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D. Bonamy, F. Célarié, C. Guerra-Amaro, L. Ponson, C.L. Rountree, E. Bouchaud GROUPE FRACTURE

MatGenIV, Cargèse, September 2007. FRACTURE MECHANISMS & SCALING PROPERTIES OF FRACTURE SURFACES. D. Bonamy, F. Célarié, C. Guerra-Amaro, L. Ponson, C.L. Rountree, E. Bouchaud GROUPE FRACTURE S ervice de P hysique et C himie des S urfaces et des I nterfac es CEA-Saclay, France

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D. Bonamy, F. Célarié, C. Guerra-Amaro, L. Ponson, C.L. Rountree, E. Bouchaud GROUPE FRACTURE

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  1. MatGenIV, Cargèse, September 2007 FRACTURE MECHANISMS & SCALING PROPERTIES OF FRACTURE SURFACES D. Bonamy, F. Célarié, C. Guerra-Amaro, L. Ponson, C.L. Rountree, E. Bouchaud GROUPE FRACTURE Service de Physique et Chimie des Surfaces et des Interfaces CEA-Saclay, France Collaboration S. Morel (US2B, Bordeaux, France) H. Auradou, J.-P. Hulin (FAST, Orsay, France)

  2. Macroscopic scale Include the basic mechanisms into a statistical description MatGenIV, Cargèse, September 2007 Scale of the material heterogeneities Mechanics of materials

  3. s0 Inglis (1913), Griffith (1920) c s (r) s0 r MatGenIV, Cargèse, September 2007 • No easy averaging at a crack tip: • Strong stress gradient • The most brittle link breaks first •  Rare events statistics • No «equivalent effective» material

  4. Fractography: In situ observations: s s +3D observations: Collective effects -History reconstruction +Real timeobservation of basic mechanisms -Confined to the free surface MatGenIV, Cargèse, September 2007 Experimental tools

  5. MatGenIV, Cargèse, September 2007 OUTLINE 1-Scaling properties of fracture surfaces 2- Statistical model… & model experiment 3- Damage: a general mechanism? 4-Conclusion & Work in progress

  6. 1- Scaling properties… h h x z z Self-affine profile x =0.75 Slope: =0.75 < h2 >1/2(nm) ζ ~ 0.8 independent of material & loading; x depends on material

  7. 1- Scaling properties… Ti3Al-based alloy z = 0.78 5 nm  0.5mm Dhmax(z) z = 0.78 z MatGenIV, Cargèse, September 2007 Profiles perpendicular to the direction of crack propagation

  8. 1- Scaling properties… Aluminum alloy z=0.77 3nm0.1mm Dhmax(z) z = 0.77 z MatGenIV, Cargèse, September 2007 Profiles perpendicular to the direction of crack propagation

  9. L. Ponson, D. Bonamy, E.B. PRL 2006 L. Ponson et al, IJF 2006 1- Scaling properties… Quasi-cristaux (STM) Alliage métallique (SEM+Stéréoscopie) Δh2D(Δz, Δx) = (<(h(zA+Δz, xA+Δx) - h(zA, xA))2>A)1/2 A B Δz z Glass (AFM) Δx h (nm) h/x  = 0.75  = 0.6 Z= / ~ 1.2 z/ x1/ z z (nm) Béton (Profilométrie) 130mm

  10. 1- Scaling properties… Quasi-crystals (STM) Alliage métallique (SEM+Stéréoscopie) A B Δz Glass (AFM) Δx  = 0.75  = 0.6 z = / ~ 1.2 Béton (Profilométrie) 130mm Δh2D(Δz, Δx) = (<(h(zA+Δz, xA+Δx) - h(zA, xA))2>A)1/2 z h (Å) Quasi-crystals Courtesy P. Ebert z Coll. L. Barbier, P. Ebert

  11. 1- Scaling properties… Quasi-crystals (STM) Aluminum alloy (SEM+Stereo) A B Δz Glass (AFM) Δx  = 0.75  = 0.6 z = / ~ 1.2 z/ x1/z Béton (Profilométrie) 130mm Δh2D(Δz, Δx) = (<(h(zA+Δz, xA+Δx) - h(zA, xA))2>A)1/2 h/x h (Å)

  12. 1- Scaling properties… Quasi-crystals (STM) Aluminum alloy (SEM+Stereo) A B Δz Glass (AFM) Δx  = 0.75  = 0.6 z= / ~ 1.2 z/ x1/z (Coll. S. Morel & G. Mourot) Mortar (Profilometry) 130mm Δh2D(Δz, Δx) = (<(h(zA+Δz, xA+Δx) - h(zA, xA))2>A)1/2 h/x h (Å) Mortar

