3. Fracture mechanisms in real materials Fracture of crystals: Different fracture mechanisms

1. The Chinese University of Hong-Kong, September 2008 OUTLINE • 3. Fracture mechanisms in real materials • Fracture of crystals: Different fracture mechanisms The importance of plasticity • Quasi-brittle fracture: R-curve and size effect • Sub-critical fracture in silicate glasses: stress corrosion… Brittle or quasi-brittle?

2. 3- Fracture mechanisms in real materials Intergranular Metallic alloys: Cleavage Ductile Cleavage of single crystals: rapid, crystallographic (M. Marder, Austin University, USA single silicon crystal)

3. 3- Fracture mechanisms in real materials Plasticity in metals Edge dislocation

4. 3- Fracture mechanisms in real materials Stress corrosion in metallic alloys: 316L steel & liquid mercury(L. Medina, D. Gorse et al., 07)

5. 3- Fracture mechanisms in real materials Dimples around Si particles in an AlSi alloy (C. Prioul, Centrale Paris, France) Void formation by fracture of brittle precipitates In an aluminum alloy (C. Prioul, Centrale Paris, France)

6. 3- Fracture mechanisms in real materials Ti3Al-based alloy

7. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 Fracture surface polycristalline Ni3Al

8. 3- Fracture mechanisms in real materials s syS y e Elastic Plastic syS x Actual stress field after local yielding Dan ry a Plastic zone size Irwin’s estimate of the plastic zone size • Perfect plasticity (no work hardening) • No angular dependence • Plane stress Effective (notional) elastic crack :

9. 3- Fracture mechanisms in real materials 2 KIc 1 RC=2ry= ------ (------- ) syS p Dan=ry KI= s p (a+Dan) 2 KIc p RC=2ry= ------ (------- ) syS 8 Dugdale’s estimate of the plastic zone size Shape of the plastic zone Von Mises criterion: (s1-s2)2+ (s2-s3)2+ (s3-s1)2=2syS2

10. 3- Fracture mechanisms in real materials E. Landis & al. S. Morel & al. The Chinese University of Hong-Kong, September 2008 Quasi-brittle fracture: wood, concrete, rocks… No intrinsic plasticity Extended FPZ: microcracks • release of stored energy • stress redistribution

11. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 Paper creep (Santucci, Vanel & Ciliberto)

12. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 FPZ size Screening of the external stress field Quasi-brittle case: R-curve behaviour Perfectly brittle case

13. 3- Fracture mechanisms in real materials R(J/m2) Da(mm) The Chinese University of Hong-Kong, September 2008 Experimental resistance curves for spruce (S. Morel et al. 01)

14. 3- Fracture mechanisms in real materials Size of the notional crack { : FPZ size The Chinese University of Hong-Kong, September 2008 Size effect on the stress to failure: (Bažant 04) Short cracks: Long cracks:

15. Limestone Sea Ice SiC 2a a 2L L Concrete Carbon Composite Vinyl Foam Concrete Concrete (L/L0)

16. 3- Fracture mechanisms in real materials Intrinsic strength: Vacuum sc≈10-12GPa Humid air sc≈3-4GPa RC ≈1.5-2nm RC ≈13-23nm KIc=0.8MPa m The Chinese University of Hong-Kong, September 2008 Stress corrosion fracture of silicate glasses Brittle or quasi-brittle?

17. 3- Fracture mechanisms in real materials Wiederhorn et al. (1967,1970) Higher humidity rate Transition to dynamic fracture Diffusion controlled 10-5 m/s Chemically controlled 10-13 m/s KIc KI Crack propagation in a humid environment Same behaviour for mica, sapphire… Same ammonia on glass III II I

18. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 Stress corrosion: classical theory (Charles & Hillig 65, Wiederhorn 67, Michalske & Freiman 82) Hydrolysis: H2O+(-Si-O-Si-)(-Si-OH.HO-Si-)

19. 3- Fracture mechanisms in real materials Si Si Si O H O H O H O H H H O O Si Si Si

20. 3- Fracture mechanisms in real materials a(G-G*)+o(G-G*) DF±=DF∙ ± > G G* ~ Stage I chemically controlled Molecular reaction rate at the tip: Energy barrier to reform the SiO bond Energy barrier to break the SiO bond

21. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 45% humidity

22. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 Griffith’s criterion: G=G at the onset of fracture In humid air, G=G* V=0 G=G*: replaces Griffith’s criterion G*<G: easier to break in the presence of water!

