1 / 28

530.352 Materials Selection

530.352 Materials Selection. Lecture #22 : Fracture Monday November 7 th , 2005. Fracture. Liberty Ships in WWII. Fracture. Quebec Bridge - August 29, 1907. Quebec Bridge - Sept. 11, 1916. Tacoma Narrows Bridge Failure. Tacoma Narrows Bridge Failure. Tacoma Narrows Bridge Failure.

tracey
Download Presentation

530.352 Materials Selection

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related