.13138	10662.95896
4.13972	10670.82956
4.14806	10657.15123
4.1564	10646.25569
4.16474	10665.34314
4.17308	10670.53247
4.18142	10658.85555
4.18976	10646.99609
4.1981	10665.32638
4.20644	10670.44958
4.21478	10660.15195
4.22311	10653.4753
4.23142	10666.00066
4.23225	10671.8149
4.23972	10658.16637
4.24808	10649.90181
4.25644	10664.87469
4.26476	10664.70798
4.27307	10648.63708
4.28137	10644.17046
4.28972	10658.63203
4.29809	10659.60526
4.30643	10646.68503
4.31474	10636.50288
4.32306	10656.72468
4.3314	10657.39989
4.33974	10639.57717
4.34808	10631.83602
4.35641	10646.39259
4.36475	10649.08411
4.37309	10635.51661
4.38143	10623.71023
4.38977	10638.19136
4.39811	10644.77302
4.40642	10626.42317
4.41472	10617.9323
4.42306	10630.16988
4.4314	10630.40737
4.43974	10616.61635
4.44808	10605.82139
4.45642	10620.3435
4.46476	10616.79702
4.4731	10598.44717
4.48143	10586.70972
4.48973	10599.57314
4.49806	10602.11286
4.50643	10582.61935
4.51477	10568.85906
4.52307	10586.91461
4.53139	10585.60144
4.53976	10570.45627
4.54812	10556.04406
4.55644	10567.7573
4.56475	10566.20385
4.57305	10551.13226
4.58142	10534.98872
4.58977	10546.66657
4.5981	10545.25562
4.60641	10526.88807
4.61472	10515.2186
4.62306	10524.42659
4.6314	10519.43935
4.63974	10503.0397
4.64808	10479.77526
4.65642	10496.08644
4.66476	10490.60654
4.6731	10470.81407
4.68144	10458.34739
4.68978	10469.41243
4.6981	10462.43403
4.70641	10445.98594
4.71473	10427.58673
4.72307	10435.93511
4.73141	10433.23707
4.73975	10412.30466
4.74809	10394.30592
4.75643	10402.93183
4.76475	10402.09737
4.77306	10383.63017
4.7814	10363.36925
4.78974	10370.47431
4.79808	10365.52526
4.80642	10343.27131
4.81476	10328.35152
4.8231	10337.37324
4.83143	10329.99437
4.83973	10310.065
4.84806	10290.13656
4.8564	10298.46538
4.86474	10289.83388
4.87308	10269.20229
4.88142	10247.92902
4.88976	10258.46321
4.8981	10253.92674
4.90644	10228.4234
4.91478	10211.83841
4.92312	10219.90273
4.93144	10212.9085
4.93974	10187.91739
4.94805	10173.30401
4.95639	10174.1869
4.96472	10171.03903
4.97306	10145.84582
4.9814	10128.10972
4.98974	10138.35333
4.99808	10133.6455
5.00642	10103.54515
5.01476	10087.10917
5.0231	10091.49849
5.03144	10082.35104
5.03975	10059.56158
5.04806	10044.35401
5.0564	10045.07206
5.06473	10037.86363
5.07307	10029.29639
5.08141	10014.18009
5.08975	9992.73732
5.09809	9995.82093
5.10643	9994.13617
5.11477	9971.66429
5.12311	9946.20845
5.13142	9951.87089
5.13973	9946.00914
5.14806	9920.64923
5.1564	9899.47747
5.16474	9904.4349
5.17308	9892.25972
5.18142	9864.89095
5.18976	9847.83471
5.19809	9855.80776
5.20643	9843.72851
5.21477	9817.90293
5.22311	9796.55981
5.23142	9802.2297
5.23973	9792.77119
5.24806	9767.72606
5.25644	9747.00693
5.26478	9753.07822
5.27309	9744.59853
5.2814	9713.23717
5.28973	9694.66008
5.29807	9698.88922
5.30641	9686.96363
5.31475	9662.77532
5.32309	9640.07713
5.33143	9645.37915
5.33977	9635.51085
5.34811	9605.34532
5.35643	9587.83086
5.36474	9588.97546
5.37306	9576.13438
5.38144	9551.07436
5.38976	9532.68446
5.39807	9533.70426
5.40641	9523.52863
5.41475	9498.1296
5.42309	9472.54989
5.43142	9480.73622
5.43976	9467.49467
5.4481	9443.97133
5.45644	9423.11436
5.46477	9423.34905
5.47307	9410.80321
5.48139	9397.96958
5.48976	9384.18042
