1. 530.352 Materials Selection Lecture #22 : FractureMonday November 7th, 2005

2. Fracture Liberty Ships in WWII

3. Fracture

4. Quebec Bridge - August 29, 1907

5. Quebec Bridge - Sept. 11, 1916

6. Tacoma Narrows Bridge Failure

7. Tacoma Narrows Bridge Failure

8. Tacoma Narrows Bridge Failure

9. Tacoma Narrows Bridge Failure

10. Stress Magnification:  Inglis 1913 max = (1+2c / h) for an ellipse:  = h2 / c max = 2 (c / )1/2 lim = ao max = 2 (10-2 / )1/2 max = 20,000  max  2c  2h  

11. 2c t w Griffith Analysis Thermodynamic Method (1920) - rigorous but do not need to know  Uo = potential E of uncracked plate. How does U change when a crack is formed ??

12. 2c t w Energies of Crack Growth Utotal = Uo + Usurfaces + Uelastic + Uwork

13. Surface Energy Usurface = 2 s 2c 1 = 4 s c 2 new surfaces

14. Elastic Energy Uelastic = c22 E Note: of the form (r2) (

15. Po xo x1 x Po Work Done Uwork done = -2 Uelastic = - 2 c22 E Derivation:  Uel = U1el - U2el = 1/2Pox1 - 1/2Poxo = 1/2 Po (u1-uo) Uwork = - Po (u1-uo) = - 2 Ue

16. Total Energy Utotal = Uo + 4 s c + c22 - 2 c22 E E Utotal = Uo + 4 s c - c22 E stable unstable Utotal Uo c c*

17. Utotal stable unstable Uo c* Griffith Equation Utotal = 4 s - 2 c 2 = 0 c E c* = 2 s E 2 let c=c* ; solve for s  = (2 s E /  c)1/2

18. Basis for Fracture Mechanics  ( c )1/2= (2 s E )1/2 Stress Intensity Factor K geometrical loading Fracture Toughness KIc Material Parameters

19. Key to Fracture Mechanics 1. Determine Kc - measure on specimens of known geometry 2. Calculate K - from current geometry and loading 3. Compare K with Kc - K < Kc is OK - K > Kc will fracture

20. Stress Intenisty Factors K = f (,c) Infinite plate; through crack Semi-infinite plate; through crack K =  (c)1/2 Y = 1 K = Y (c)1/2 Y = 1.12 2c c Finite plate; through crack Penny crack K = Y (c)1/2 w K = Y  (c)1/2 Y = 2/ 2.2 2.0 1.8 Y 2c .1 .5 2c/w

21. Yielding vs. Fracture If plastic < fracture • dislocation motion and yielding If fracture < plastic • fracture • brittle - or - ductile at crack tip

22. GIC and KIC • Brittle Materials • Gc = 2 s • Ductile Materials • Gc = 2 (s + p ) Kc = (EGc)1/2 KC = Fracture Toughness [MPa √m] GC = Energy Absorbed in making a Crack [MPa m]

23. Typical Values for GIC ; KIC

24. Ductile Fracture • local > yield • dislocation motion blunts the crack tip !!! • harder for crack to propagate  r

25. Ductile Fracture

26. Brittle Fracture  r local < yield No dislocation motion !!! Atoms cleave

27. Brittle Fracture

28. DBTT Ductile Brittle Transition Temperature BCC yield  fracture fast fracture yielding DBTT T