Mohammad Albuloushi

Experiment #1

The Stress-Strain Relationship in Tension

September 22, 2014

Bader Alrashidi -Yousif Ali-Christian Aguinaga

Abstract

The main objective of conducting this experiment was to show that the properties of the materials differ from one material to another. This experiment was conducted using the MTS Insight Tensile Testing machine, which applies load to the material being tested and gives us numbers such as the amount of load being applied and the elongation, and by using these data we can then calculate the stress and strain of the material and obtain a stress-strain graph for each sample being tested and designate important points on the curve, such as the elastic region, yield point, ultimate strength, and the breaking point. We used the numerical values to calculate also the margin of errors in our experiment, which will be shown in the sample calculations and error analysis page. These errors may be caused because of the materials not being handled well or because of the margin error within the devices being used in the experiment.

Introduction and Theory

There is no doubt that the properties of the materials are the main focus in studying the mechanics of deformable bodies. The only way that we can determine those properties is by conducting experiments on these materials. On our first lab experiment, we conducted the tension test, which means that a tension load will be performed on the material itself and notice its behavior.

When a steel bar is subjected to a load, it either extends or stretches, and if it goes back to its original length after the load is removed, it is known to be ‘elastic’. This behavior only occurs till a certain or limited range of loads. The stretching can also occur in a linear proportion to the load, then which it will satisfy Hooke’s Law and is called ‘Linearly Elastic’. However, when the load increases than the certain limit, it will cause a permanent deformation to the material itself, and this behavior is called ‘plastic’

This lab experiment teaches that to determine those behaviors, we need to define stress and strain that are dependent on the amount of loads applied and elongations that are in unit basis. In order to determine the elastic and plastic properties of the material, we need to be able to calculate the stress and strain by using the following equations:

Stress: (I-1)

Strain: (I-2)

Hooke’s Law: (I-3)

Where:

= The stress ( psi )

P = The applied load on the bad (lb , kN)

A= The cross-sectional area of the bar ( in2, m2 )

δ= Elongation (in, mm)

L = original length of the bar

E= Young’s modulus

Procedures

The following steps are the procedures we did in order to conduct this experiment. When we first started, the computers were already logged in and the program was already opened. Our instructor made sure that the Emergency Stop switch on the MTS frame was off by twisting it to pop up. He then proceeded to identify the samples we were going to test, which were coded Blue: 1018 Steel. Red: 1045 Steel. Aluminum: 6061 Steel. The first step we had to do was to measure the top, middle, and bottom diameter of each sample we were going to test. One condition was that the middle diameter has to be smaller than the top and bottom diameter. After checking that it’s smaller, we measured the middle diameter three times then took the average number of our measurements in order to be as accurate as possible. Our next step was to begin securing the sample bars in the jaws of the testing machine. There was a handset that controlled the machine; it helped us to jog the crosshead down and up. After inserting the specimen into the upper jaw, approximately a quarter inch should be left between the jaw frame and the end of the specimen. After that you close the jaw by turning the T-handle. One mistake we did during this experiment was not leaving an extra quarter inch between the jaw frame and the specimen, which led to damaging the specimen and getting a new one from the instructor.

After locking the specimen, we attach the extensometer. The blades of the extensometer must be placed against the sample and located as close as the center of the sample. After that we secure the extensometer to the specimen using the wire clips, the we remove the safety pin, which keeps the extensometer blades at the 2-insh spacing.

Zero all the numerical values about the load, crosshead, and extensometer by right clicking on each one of them and selection “zero channel”. Then click on the green arrow and enter the sample’s name and the average diameter measured in the beginning of the experiment, then click “ok”. We then observe the change in the load and the extensometer reading, and see how it is affecting the sample test. We collect the data till the sample breaks. After it breaks, we follow the instructions that are given on the computer, which were removing the extensometer and re-inserting the pin in the extensometer, and then removing the broken sample test. We then measure the new cross-sectional diameter after the break. The on-screen instructions will take the crosshead back to its normal position.

We then have to store the data and report the maximum load that the machine applied on the tested sample. To store the data, we give the file and appropriate name and select save. After that we click on File < Export Preview < Specimen. We save the data on the desktop and on a USB flash drive. The file can be imported into Excel by opening the same file from within Excel. Make sure after you import the file into Excel to save it again as an Excel file. Not saving is as an Excel file may cause of losing the graphs.

