1. Mechanics of Materials Lab
Lecture 21
Failure Criteria and Plasticity
Mechanical Behavior of Materials Sec ,
Jiangyu Li
University of Washington 1
Jiangyu Li, University of Washington

2. Jiangyu Li, University of Washington
Failure Mode
Ductile: yielding
Brittle: Fracture 2
Jiangyu Li, University of Washington

3. Jiangyu Li, University of Washington
Multi-axial Load
Figure: 07-01a-d
Tension or compression 3
Jiangyu Li, University of Washington

4. Maximum Normal Stress Fracture Criterion
Figure: 07-02a-b 4
Jiangyu Li, University of Washington

5. Maximum Shear Stress Yielding Criterion
Figure: 07-05 5
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6. Three-dimensional Stress State
Figure: 07-06a-b 6
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7. Octahedral Shear Stress7
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8. Octahedral Shear Stress Criterion
Figure: 07-08 8
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9. Three-dimensional Stress State
Figure: 07-09 9
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10. Jiangyu Li, University of Washington
Comparison
Figure: 07-10 10
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11. Jiangyu Li, University of Washington
Example
For a stress state of sx=120, sy=-50, sz=200, txy=60 Mpa, and a safety factor of 2.0 again yielding, what is the minimum yield strength by (1) maximum shear stress criterion and (2) octahedral shear stress criterion 11
Jiangyu Li, University of Washington

12. Note the difference when stress have opposite sign
Comparison
Figure: 07-11
Note the difference when stress have opposite sign 12
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13. Jiangyu Li, University of Washington
Load Factor Design
7. 32 A circular bar must support a axial loading of 200 kN and a torque of 1.5 kN.m. Its yield strength is 260 MPa.
What diameter is needed if load factors YP=1.6 and YT=2.5 are required. 13
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14. Jiangyu Li, University of Washington
Stress Strain Curve
Figure: 12-01a-b 14
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15. Jiangyu Li, University of Washington
Cyclic Loading
Figure: 12-02 15
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16. Elastic-Perfect Plastic and Linear Hardening
Figure: 12-04a-b 16
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17. Power Hardening and Ramberg-Osgood Relation
Figure: 12-05a-b 17
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18. Rheological Modeling of Nonlinear Hardening
Figure: 12-06 18
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19. Jiangyu Li, University of Washington
Assignment
Mechanical Behavior of Materials
7.2, 7.6, 7.33, 12.4 19
Jiangyu Li, University of Washington