1. 530.352 Materials Selection Lecture #23 FatigueTuesday November 8th, 2005

2. Failure even at low Stresses • Failure often occurs even when:applied < fractureand applied < yielding • 90% of all mechanical failures are related todynamic loading. • Dynamic Loading -> Cyclic Stresses

3. Examples of Fatigue Failures Plastic Tricycle:

4. Examples of Fatigue Failures Door Stop:

5. Versailles 1842 first fatigue problem axial failure Today flaws in 10% of rails. Examples of Fatigue Failures Railway Accidents:

6. Types of Fatigue • Fatigue of uncracked components • No pre-cracks; initiation controlled fracture • Examples : most small components: pins, gears, axles, ... • High cycle fatigue • fatigue < yield ; Nf > 10,000 • Low cycle fatigue • fatigue > yield ; Nf < 10,000

7. Types of Fatigue: • Fatigue of cracked structures • Pre-cracks exist: propagation controls fracture • Examples : most large components, particularly those containing welds: bridges, airplanes, ships, pressure vessels, ...

8. Cyclic Loading  Weight + time -

9. + max mean  0 time min - Basic Fatigue Terminology: maxmin mean maxmin amplitudemaxmin N = number of fatigue cycles Nf = number of cycles to failure

10. High Cycle Fatigue • Apply controlled applied < ~ 2/3yield • Stress is elasticon gross scale. • Locally the metal deforms plastically. S-N Curves Mild Steel 50 40 30 10 0 Fatigue limit Stress Al alloys 105 106 107 108 109 Nfailure

11. Low Cycle Fatigue • Apply controlled amounts of total • total = elastic + plastic • Empirical Observations and Rules • Coffin-Manson Law • Miner’s Rule

12. Coffin-Manson Law For low cycle fatigue: plastic Nfailure1/2 = Const. log pl y=y/E ~104 log Nfailure

13. Miner’s Rule Rule of Accumulative damage: Ni Nfailure@ i = 1 N1 N2 N3 Fraction of life time @ i

14. The Fatigue Process • Crack initiation • early development of damage • Stage I crack growth • deepening of initial crack on shear planes • Stage II crack growth • growth of well defined crack on planes normal to maximum tensile stress • Ultimate Failure

15. Crack initiation Cracks start at: • Surfaces • Inclusions • Existing cracks Alternate stresses -> slip bands -> surface rumpling

16. Crack Initiation:

17. Crack Growth Striation indicating steps in crack advancement.

18. Propagation in Cracked Structures ao~ adetectible < acritical ao -> acritical = FAILURE !!! K = Kmax - Kmin = (a)1/2 da = A1KmdN Fast fracture log da/dN threshold linear log K

19. Real world comparisons: Fast fracture log da/dN threshold linear log K

20. Fracture surfaces:

21. Fracture Surfaces: Initiation site Fatigue cracking Final fracture