After finishing these steps, we then do all these steps again to the other next samples by clicking on File < New Sample.

Sample Calculations and Error Analysis

% Area Reduction=100x) (I-4)

Specimen Diameter % Area Reduction

1018 Steel in 100x()=39.9%

1045 Steel 100x()=27.9%

6061 Aluminum 100x()=32.2%

1018 Steel

+= 0.00579 0.579%

1045 Steel

+= 0.0071 0.71%

6061 Aluminum

+= 0.0029 0.29%

Calculating Stress:

σ= = 101107.64 psig

Calculating Strain:

Calculating the modulus of elasticity:

Summary of Important Results

Macintosh HD:Users:mohammedbloushi:Desktop:Green bar 2.jpg

Figure I-1. Stress vs. Strain Over the Elastic Range for 6061 Steel

Macintosh HD:Users:mohammedbloushi:Documents:blue bar1.jpg

Figure I-2. Stress vs. Strain Over the Entire Range for 6061 Steel

Macintosh HD:Users:mohammedbloushi:Desktop:Blue bar 1.jpg

Figure I-3. Stress vs. Strain Over the Entire Range for 1018 Steel

Macintosh HD:Users:mohammedbloushi:Desktop:Blue bar 2.jpg

Figure I-4. Stress vs. Strain Over the Elastic Range for 1018 Steel

Macintosh HD:Users:mohammedbloushi:Desktop:Red bar 1.jpg

Figure I-5. Stress vs. Strain Over the Elastic Range for 1045 Steel

Macintosh HD:Users:mohammedbloushi:Desktop:Red bar 2.jpg

Figure I-6. Stress vs. Strain Over the Entire Range for 1045 Steel

In every graph, by convention, strain is always plotted on the horizontal axis and stress on the vertical axis. For each sample, we plotted the stress-strain curve over both the elastic range and the plastic range. On the graph we can notice the elastic region, which is the linear equation “the straight line at the beginning of the curve”. And then the graph starts to curve, which indicates that the behavior of the material changed into the plastic behavior. The point that separates between the elastic region and plastic region is called “the yield point”. We also define on the graph both the ultimate strength and the breaking point. The ultimate strength is the highest point on the graph that has the highest stress value. The breaking point is the last point on the graph, which indicates that after this point the sample got fractured. The slope of this curve is known as Young’s Modulus or the modulus of elasticity. The error result for 1018 Steel was only 0.579% which means that this could have been caused by the material itself or by the margin of error within the devices used in this experiment. Moreover, for 1045 Steel the percent error was 0.71% percent which was a bit higher than the percent error for 1018 Steel. One explanation for this could be the fact that the material should have been better developed or that I should have handled the devices with greater efficiency. In addition, the percent error for 6061 Aluminum happened to be 0.29% which is lower than both the previous steel specimen. Another possibility for this could be that the material itself was better developed or that the software itself reduced its margin of error. Not to forget mentioning that human errors or calculation errors are hard to avoid.

Discussion and Conclusion

After successfully conducting the experiment and retrieving the data, we were able to calculate the stress, strain, and the modulus of elasticity and put them on a table form and graphs. Using these tables and graphs, it made it easier for us to find the percentage error for each specimen that was tested. We noticed that each material has its own unique stress and strain curve. These curves showed us a lot of properties including data to determine Young’s Modulus. After calculating the percentage error, we notice that it was minimal that could have been caused by the devices used or by the specimen since we used the same devices for all the samples and still got different values for the percentage error of each sample. Another reason can be the accuracy or the precision of the tools used as all tools have margin errors that eventually add up.

According to outer sources, the published Young’s modulus value for the Aluminum T6 6061 Steel is 68.9 (GPa), which equals to 9,993,256 (psi). Our calculated value that is shown in (Figure I-1) is 9,743,212 (psi), which shows the minimal difference between them. Moreover, for the blue bar we were able to find the published Young’s Modulus and determine which type of steel the sample is. The published modulus of elasticity is 205 (Gpa), which equals to 2.9733x107 (psi) compared to our calculated Young’s Modulus that equals to 2.80x107 (psi). We were able to determine that it is AISI 1018 Mild/Low Carbon Steel. In addition, for the third sample, which is the Red Bar 1045 Steel, we determined that it is AISI 1045 Medium Carbon Steel. Its published modulus of elasticity is 80 (Gpa) that equals 2.90x107 (psi) compared to our calculated 2.81x107 (psi).

