MEMORANDUM - University of Pittsburghdez11/papers/me2.pdf · MEMORANDUM TO: Pei Yuan Hsiao FROM:...
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MEMORANDUM TO: Pei Yuan Hsiao FROM: Desmond Zheng DATE: July 22, 2019 SUBJECT: Mechanics/Materials-2: Stress Concentration Factors I am writing to inform you about the lab that was conducted on July 17 th . The goal of the experiment was to continue examining the effect that holes and notches produce on stress in a bar during an applied uniaxial tension through the use of computational modeling in ANSYS. This lab continues the previous week’s experiment where we physically observed the effect. In this lab, we observed the stress concentrations of holes and notches and compared them to the experimental data from the first lab and theoretical stress concentrations curves (reproduced from Shigley) seen in Figures 1 and 2. For the first part of the experiment, we created each of the eight bars from the previous lab on Solidworks as IGS files. Then we modeled each bar on ANSYS and conducted a strain analysis to determine the strain distribution and maximum strain on each bar. Next, we compared the strain distribution for each notch and hole from the VIC-2D image and ANSYS profile in Figures 3-10. As shown in these figures, the results from the ANSYS profile do not match those of the VIC-2D image. Specifically, the strain distribution and location of maximum strain do not match. This can be explained by the mesh created for the ANSYS profile. When created for these profiles, the mesh is smaller for the notches and the holes. This results in a greater concentration around the notch and hole, resulting in different locations for maximum strain than the VIC-2D image. Furthermore, ANSYS does not account for real-world factors such as torsion and material imperfections, which occurred in the VIC-2D image. Next in the experiment, we created an ANSYS profile for the complex bar with both the notch and hole. The comparison of the VIC-2D image and ANSYS profile can be seen in Figure 11. We used our recorded load of 793.1 lbf for this model. As you can see, the strain distributions are similar as the strain gets larger the closer to the notch. However, the maximum strain is at the notch directly and is almost three times as large as the VIC-2D image. Our prediction of the correct failure location of the notch the previous lab matches the computational results here. This makes sense based on our earlier comparisons. The specimens with holes withstood larger amounts of force and strain than the notches. Finally, our computational data was used to calculate stress concentration factors for each notch and hole size using Equations 1-3 below. The resulting stress concentration factors can be seen in Table 2. These were then compared with the recorded data from the previous lab in Table 1. I plotted the stress concentration factors versus notch and hole size for both computational and recorded data in Figures 12-13. The computational data matches the experimental data at some points, but has large differences elsewhere. This is likely due to real world errors such as in loading, clamping, the VIC-2D capture system, and torsion from the tension machine. Next, theoretical plots were created similar to the Shigley trend curves using the computational results from ANSYS. Shown in Figures 14-15, the computational data does match the corresponding
Transcript of MEMORANDUM - University of Pittsburghdez11/papers/me2.pdf · MEMORANDUM TO: Pei Yuan Hsiao FROM:...
MEMORANDUM TO: Pei Yuan Hsiao
FROM: Desmond Zheng
DATE: July 22, 2019
SUBJECT: Mechanics/Materials-2: Stress Concentration Factors
I am writing to inform you about the lab that was conducted on July 17th. The goal of the experiment was to continue examining the effect that holes and notches produce on stress in a bar during an applied uniaxial tension through the use of computational modeling in ANSYS. This lab continues the previous week’s experiment where we physically observed the effect. In this lab, we observed the stress concentrations of holes and notches and compared them to the experimental data from the first lab and theoretical stress concentrations curves (reproduced from Shigley) seen in Figures 1 and 2.
For the first part of the experiment, we created each of the eight bars from the previous lab on Solidworks as IGS files. Then we modeled each bar on ANSYS and conducted a strain analysis to determine the strain distribution and maximum strain on each bar. Next, we compared the strain distribution for each notch and hole from the VIC-2D image and ANSYS profile in Figures 3-10. As shown in these figures, the results from the ANSYS profile do not match those of the VIC-2D image. Specifically, the strain distribution and location of maximum strain do not match. This can be explained by the mesh created for the ANSYS profile. When created for these profiles, the mesh is smaller for the notches and the holes. This results in a greater concentration around the notch and hole, resulting in different locations for maximum strain than the VIC-2D image. Furthermore, ANSYS does not account for real-world factors such as torsion and material imperfections, which occurred in the VIC-2D image.
Next in the experiment, we created an ANSYS profile for the complex bar with both the notch and hole. The comparison of the VIC-2D image and ANSYS profile can be seen in Figure 11. We used our recorded load of 793.1 lbf for this model. As you can see, the strain distributions are similar as the strain gets larger the closer to the notch. However, the maximum strain is at the notch directly and is almost three times as large as the VIC-2D image. Our prediction of the correct failure location of the notch the previous lab matches the computational results here. This makes sense based on our earlier comparisons. The specimens with holes withstood larger amounts of force and strain than the notches.
