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? OUTLINE The Chinese University of Hong-Kong, September 2008

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

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

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

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

3- Fracture mechanisms in real materials Ti 3 Al-based alloy

Fracture surface polycristalline Ni 3 Al 3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008

3- Fracture mechanisms in real materials Irwin’s estimate of the plastic zone size - Perfect plasticity (no work hardening) - No angular dependence - Plane stress Elastic Plastic    yS Effective (notional) elastic crack : y x Plastic zone size  yS a Actual stress field after local yielding anan ryry

3- Fracture mechanisms in real materials R C =2r y = ( )  1 K Ic  yS 2  a n =r y K I =  (a+  a n ) Dugdale’s estimate of the plastic zone size R C =2r y = ( )  8 K Ic  yS 2 Shape of the plastic zone Von Mises criterion: (  1 -  2 ) 2 + (       + (  3 -  1 ) 2 =2  yS 2

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

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

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

3- Fracture mechanisms in real materials The Chinese University of Hong-Kong, September 2008 Experimental resistance curves for spruce (S. Morel et al. 01)  a(mm) R(J/m 2 )

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

a L 2a 2L (L/L 0 ) Limestone Sea Ice SiC Concrete Carbon Composite Vinyl Foam Concrete

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

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

3- Fracture mechanisms in real materials Stress corrosion: classical theory (Charles & Hillig 65, Wiederhorn 67, Michalske & Freiman 82) Hydrolysis: H 2 O+(-Si-O-Si-)  (-Si-OH.HO-Si-) The Chinese University of Hong-Kong, September 2008

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

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

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

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

cracks 5 mm 2,5 cm In situ AFM observations

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

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

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

3- Fracture mechanisms in real materials

Experiment FRASTA reconstruction

d  d 0 (V stageII / V) 1/3    0 exp (K 2 I /K 2 0 ) V  V 0 exp (K 2 I /K 2 0 )    0 for V > V stageII V stageII  m/s (Wiederhorn et al., 67) Dynamic fracture d 0 ~ 1 nm (C. Rountree et al) Stress corrosion V= m/s => d ~ 40 nm V= m/s => d ~ 100 nm    0 V / V 0 The Chinese University of Hong-Kong, September Fracture mechanisms in real materials

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

x y z RcRc Crack tip z x 280 nm The Chinese University of Hong-Kong, September Fracture mechanisms in real materials

120nm Notch Depression log[u z (nm)] r(nm) 0.1 log[u z (nm)] Cumulated porosity r (nm) 1/r The Chinese University of Hong-Kong, September Fracture mechanisms in real materials

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

1.5 nm -1.5 nm x Image 146 Kinematics of cavity growth Image 50 x A B C x Image 1 A t (h) x (nm) A BC The Chinese University of Hong-Kong, September Fracture mechanisms in real materials

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

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

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

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 The Chinese University of Hong-Kong, September 2008