References

[1] Stress-Strain Relationship, Mechanical Design in Optical Engineering, OPTI 222, http://fp.optics.arizona.edu/optomech/references/OPTI_222/OPTI_222_W4.pdf

[2] http://www.azom.com/article.aspx?ArticleID=6115

[3] http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6

[4] CSUF EGME 306A Lab Manual

Appendix

Blue Bar 1018 Steel

Load (lbf)

Extensometer (in)

Elongation

Load

Strain

Stress

63.498

0.00027

0.00027

63.498

0.000135

682.7741935

101.654

0.0003

0.00044

300.099

0.00022

3226.870968

123.562

0.00035

0.00057

529.554

0.000285

5694.129032

145.372

0.00036

0.00077

795.192

0.000385

8550.451613

166.781

0.00037

0.00094

1083.729

0.00047

11653

188.031

0.00036

0.0012

1382.212

0.0006

14862.49462

210.688

0.00038

0.0014

1687.678

0.0007

18147.07527

232.695

0.00041

0.0016

1999.739

0.0008

21502.56989

255.138

0.00043

0.00185

2318.691

0.000925

24932.16129

277.936

0.00042

0.00208

2642.969

0.00104

28419.02151

300.099

0.00044

0.00231

2972.337

0.001155

31960.6129

323.018

0.00045

0.00255

3307.301

0.001275

35562.37634

345.377

0.00048

0.00285

3648.462

0.001425

39230.77419

365.432

0.00048

0.0031

3991.776

0.00155

42922.32258

387.894

0.0005

0.00335

4341.019

0.001675

46677.62366

410.746

0.00051

0.00364

4698.8

0.00182

50524.73118

433.018

0.00053

0.00386

5058.205

0.00193

54389.30108

456.61

0.00054

0.00414

5424.87

0.00207

58331.93548

480.203

0.00056

0.0044

5793.902

0.0022

62300.02151

504.191

0.00056

0.00474

6169.28

0.00237

66336.34409

529.554

0.00057

0.00488

6544.926

0.00244

70375.54839

554.502

0.00062

0.00518

6928.375

0.00259

74498.65591

580.036

0.00061

0.00549

7319.958

0.002745

78709.22581

605.823

0.00063

0.00621

7699.909

0.003105

82794.72043

631.07

0.00065

0.00728

8064.585

0.00364

86715.96774

658.198

0.00066

0.00838

8395.888

0.00419

90278.36559

685.142

0.0007

0.00997

8686.517

0.004985

93403.4086

711.462

0.0007

0.01156

8920.046

0.00578

95914.47312

739.724

0.00072

0.0149

9118.811

0.00745

98051.73118

767.284

0.00073

0.01823

9253.064

0.009115

99495.31183

795.192

0.00077

0.02258

9334.266

0.01129

100368.4516

823.786

0.00077

0.02819

9395.576

0.014095

101027.6989

851.441

0.0008

0.03372

9430.239

0.01686

101400.4194

879.87

0.00082

0.03957

9448.181

0.019785

101593.3441

908.665

0.00084

0.04517

9437.436

0.022585

101477.8065

937.417

0.00085

0.05235

9401.406

0.026175

101090.3871

967.068

0.00089

0.05896

9304.557

0.02948

100049

995.755

0.00089

0.0665

9189.213

0.03325

98808.74194

1024.617

0.00092

0.07402

9051.373

0.03701

97326.5914

1054.258

0.00092

0.08116

8908.345

0.04058

95788.65591

1083.729

0.00094

0.08843

8762.937

0.044215

94225.12903

1113.202

0.00099

0.09568

8614.796

0.04784

92632.21505

1143.35

0.00099

0.10372

8475.556

0.05186

91135.01075

1172.126

0.00102

0.11062

8319.053

0.05531

89452.1828

1202.3

0.00105

0.11827

8168.239

0.059135

87830.52688

1232.426

0.00107

0.12626

8013.301

0.06313

86164.52688

1262.25

0.0011

0.13338

7835.625

0.06669

84254.03226

1291.32

0.00111

0.14149

7665.719

0.070745

82427.08602

1321.777

0.00112

0.14874

7473.656

0.07437

80361.89247

1351.002

0.00117

0.15638

7275.143

0.07819

78227.34409

1382.212

0.0012

0.16429

7060.854

0.082145

75923.16129

1412.172

0.0012

0.17263

6832.03

0.086315

73462.68817

1441.929

0.00122

0.1805

6580.751

0.09025

70760.76344

1472.035

0.00123

0.18885

6299.696

0.094425

67738.66667

Red Bar 1045 Steel

Load (lbf)

Extensometer (in)