  13. 1- Scaling properties… Quasi-crystals (STM) Metallic alloy (SEM+Stereo) A B Δz Glass (AFM) Δx (h/lx)/(x/lx) h/x Universal structurefunction Very different length scales (lz/lx)1/(z/lz)/(x/lx)1/z z/ x1/z Mortar (Profilometry) 130mm h (Å)

  14. 2- Statistical models Crack front= «elastic line» Fracture surface = trace left behind by the front J.-P. Bouchaud, EB, G. Lapasset, J. Planès (93) General result : anisotropic self-affine surface z, b independent of disorder

  15. 2- Statistical models KI0 f(x,z) • Linear elastic material • Weak distorsions h(x,z) z x KI0 KII Principle of local symmetry D. Bonamy et al, PRL 2006 KII = 0

  16. 2- Statistical models +ht(z,x) ζ=0.39 A. Rosso & W. Krauth (02) β=0.5andz=0.8 O.Duemmer & W. Krauth (05) MatGenIV, Cargèse, September 2007 h(x,z,h(x,z))=hq(z,h(x,z))+ht(z,x) Logarithmic roughness S. Ramanathan, D. Ertaş & D. Fisher (97)

  17. 2- …& model experiment • Linear Elastic Material MatGenIV, Cargèse, September 2007 « Model» material: sintered glass beads (L. Ponson et al, PRL06; coll. H. Auradou, J.-P. Hulin & P. Vié) Porosity 3 to 25% Grain size 50 to 100 mm Vitreous grain boudaries

  18. 2- …& model experiment 1/z Structure 2D Packing of sintered glass beads ζ=0.4± 0.05 β=0.5± 0.05 z=ζ/β=0.8 ±0.05 3 exponents Universal 2D correlation function +

  19. 3- Damage… Ti3Al-based alloy Amorphous silica MatGenIV, Cargèse, September 2007 What did we MISS ? Damage ! x damaged zone size Roughness measurements performed within the damaged zone !

  20. 3- Damage… Transmission of stresses through undamaged material:long range interactions (1/r2)  very rigid line  Long range Undamaged material Transmission of stresses through a « Swiss cheese »: Screening of elastic interactions lower rigidity MatGenIV, Cargèse, September 2007 • Disorder  line roughness • Elastic restoring forces  rigidity of the line  Short range

  21. 3- Damage… Rc MatGenIV, Cargèse, September 2007 ? r « Rc r » Rc Damage zone scale Large scales : elastic domain z=0.75, b=0.6 z=0.4, b=0.5 OR log

  22. 3- Damage… 75 nm =0.75 h ~ logz =0.75 h ~ logz Rc ~ 30nm Rc ~ 30nm

  23. 3- Damage… =0.4 =0.75 =0.4 x2 x1 =0.75 Rc(x1) Rc(x2) 75nm Rc(x1) MatGenIV, Cargèse, September 2007 Quasi-brittle material: Mortar… … In transient roughening regime Coll. S. Morel Rc increases with time

  24. 3- Damage… toughness T=20K,Y = 1305MPa, KIc = 23MPa.m1/2  Rc = 20 µm yield stress T=98K,Y = 772MPa, KIc = 47MPa.m1/2  Rc = 200 µm =0.75 h ~ logz h ~ logz =0.75 Rc Rc Steel broken at different temperatures (Coll. S. Chapuilot)

  25. 4- Conclusion… ~ 100 nm 20mm to 200mm MatGenIV, Cargèse, September 2007 Analytical model of fracture of an elastic linear disordered material Out-of-plane roughness  z=0.4, b=0.5 sintered glass beads, sandstone, wood  logarithmic roughness glass, steel Length scales >> Process zone size

  26. 4- Conclusion… In-plane fracture (Santucci, Bonamy, Ponson & Måløy, 07 ) c0+f(z,t) 0+Vt z MatGenIV, Cargèse, September 2007 Dynamic phase transition Stable crack KI<KIc Propagating crack KI>KIc

  27. 4- … & work in progress MatGenIV, Cargèse, September 2007 • ELASTIC REGIME • Algebraic/logarithmic roughness ? • « Map » of disorder: PROCESS ZONE REGIME Out-of-plane roughness  z=0.8, b=0.6 glass wood metallic alloys … Length scales ‹‹ Process zone size  A model ?

