1 / 57

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

riley-rhodes
Download Presentation

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

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. 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

More Related