Elongation

Load

Strain

Stress

30.667

0.0002

0.0002

30.667

0.0001

494.6290323

46.478

0.00022

0.00037

144.235

0.000185

2326.370968

61.173

0.00026

0.00039

237.378

0.000195

3828.677419

75.462

0.00028

0.00049

342.675

0.000245

5527.016129

89.204

0.00029

0.00062

457.502

0.00031

7379.064516

100.31

0.00033

0.00076

583.093

0.00038

9404.725806

110.154

0.00033

0.0009

715.81

0.00045

11545.32258

119.696

0.00036

0.00105

853.857

0.000525

13771.8871

127.705

0.00034

0.00118

996.213

0.00059

16067.95161

135.268

0.00034

0.00134

1142.489

0.00067

18427.24194

144.235

0.00037

0.00151

1291.891

0.000755

20836.95161

152.101

0.00036

0.00167

1441.859

0.000835

23255.79032

160.465

0.00035

0.00183

1592.143

0.000915

25679.72581

169.802

0.00037

0.00198

1745.393

0.00099

28151.5

179.473

0.00035

0.00218

1901.418

0.00109

30668.03226

188.585

0.00039

0.00236

2059.233

0.00118

33213.43548

199.038

0.00037

0.00252

2218.599

0.00126

35783.85484

208.264

0.00036

0.00269

2378.81

0.001345

38367.90323

217.825

0.00039

0.00288

2543.2

0.00144

41019.35484

227.386

0.00037

0.00304

2708.027

0.00152

43677.85484

237.378

0.00039

0.00323

2876.517

0.001615

46395.43548

247.232

0.00041

0.00341

3047.048

0.001705

49145.93548

257.585

0.00039

0.00363

3221.911

0.001815

51966.30645

267.798

0.00043

0.00379

3395.177

0.001895

54760.91935

277.593

0.00042

0.00402

3570.511

0.00201

57588.8871

288.277

0.00044

0.00425

3748.953

0.002125

60466.98387

299.14

0.00045

0.00445

3925.772

0.002225

63318.90323

309.208

0.00045

0.0047

4103.409

0.00235

66184.01613

319.996

0.00045

0.00494

4280.554

0.00247

69041.19355

331.59

0.00048

0.00521

4458.905

0.002605

71917.82258

342.675

0.00049

0.00548

4635.773

0.00274

74770.53226

353.191

0.00052

0.00583

4813.199

0.002915

77632.24194

364.944

0.00051

0.00619

4987.469

0.003095

80443.04839

375.763

0.00052

0.00659

5161.203

0.003295

83245.20968

387.172

0.00054

0.00699

5330.322

0.003495

85972.93548

399.179

0.00056

0.00744

5497.583

0.00372

88670.69355

410.839

0.00057

0.00799

5662.493

0.003995

91330.53226

422.263

0.00058

0.00856

5820.862

0.00428

93884.87097

434.568

0.0006

0.00915

5974.738

0.004575

96366.74194

445.88

0.00061

0.00986

6122.485

0.00493

98749.75806

457.502

0.00062

0.0108

6268.555

0.0054

101105.7258

469.995

0.00063

0.01167

6407.313

0.005835

103343.7581

482.315

0.00064

0.01269

6535.836

0.006345

105416.7097

493.801

0.00064

0.01312

6652.264

0.00656

107294.5806

506.749

0.00067

0.01443

6770.737

0.007215

109205.4355

519.956

0.00069

0.01534

6877.394

0.00767

110925.7097

531.768

0.0007

0.01667

6981.501

0.008335

112604.8548

544.611

0.00071

0.01808

7074.723

0.00904

114108.4355

557.99

0.00072

0.01953

7161.444

0.009765

115507.1613

570.505

0.00074

0.0213

7237.886

0.01065

116740.0968

583.093

0.00076

0.02272

7304.349

0.01136

117812.0806

596.569

0.00077

0.02475

7367.012

0.012375

118822.7742

609.141

0.00078

0.02702

7423.115

0.01351