  28. 4- … & work in progress MatGenIV, Cargèse, September 2007 Cavity scale? • Metallic glasses: isotropic fracture surfaces! • Coll. G. Ravichandran (Caltech), D. Boivin & JL Pouchou (Onera) • Coupled equations: growth of cavities/ line progression Silicate glasses: damage formation at the crack tip Coll. E. Charlaix (Lyon I), M. Ciccotti (Montpellier II)

  29. 3- Damage… 300 mm 30 mm MatGenIV, Cargèse, September 2007 Zr-based metallic glass (Coll. D. Boivin, J.-L. Pouchou, G. Ravichandran)

  30. 3- Damage… ? MatGenIV, Cargèse, September 2007

  31. 4- Conclusion… MatGenIV, Cargèse, September 2007 3 classes of universality ? 1 Linear elastic region z=0.4 b=0.5 2 Intermediate region: damage = « perturbation » of the front (screening) z=0.8 b=0.6 3 Cavity scale: isotropic region z=b=0.5 3 2 1

  32. 4- … & Work in progress UCLA, May 31, 2007 • Models: • - in-plane roughness • (D. Bonamy, S. Santucci & K.J. Målǿy) • - how to take damage into account? • Evolution of ductility: steel (C. Guerra/S. Chapuilot) • Metallic glasses Silicate glasses • ( C. Rountree, D. Bonamy) T

  33. 3- Damage… Correlation length x (nm) Rc (nm) V (m/s) Velocity (m/s) NLE zone size x and Rc decrease with v x‹=Rc D. Bonamy et al., (06)

  34. 3- Endommagement… KI0 KI0 Endommagement en pointe de fissure Ecrantage des interactions entre deux points du front x z z=0.75; b=0.6; z=1.2 a > 2

  35. 3- Endommagement Base-Ce KIc=10MPa√ Base-Mg KIc=2MPa√ m m Verres métalliques (Xi et al, PRL 94, 2005)

  36. 3- Endommagement 100 Log (Δh) (mm) 10-1 10-1 100 101 10-2 log(Δz) (mm) Siz > 1 mmζ ~ 0.4 Siz < 1 mmζ ~ 0.8 Collaboration avec S. Morel & G. Mourot, Bordeaux I, France

  37. 3- Des surfaces de rupture “anormalement” rugueuses: les céramiques de verre Analyse 1D Exposant de rugosité indépendant de la microstructure: ζ = 0.40 ± 0.04

  38. 3- Des surfaces de rupture “anormalement” rugueuses: les céramiques de verre Matériau modèle dont on peut moduler: -la porosité  -la taille des billes d

  39. 3- Des surfaces de rupture “anormalement” rugueuses: les céramiques de verre Analyse 2D Forme universelle de la fonction de corrélation 2D Les 3 exposants ζ=0.4± 0.05 β=0.5± 0.05 z=ζ/β=0.8 ±0.05 + L. Ponson, H. Auradou et J.P. Hulin, soumis à Phys. Rev. E

  40. 3- Des surfaces de rupture “anormalement” rugueuses: les céramiques de verre Analyse 2D Diamètre des billes: 100 µm Porosité: 5%

  41. 3- Des surfaces de rupture “anormalement” rugueuses: le mortier à grande échelle Collaboration S. Morel et G. Mourot, LRBB, Bordeaux Si z > 1 mmζ ~ 0.4  = 1 mm Si z < 1 mmζ ~ 0.8

  42. 3- Des surfaces de rupture “anormalement” rugueuses: le verre à grande échelle S. Wiederhorn et al. 05 Si z > 100 nm ζ ~ 0.4  = 100 nm Si z < 100 nm ζ ~ 0.8

  43. Humid air n-tetradecane

  44. STM tip A D2 δ=h2-h1 h D1 h2 h1 C2 v a D C1 B s l wedge

  45. 1- Scaling properties … Crossover function is also universal Topothesies lz and lx: metal glass mortar

  46. 2- Fracture surfaces “abnormally” rough: glass ceramics Distribution of ΔhΔz Δh Δz P.Δzζ P(Δh) ~ Δz-ζ g(Δh/Δzζ) Mono-affine ζ = 0.40 ± 0.04 Δh/Δzζ

  47. 2- Fracture surfaces “abnormally” rough: glass ceramics Distribution of ΔhΔz Δh Δz P.Δzζ Gaussian distribution Δh/Δzζ

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