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5.50641	9365.73651
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5.5731	9245.63594
5.58144	9233.70197
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5.62307	9144.4198
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5.68968	9018.12129
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5.70631	8999.9456
5.71469	8985.80905
5.72306	8954.30427
5.73143	8929.08592
5.73486	8934.1728
5.73977	8923.37412
5.74808	8893.68914
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5.76469	8866.42095
5.773	8854.09582
5.78132	8826.01086
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5.79807	8805.50407
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5.82305	8761.9815
5.83136	8741.64514
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5.87309	8668.88277
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6.01474	8370.06047
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6.06465	8241.01642
6.07301	8237.24456
6.08139	8220.42394
6.08976	8193.71734
6.09809	8161.99929
6.1064	8161.92571
6.1147	8155.27979
6.12301	8147.84504
6.13131	8116.13072
6.13466	8086.29487
6.13969	8087.15355
6.14806	8069.2973
6.15643	8041.48521
6.16477	8016.25289
6.17307	8010.82607
6.18138	7998.12749
6.18968	7960.96399
6.19799	7936.66858
6.20633	7937.30281
6.2147	7911.04045
6.22308	7881.34802
6.23144	7855.88566
6.23974	7848.72845
6.24805	7834.41123
6.25635	7799.97604
6.26466	7773.38771
6.27301	7772.64358
6.28138	7748.40266
6.28975	7714.10763
6.2981	7690.33236
6.30641	7683.0755
6.31471	7668.14128
6.32302	7634.18386
6.33132	7608.5953
6.33965	7600.52865
6.34802	7588.19096
6.3564	7549.27099
6.36477	7527.04032
6.3731	7530.86479
6.38141	7520.95832
6.38972	7501.94769
6.39802	7461.81514
6.40633	7436.21355
6.41467	7427.43909
6.42304	7409.23546
6.43142	7373.6296
6.43979	7341.62563
6.4481	7338.98254
6.4564	7320.74818
6.46471	7283.26663
6.46745	7255.8145
6.47302	7245.50476
6.48133	7225.3258
6.4897	7187.64635
6.49807	7162.54115
6.50645	7158.28408
6.51475	7136.66249
6.52306	7104.2669
6.53137	7073.91277
6.53967	7066.09897
6.548	7041.65595
6.55637	7004.81748
6.56475	6974.15974
6.5731	6966.34268
6.58141	6947.20633
6.58972	6907.38857
6.59802	6903.78249
6.60633	6876.70754
6.61468	6866.23855
6.62306	6842.63045
6.63143	6797.91067
6.63979	6766.21776
6.64809	6724.53968
6.6564	6657.016
6.66471	6627.6635
6.67301	6510.55248
6.68133	6473.10587
6.6897	6424.78187
6.69807	6360.94389
6.70645	6278.75328
6.71476	6177.2
6.72307	6056.82889
6.73137	5919.72703
6.73968	5768.82856

Expert Solution

Given Initial length Lo=45mm=0.045m

initial diameter D=4.5mm=0.0045m

so initial area of cross section Ao = =

a)

engineering stress is given by the equation .

engineering strain is given by the equation

stress and strains at each loading point can be calculated using the above equations

engineering stress-strain curve is plotted in Excel as shown below:

b)

1) Young's modulus = 22831.4044358222 MPa (Slope of the line can be determined from the graph)

2) 0.2% 0ffset yield strength = 603.637MPa (Can be seen in the above figure)

3) Ultimate Tensile Strength = 671.0013 (maximum stress value Obtained

4) Strain at Fracture = 0.149770667m (Strain value obtained at fracture)

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