119727.6613

622.057

0.00079

0.02908

7460.082

0.01454

120323.9032

635.693

0.0008

0.03174

7496.9

0.01587

120917.7419

648.306

0.00081

0.03437

7517.313

0.017185

121246.9839

661.79

0.00082

0.03714

7521.128

0.01857

121308.5161

675.503

0.00086

0.04018

7510.985

0.02009

121144.9194

688.426

0.00085

0.04322

7481.148

0.02161

120663.6774

701.448

0.00088

0.04673

7432.668

0.023365

119881.7419

715.81

0.0009

0.05056

7386.451

0.02528

119136.3065

729.561

0.00092

0.05391

7323.58

0.026955

118122.2581

742.474

0.00091

0.05785

7270.182

0.028925

117261

756.676

0.00094

0.06128

7205.304

0.03064

116214.5806

770.459

0.00093

0.06506

7144.629

0.03253

115235.9516

783.996

0.00098

0.06847

7079.438

0.034235

114184.4839

797.964

0.00096

0.07231

7017.17

0.036155

113180.1613

812.09

0.001

0.07609

6954.528

0.038045

112169.8065

825.23

0.00099

0.07957

6886.387

0.039785

111070.7581

839.642

0.00103

0.0833

6816.279

0.04165

109939.9839

853.857

0.00105

0.08705

6745.106

0.043525

108792.0323

867.226

0.00104

0.09091

6672.935

0.045455

107627.9839

881.414

0.00105

0.09461

6594.783

0.047305

106367.4677

896.058

0.00108

0.09847

6513.954

0.049235

105063.7742

909.18

0.0011

0.10227

6427.273

0.051135

103665.6935

923.827

0.0011

0.10626

6317.163

0.05313

101889.7258

Aluminum Bar 6061 Steel

Load (lbf)

Extensometer (in)

elongation

load

strain

stress

39.744

0.00035

0.00035

39.744

0.000175

446.5617978

74.341

0.00042

0.0008

268.89

0.0004

3021.235955

109.517

0.00052

0.00114

428.76

0.00057

4817.52809

139.091

0.00057

0.00148

594.728

0.00074

6682.337079

164.936

0.00063

0.00184

762.457

0.00092

8566.932584

186.783

0.00068

0.00221

934.669

0.001105

10501.89888

206.421

0.00071

0.00259

1108.793

0.001295

12458.34831

223.247

0.00072

0.00299

1285.545

0.001495

14444.32584

238.859

0.00077

0.00339

1466.866

0.001695

16481.64045

253.134

0.0008

0.00381

1651.487

0.001905

18556.03371

268.89

0.0008

0.00424

1841.176

0.00212

20687.37079

284.535

0.00084

0.00465

2032.503

0.002325

22837.11236

300.568

0.00087

0.0051

2229.19

0.00255

25047.07865

316.736

0.0009

0.00555

2429.169

0.002775

27294.03371

332.453

0.00093

0.00601

2631.621

0.003005

29568.77528

348.325

0.00097

0.00647

2837.248

0.003235

31879.19101

364.689

0.00099

0.00694

3046.656

0.00347

34232.08989

380.29

0.00101

0.00745

3260.57

0.003725

36635.61798

396.763

0.00106

0.00797

3473.739

0.003985

39030.77528

412.916

0.0011

0.00872

3682.28

0.00436

41373.93258

428.76

0.00114

0.01008

3863.64

0.00504

43411.68539

445.433

0.00118

0.01468

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0.0012

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3970.849

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44616.2809

477.473

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0.0014

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39464.64045

987.356

0.00234

0.20704

3402.949

0.10352

38235.38202

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