Yielding and Failure Criteria Plasticity Fracture Fatigue Jiangyu Li University of Washington

1. Mechanics of Materials Lab Yielding and Failure Criteria Plasticity Fracture Fatigue Jiangyu Li University of Washington Jiangyu Li, University of Washington

2. Failure Criteria • Materials have flaw or crack in them: • Linear Elastic Fracture Mechanics (LEFM) • Stress intensity factor (K) describes the severity of the existing crack condition • If K exceeds the Critical stress intensity (Kc), then failure will occur • Materials Assumed to be perfect: • Brittle Materials • Max Normal Stress • Ductile Materials • Max Shear Stress • Octahedral Shear Stress Jiangyu Li, University of Washington

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

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

5. Safety Factor and Load Factor • 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

6. Stress Strain Curve Bauschinger Effect Jiangyu Li, University of Washington

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

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

9. Secant Modulus Jiangyu Li, University of Washington

10. Stress-Strain Curve Jiangyu Li, University of Washington

11. Displacement Mode Sliding mode Opening mode Tearing mode Jiangyu Li, University of Washington

12. Stress Concentration Jiangyu Li, University of Washington

13. Stress Intensity Factor: Tension Jiangyu Li, University of Washington

14. Stress Intensity Factor: Bending Jiangyu Li, University of Washington

15. Stress Intensity Factor: Circumferential Crack - Jiangyu Li, University of Washington

16. Stress Intensity Factor Jiangyu Li, University of Washington

17. Superposition Jiangyu Li, University of Washington

18. Brittle vs. Ductile Behavior Jiangyu Li, University of Washington

19. Plastic Zone Jiangyu Li, University of Washington

20. Limitation of LEFM Jiangyu Li, University of Washington

21. Effect of Thickness Jiangyu Li, University of Washington

22. Correlation with Strength Jiangyu Li, University of Washington

23. Jiangyu Li, University of Washington

24. Energy Release Rate Jiangyu Li, University of Washington

25. Strain Energy Increasing the strain rate increase strength, but decrease ductility Modulus of toughness & modulus of resilience Jiangyu Li, University of Washington

26. Charpy V-notch & Izod tests most common Energy calculated by pendulum height difference Charpy – metals, Izod - plastics Impact Test Jiangyu Li, University of Washington

27. Toughness is generally proportional to ductility Also dependent on strength, but not so strongly Brittle Fractures Lower energy Generally smooth in appearance Ductile Fracture Higher energy Rougher appearance on interior with 45° shear lips Trend in Impact Behavior Jiangyu Li, University of Washington

28. Effect of Temperature Decrease temperature increase strength, but decrease ductility Jiangyu Li, University of Washington

29. Ductile-Brittle Transition Jiangyu Li, University of Washington

30. Static Failure • Load is applied gradually • Stress is applied only once • Visible warning before failure Jiangyu Li, University of Washington

31. Cyclic Load and Fatigue Failure • Stress varies or fluctuates, and is repeated many times • Structure members fail under the repeated stresses • Actual maximum stress is well below the ultimate strength of material, often even below yield strength • Fatigue failure gives no visible warning, unlike static failure. It is sudden and catastrophic! Jiangyu Li, University of Washington

32. Characteristics • Primary design criterion in rotating parts. • Fatigue as a name for the phenomenon based on the notion of a material becoming “tired”, i.e. failing at less than its nominal strength. • Cyclical strain (stress) leads to fatigue failure. • Occurs in metals and polymers but rarely in ceramics. • Also an issue for “static” parts, e.g. bridges. • Cyclic loading stress limit<static stress capability. Jiangyu Li, University of Washington

33. Characteristics • Most applications of structural materials involve cyclic loading; any net tensile stress leads to fatigue. • Fatigue failure surfaces have three characteristic features: • A (near-)surface defect as the origin of the crack • Striations corresponding to slow, intermittent crack growth • Dull, fibrous brittle fracture surface (rapid growth). • Life of structural components generally limited by cyclic loading, not static strength. • Most environmental factors shorten life. Jiangyu Li, University of Washington

34. Fatigue Failure Feature • Flat facture surface, normal to stress axis, no necking • Stage one: initiation of microcracks • Stage two: progress from microcracks to macrocracks, forming parallel plateau-like facture feature (beach marks) separated by longitudinal ridge • Stage three: final cycle, sudden, fast fracture. Bolt, unidirectional bending Jiangyu Li, University of Washington

35. Fatigue-Life Method • Stress-life method • Facture mechanics method Jiangyu Li, University of Washington

36. Alternating Stress a = (max-min)/2 m = (max+min)/2 Jiangyu Li, University of Washington

37. S-N Diagram sa The greater the number ofcycles in the loading history,the smaller the stress thatthe material can withstandwithout failure. smean 3 > smean 2 > smean 1 smean 1 smean 2 smean 3 log Nf Note the presence of afatigue limit in manysteels and its absencein aluminum alloys. Jiangyu Li, University of Washington

38. S-N Diagram Endurance limit Jiangyu Li, University of Washington

39. Safety Factor Jiangyu Li, University of Washington

40. Facture Mechanics Method of Fatigue Jiangyu Li, University of Washington

41. Crack Growth > > Jiangyu Li, University of Washington

42. Fatigue Life Jiangyu Li, University of Washington

43. Crack Growth Rate Jiangyu Li, University of Washington

44. Fatigue Failure Criteria Jiangyu Li, University of Washington

45. Effect of Mean Stress Jiangyu Li, University of Washington

46. Fatigue Failure Criteria Multiply the stress By safety factor n Jiangyu Li, University of Washington

47. Example: Gerber Line AISI 1050 cold-drawn bar, withstand a fluctuating axial load varying from 0 to16 kip. Kf=1.85; Find Sa and Sm and the safety factor using Gerber relation Sut=100kpsi; Sy=84kpsi; Se’=0.504Sut kpsi Table 7-10 2 Change over 1 3 Jiangyu Li, University of Washington

48. Safety Factor with Mean Stress Jiangyu Li, University of Washington