Finally, our computational data was used to calculate stress concentration factors for each notch and hole size using Equations 1-3 below. The resulting stress concentration factors can be seen in Table 2. These were then compared with the recorded data from the previous lab in Table 1. I plotted the stress concentration factors versus notch and hole size for both computational and recorded data in Figures 12-13. The computational data matches the experimental data at some points, but has large differences elsewhere. This is likely due to real world errors such as in loading, clamping, the VIC-2D capture system, and torsion from the tension machine. Next, theoretical plots were created similar to the Shigley trend curves using the computational results from ANSYS. Shown in Figures 14-15, the computational data does match the corresponding
Shigley data. This is due to the fact that the theoretical only accounts for dimensional factors and does not take other factors into consideration, similar to the ANSYS (with the exception of material). Therefore, they should produce similar results.
Overall, the computational models had high validity. They matched the Shigley theoretical plots and produced similar results to the recorded data, despite the differences in maximum strain locations. The ANSYS models provide a great tool to see ideal strain distribution profiles, but this is also the downside. These ‘perfect’ models are only useful to an extent, as real-world models are not as accurate. Thus, improvements can be made on the models. The inclusion of boundary conditions, such as applied torque from the machine and tension forces from the clamping, matching the physical experiment would be more appropriate and beneficial. ANSYS is an excellent tool for researching strain profiles, but physical experimenting should still be conducted to account for factors ANSYS cannot theorize. From this experiment, we gained greater knowledge of the effects of holes and notches as stress concentrations and learned how to utilize ANSYS modeling to analyze theoretical strain profiles.
Appendix:
Figure 1: Theoretical trend of notch concentration factors.
(Reproduced from Shigley, Mechanical Engineering Design, Figure A-15-3)
Figure 2: Theoretical trend of hole concentration factors.
(Reproduced from Shigley, Mechanical Engineering Design, Figure A-15-1)
Figure 3: Comparison of strain distribution for 1/16” notch. VIC-2D image (top) and ANSYS profile (bottom).
Figure 4: Comparison of strain distribution for 1/8” notch. VIC-2D image (top) and ANSYS profile (bottom).
Figure 5: Comparison of strain distribution for 3/16” notch. VIC-2D image (top) and ANSYS profile (bottom).
Figure 6: Comparison of strain distribution for 1/4” notch. VIC-2D image (top) and ANSYS profile (bottom).
Figure 7: Comparison of strain distribution for 1/16” hole. VIC-2D image (top) and ANSYS profile (bottom).
Figure 8: Comparison of strain distribution for 1/8” hole. VIC-2D image (top) and ANSYS profile (bottom).
Figure 9: Comparison of strain distribution for 3/16” hole. VIC-2D image (top) and ANSYS profile (bottom).
Figure 10: Comparison of strain distribution for 1/4” hole. VIC-2D image (top) and ANSYS profile (bottom).
Figure 11: Comparison of strain distribution for both hole and notch. VIC-2D image (top) and ANSYS profile (bottom).
Table 1: Recorded Experimental Data from ME-1.
Table 1: Computational Data for ME-2.
Size Maximum Stress (PSI) Nominal Stress (PSI) Kt d/wInch F(lbf) Microstrain
0.0625 1384 1240.84 12408.4 5905.066667 2.10131413 0.06250.13 1283 1803.64 18036.4 5865.142857 3.07518511 0.1250.19 1190 855.86 8558.6 5858.461538 1.46089548 0.18750.25 1084 575.39 5753.9 5781.333333 0.99525484 0.25
Size Maximum Stress (PSI) Nominal Stress (PSI) Kt r/dInch F(lbf) Microstrain
0.0625 988 1000.24 10002.4 5925.037481 1.6881581 0.033330.13 985 1236.69 12366.9 5907.046477 2.09358434 0.071430.19 984 1222.94 12229.4 5901.049475 2.07241103 0.115380.25 990 1067.36 10673.6 5937.031484 1.79780081 0.16667
Hole
Notch
Size Maximum Stress (PSI) Nominal Stress (PSI) Kt d/wInch F(lbf) Microstrain
0.0625 1384 1574.1 15741 5905.066667 2.66567693 0.06250.13 1283 1342.5 13425 5865.142857 2.2889468 0.1250.19 1190 1256.4 12564 5858.461538 2.14459034 0.18750.25 1084 1229.1 12291 5781.333333 2.12598017 0.25
Size Maximum Stress (PSI) Nominal Stress (PSI) Kt r/dInch F(lbf) Microstrain
0.0625 988 1894 18940 5925.037481 3.19660425 0.033330.13 985 1274.9 12749 5907.046477 2.1582698 0.071430.19 984 1222.94 12229.4 5901.049475 2.07241103 0.115380.25 990 1186.9 11869 5937.031484 1.99914722 0.16667
Notch
Hole
Figure 12: Stress Concentration Factor vs Hole Size.
Figure 13: Stress Concentration Factor vs Notch Size.
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Stress Concentration Factor vs Hole Size
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Figure 14: Theoretical Trend of Hole Concentration Factors.
Figure 15: Theoretical Trend of Notch Concentration Factors.
Equations for stress concentration factors:
𝐾" =$%&'$(
(1)
where
𝜎*+, = 𝐸𝜀*+, (2)
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Theoretical Trend of Hole Concentration Factors
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
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Theoretical Trend of Notch Concentration Factors
𝜎/ =01 (3)
𝜎*+, and 𝜎/ are the maximum and nominal stress, E is Young’s Modulus (10 Mpsi), and 𝜀*+, is the maximum strain.
