FRACTURE OF HETEROGENEOUS SOLIDS Elisabeth Bouchaud GROUPE FRACTURE
FRACTURE OF HETEROGENEOUS SOLIDS Elisabeth Bouchaud GROUPE FRACTURE Service de Physique et Chimie des Surfaces et des Interfaces CEA-Saclay The Chinese University of Hong-Kong, September 2008
Montpellier University Bordeaux University Matteo Ciccotti Mathieu Georges Stéphane Morel Laurent Ponson Christian Marlière Cindy Rountree Orsay University The Fracture CEA-Saclay Harold Auradou Jean-Philippe Bouchaud Jean-Pierre Hulin Group Stéphane Chapuilot Daniel Bonamy Caltech Onera Denis Boivin Jean-Louis Pouchou Claudia Guerra Akshay Singh G. Ravichandran Gaël Pallarès
Leonardo da Vinci’s fracture experiments on metallic wires The Chinese University of Hong-Kong, September 2008
Compromise of mechanical properties: The importance of being imperfect… Pure metals are too « soft » Alloys: ▪solid solution atoms ▪ dislocations (atomic) ▪ intermetallic inclusions (1 -50 mm) & interphase boundaries ▪ grains & grain boundaries (up ~0. 1 mm) Polymers rigid but brittle reinforced by soft rubber particles ( 100 nm -1µm) Glasses? Amorphous structure (1 nm) The Chinese University of Hong-Kong, September 2008
Composite material: epoxy matrix, graphite fibers (Columbia University) The Chinese University of Hong-Kong, September 2008
Balsa wood (Vural & Ravichandran, Caltech) The Chinese University of Hong-Kong, September 2008
Ni-based alloy – grain size 20 to 80 mm (Onera) The Chinese University of Hong-Kong, September 2008
Ni-based alloy – grain size 2 to 30 mm (Onera) The Chinese University of Hong-Kong, September 2008
Polyamide reinforced with rubber particles (L. Corte, L. Leibler, ESPCI) The Chinese University of Hong-Kong, September 2008
Polymeric foams (S. Deschanel, ENS LYON-INSA) The Chinese University of Hong-Kong, September 2008
Tomographic images during deformation Polymeric foams (S. Deschanel, ENS LYON-INSA)
AMORPHOUS SILICA O Si O O O Silica tetrahedron Silica tetrahedra sharing an oxygen atom: membered rings The Chinese University of Hong-Kong, September 2008
s How to estimate the properties of a composite ? Young’s modulus: s=Ee Ecomposite F E + F E s Except if… cracks develop ! Why ? The Chinese University of Hong-Kong, September 2008
GENERAL OUTLINE 1 - What is so specific about fracture? 2 - Elements of Linear Elastic Fracture Mechanics 3 - Fracture mechanisms in real materials 4 - Statistical characterization of fracture 5 - Stochastic models
OUTLINE 1. What is so specific about fracture? § A crude estimate of the strength to failure § Stress concentration at a crack tip § Damage zone formation in heterogeneous materials: rare events statistics 2. Elements of Linear Elastic Fracture Mechanics § Griffith’s criterion § Fracture toughness and energy release rate § Weakly distorted cracks § Principle of local symmetry The Chinese University of Hong-Kong, September 2008
1 - What is so special about fracture? A crude estimate of the strength to failure s s=E a Dx a Failure : Dx≈a sf ≈ E/100 s Presence of flaws! The Chinese University of Hong-Kong, September 2008
1 - What is so special about fracture? Stress concentration at a crack tip (Inglis 1913) s s. A > s: stress concentration A 2 b 2 a s The Chinese University of Hong-Kong, September 2008
1 - What is so special about fracture? Infinitely sharp tip: s s (r) Irwin (1950) r s K=stress intensity factor Strong stress gradient Crack mostly sensitive at tip! Sample geometry
1 - What is so special about fracture? Mode I Tension, opening KI Mode II In-plane, shear, sliding KII Mixed mode, to leading order: Mode III Out-of-plane, shear Tearing KIII
1 - What is so special about fracture? Heterogeneous material: Fracture of a link if s(r, q)>sc_local P(sc_local) Length RC of the damaged zone? sc_min sc_local sc_max Statistics of rare events The Chinese University of Hong-Kong, September 2008
2 - Elements of fracture mechanics s Griffith’s energy balance criterion Elastic energy Surface energy B Total change in potential energy: 2 a Propagation at constant applied load:
2 - Elements of fracture mechanics Happens for a critical load: Stress intensity approach: Crack increment a: r Elastic energy per unit volume: da The Chinese University of Hong-Kong, September 2008
2 - Elements of fracture mechanics At the onset of fracture: a=1/2 Fracture toughness Energy release rate
2 - Elements of fracture mechanics T-stress: (Cotterell & Rice 80) - Stability of the crack - SIF variation due to out-of-plane meandering The Chinese University of Hong-Kong, September 2008
2 - Elements of fracture mechanics WEAKLY DISTORTED 2 D CRACK Weight function (geometry) Infinite plate: 1/√-px (Cotterell & Rice 80; Movchan, Gao & Willis 98) The Chinese University of Hong-Kong, September 2008
2 - Elements of fracture mechanics WEAKLY DISTORTED PLANAR CRACK (Meade & Keer 84, Gao & Rice 89) The Chinese University of Hong-Kong, September 2008
2 - Elements of fracture mechanics Weakly distorted 3 D crack front (Movchan, Gao & Willis 98) The Chinese University of Hong-Kong, September 2008
2 - Elements of fracture mechanics Crack path: principle of local symmetry q q KII=0 The Chinese University of Hong-Kong, September 2008
Summary -LEFM (Linear Elastic Fracture Mechanics): ∙ Fracture toughness KIc KI<KIc: stable crack KI≥KIc: propagating crack ∙ Weak distorsions: change in SIFs rough cracks and fracture surfaces -In real life… ∙ Dissipative processes Plasticity Brittle damage (microcracks) ∙ Subcritical crack growth due to corrosion, temperature, plasticity… The Chinese University of Hong-Kong, September 2008
3 - Fracture mechanisms in real materials Process zone size Rc (nm) Along the direction of crack propagation ln(V*/V) Perpendicular to the direction of crack propagation V (m/s) The Chinese University of Hong-Kong, September 2008
3 - Fracture mechanisms in real materials Kinematics of cavity growth B 4 A t (h) A 1. 5 nm 2 Image 1146 Image 50 Image A B C xx 6 C -1. 5 nm 100 200 x (nm) 300 The Chinese University of Hong-Kong, September 2008
Positions of fronts A, B, C (nm) 3 - Fracture mechanisms in real materials Intermittency of propagation “Macroscopic” velocity 3 10 -11 m/s! C (foreward front cavity) V = 9 ± 8 10 -12 m/s. Front arrière de la cavité V = 8 ± 5 10 -12 m/s B (rear front cavity) V= 8 ± 5 10 -12 m/s A (main crack front) V = 3 ± 0. 8 10 -12 m/s The Chinese University of Hong-Kong, September 2008
3 - Fracture mechanisms in real materials Position of the main crack front (A) 1 st coalescence Velocity 3 10 -11 m/s 2 nd coalescence Velocity 3 10 -12 m/s Time
3 - Fracture mechanisms in real materials (J. -P. Guin & S. Wiederhorn) No plasticity, but what about nano-cracks? …Fracture surfaces… 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 The Chinese University of Hong-Kong, September 2008
- Slides: 35