23. In situ AFM observations cracks 2,5 cm 5 mm

24. 75 nm In situ AFM observations amorphous aluminosilicate V=3. 10-10 m/s Collaboration with F. Célarié, L. Ferrero & C. Marlière (LdV , Montpellier University)

25. 3- Fracture mechanisms in real materials In situ AFM observations Pure silica glass V=3. 10-11 m/s

26. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 FRASTA METHOD (Kobayachi & Schokey 87) Final image: definition of contours Relative movement of the contours: going back in time.

27. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008

28. Experiment FRASTA reconstruction

29. 3- Fracture mechanisms in real materials Elastic energy G ~ KI2 + H20 Nucleation sites Low fracture toughness regions = 1/d3 0= 1/d03   0exp (K2I/K20) V  V0exp (K2I/K20)    0for V > VstageII d  d0 (VstageII / V)1/3 The Chinese University of Hong-Kong, September 2008 VstageII  10-5 m/s (Wiederhorn et al., 67)    0 V / V 0 Dynamic fracture • d0 ~ 1 nm (C. Rountree et al) • Stress corrosion • V=10-10 m/s => d ~ 40 nm • V=10-11 m/s => d ~ 100 nm

30. 3- Fracture mechanisms in real materials Plane stress linear elasticity: z  r -0.5 1 mm dz (nm) x (nm) 20 nm dz (nm) dz (nm) 80 nm dz (nm) x (nm) r (nm) The Chinese University of Hong-Kong, September 2008 r (nm) Departure from r-0.5 within the damage zone (20nmx80nm)

31. 3- Fracture mechanisms in real materials z y Crack tip z Rc x x The Chinese University of Hong-Kong, September 2008 280 nm

32. 3- Fracture mechanisms in real materials 0.48 log[uz(nm)] 0.1 120nm 0.7479 1/r 120nm log[uz(nm)] Cumulated porosity Depression -2.77 Notch 0.2263 100 r(nm) The Chinese University of Hong-Kong, September 2008 r (nm)

33. 3 - Fracture mechanisms in real materials Process zone size Along the direction of crack propagation  ln(V*/V) Rc (nm) Perpendicular to the direction of crack propagation V (m/s) The Chinese University of Hong-Kong, September 2008

34. 3- Fracture mechanisms in real materials Image 1 Image 50 Image 146 2 t (h) 4 A A B C A B x 6 C 100 300 200 x (nm) x The Chinese University of Hong-Kong, September 2008 x Kinematics of cavity growth 1.5 nm -1.5 nm

35. 3- Fracture mechanisms in real materials “Macroscopic” velocity 3 10-11 m/s! C (foreward front cavity) V = 9 ± 8 10-12 m/s B (rear front cavity) V= 8 ± 5 10-12 m/s Positions of fronts A, B, C (nm) A (main crack front) V = 3 ± 0.8 10-12 m/s The Chinese University of Hong-Kong, September 2008 Intermittency of propagation Front arrière de la cavité V = 8 ± 5 10-12 m/s

36. 3- Fracture mechanisms in real materials 1st coalescence Velocity 3 10-11 m/s 2nd coalescence Velocity 3 10-12 m/s Position of the main crack front (A) Time

37. 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 (J.-P. Guin & S. Wiederhorn) No plasticity, but what about nano-cracks? …Fracture surfaces…

38. The Chinese University of Hong-Kong, September 2008 Summary • Dissipative processes: damage formation • ∙ Fracture of metallic alloys: • the importance of plasticity • ∙Quasi-brittle materials: brittle damage • ∙ Stress corrosion of silicate glasses: • brittle or quasi-brittle? • From micro-scale mechanisms to a • macroscopic description: • ∙ Morphology of cracks and fracture surfaces • ∙ Dynamics of crack propagation