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

2. Jiangyu Li, University of Washington Failure Criteria Materials Assumed to be perfect: –Brittle Materials Max Normal Stress –Ductile Materials Max Shear Stress Octahedral Shear Stress 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 (K c ), then failure will occur

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

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

5. Jiangyu Li, University of Washington 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 Y P =1.6 and Y T =2.5 are required.

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

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

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

9. Jiangyu Li, University of Washington Secant Modulus

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

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

12. Jiangyu Li, University of Washington Stress Concentration

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

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

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

16. Jiangyu Li, University of Washington Stress Intensity Factor

17. Jiangyu Li, University of Washington Superposition

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

19. Jiangyu Li, University of Washington Plastic Zone

20. Jiangyu Li, University of Washington Limitation of LEFM

21. Jiangyu Li, University of Washington Effect of Thickness

22. Jiangyu Li, University of Washington Correlation with Strength

23. Jiangyu Li, University of Washington

24. Energy Release Rate

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

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

27. Jiangyu Li, University of Washington Trend in Impact Behavior 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

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

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

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

31. Jiangyu Li, University of Washington 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!

32. Jiangyu Li, University of Washington 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.

33. Jiangyu Li, University of Washington 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.

34. Jiangyu Li, University of Washington 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

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

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

37. Jiangyu Li, University of Washington S-N Diagram Note the presence of a fatigue limit in many steels and its absence in aluminum alloys. log N f aa  mean 1  mean 2  mean 3  mean 3 >  mean 2 >  mean 1 The greater the number of cycles in the loading history, the smaller the stress that the material can withstand without failure.

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

39. Jiangyu Li, University of Washington Safety Factor

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

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

42. Jiangyu Li, University of Washington Fatigue Life

43. Jiangyu Li, University of Washington Crack Growth Rate

44. Jiangyu Li, University of Washington Fatigue Failure Criteria

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

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

47. Jiangyu Li, University of Washington 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 Change over Table 7-10 1 2 3

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