Lecture 21 Failure Criteria and Plasticity

1. Mechanics of Materials Lab Lecture 21 Failure Criteria and Plasticity Mechanical Behavior of Materials Sec. 7.1-7.6, 12.1-12.3 Jiangyu Li University of Washington Jiangyu Li, University of Washington

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

3. Multi-axial Load Tension or compression Jiangyu Li, University of Washington

4. Maximum Normal Stress Fracture Criterion Jiangyu Li, University of Washington

5. Maximum Shear Stress Yielding Criterion Jiangyu Li, University of Washington

6. Three-dimensional Stress State Jiangyu Li, University of Washington

7. Octahedral Shear Stress Jiangyu Li, University of Washington

8. Octahedral Shear Stress Criterion Jiangyu Li, University of Washington

9. Three-dimensional Stress State Jiangyu Li, University of Washington

10. Comparison Jiangyu Li, University of Washington

11. 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 Jiangyu Li, University of Washington

12. Comparison Note the difference when stress have opposite sign Jiangyu Li, University of Washington

13. 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. Jiangyu Li, University of Washington

14. Stress Strain Curve Jiangyu Li, University of Washington

15. Cyclic Loading Jiangyu Li, University of Washington

16. Elastic-Perfect Plastic and Linear Hardening Jiangyu Li, University of Washington

17. Power Hardening and Ramberg-Osgood Relation Jiangyu Li, University of Washington

18. Rheological Modeling of Nonlinear Hardening Jiangyu Li, University of Washington

19. Assignment Mechanical Behavior of Materials 7.2, 7.6, 7.33, 12.4 Jiangyu Li, University of Washington