1 / 36

The Chinese University of Hong-Kong, September 2008

4- Statistical characterization of fracture. Fracture surface = trace of propagating front. The Chinese University of Hong-Kong, September 2008. ?. How to include these microstructure-scale mechanisms into a statistical description. Dynamics of crack propagation.

venus-sherman
Download Presentation

The Chinese University of Hong-Kong, September 2008

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. 4- Statistical characterization of fracture Fracture surface = trace of propagating front The Chinese University of Hong-Kong, September 2008 ? How to include these microstructure-scale mechanisms into a statistical description Dynamics of crack propagation

  2. 4- Statistical characterization of fracture h Dh Dz h x z z x =0.75 Slope:=0.75 < h2 >1/2(nm) Self-affine surface

  3. The Chinese University of Hong-Kong, September 2008 OUTLINE 1- Crack in 2D 2- Interfacial fracture 3- 3D crack propagation

  4. 4- Statistical characterization of fracture Paper PMMA (Salminen et al.) (Santucci et al.) The Chinese University of Hong-Kong, September 2008 Crack propagation in a 2D sample Paper

  5. 4- Statistical characterization of fracture Height h(x) (mm) Position x(mm) The Chinese University of Hong-Kong, September 2008 Paper (Salminen & al, 03)

  6. 4- Statistical characterization of fracture y Dh(r) x x+Dx The Chinese University of Hong-Kong, September 2008

  7. 4- Statistical characterization of fracture Paper (Salminen & al, 03) y Zmax(Dx) x x+Dx The Chinese University of Hong-Kong, September 2008 b≈0.5-0.7

  8. 4- Statistical characterization of fracture PMMA Rk(Dx)/RkG Dhk(Dx)/RkG Paper Dx/d0 Log10(Dx/d0) PMMA b≈0.6 Paper b≈0.6 S. Santucci et al., 07

  9. 4- Statistical characterization of fracture Interfacial fracture (K.J. Måløy et al.) The Chinese University of Hong-Kong, September 2008

  10. 4- Statistical characterization of fracture Interfacial fracture (J. Schmittbuhl et al. 97) x(mm) z’≈0.55 Log10(P(f)) z(mm) Log10(f) z(mm) The Chinese University of Hong-Kong, September 2008 L≈50mm ≈ size of heterogeneities

  11. 4- Statistical characterization of fracture Interfacial fracture (K.J. Måløy et al. 06) x x x The Chinese University of Hong-Kong, September 2008 Front location Waiting time matrix: t=0 W(z,x)=0 t>0 Wt(z,x)=1+Wt-1(z,x) if front in (z,x) Spatial distribution of clusters (white) v(z,x)>10 <v> <v>=28.1µm/s; a=3.5µm

  12. 4- Statistical characterization of fracture Interfacial fracture (K.J. Måløy et al. 06) Slope -2.55 Slope -1.6 The Chinese University of Hong-Kong, September 2008 0.39µm/s≤<v>≤40µm/s 1.7µm ≤a≤10µm C=3 Velocity distribution Cluster size distribution

  13. 4- Statistical characterization of fracture The Chinese University of Hong-Kong, September 2008 Interfacial fracture, S. Santucci et al., 08

  14. 4- Statistical characterization of fracture The Chinese University of Hong-Kong, September 2008 Intermittency of interfacial crack propagation (A. Marchenko et al., 06)

  15. Humid air n-tetradecane

  16. 4- Statistical characterization of fracture The Chinese University of Hong-Kong, September 2008 Tetradecane Humid air

  17. 4- Statistical characterization of fracture Out-of-plane Projection on the yz plane In-plane Projection on the xz plane f(z) The Chinese University of Hong-Kong, September 2008 Fracture of 3D specimens

  18. 4- Statistical characterization of fracture x P.Daguier et al. (95) Al-alloy & Ti3Al-based alloy z’≈0.55-06

  19. 4- Statistical characterization of fracture The Chinese University of Hong-Kong, September 2008 Out-of-plane roughness measurements Polishing

  20. 4- Statistical characterization of fracture r/x The Chinese University of Hong-Kong, September 2008 C(r)r-z z≈0.8 Al alloy Ni-plated BS SEM (E.B. et al., 89)

  21. 4- Statistical characterization of fracture The Chinese University of Hong-Kong, September 2008 Profiles perpendicular to the direction of crack propagation

  22. 4- Statistical characterization of fracture Profiles perpendicular to the direction of crack propagation (Dz) (µm) z= 0.78 from 5nm to 0.5mm Dz The Chinese University of Hong-Kong, September 2008 (P. Daguier & al., 96)

  23. 4- Statistical characterization of fracture Aluminium alloy z=0.77 3nm0.1mm Zmax(Dz) (µm) z = 0.77 Dz (µm) The Chinese University of Hong-Kong, September 2008 Profiles perpendicular to the direction of crack propagation (M. Hinojosa et al., 98)

  24. 4- Statistical characterization of fracture z≈0.8 The Chinese University of Hong-Kong, September 2008 Profiles perpendicular to the direction of crack propagation: granite z≈0.85 (J. Schmittbuhl et al, 95)

  25. 4- Statistical characterization of fracture L. Ponson, D. Bonamy, E.B. (05) Direction of crack propagation 10  ~ 0.6 Log (Δh) 1 Direction of crack front  ~ 0.8 0.1 1 10 102 103 Log(Δx), log(Δz) The Chinese University of Hong-Kong, September 2008 Anisotropy of fracture surfaces x (µm) direction of crack propagation z (µm) direction of crack front

  26. L. Ponson, D. Bonamy, E.B. PRL 2006 L. Ponson et al, IJF 2006 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

  27. 4- Statistical characterization of fracture 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. D.B., L.P., L. Barbier, P. Ebert

  28. 4- Statistical characterization of fracture 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) Coll. D.B., L.P., L. Barbier, P. Ebert

  29. 4- Statistical characterization of fracture 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 Coll. D.B., L.P., L. Barbier, P. Ebert

  30. 4- Statistical characterization of fracture 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) Coll. D.B.,L.P.,L. Barbier,P. Ebert

  31. 4- Statistical characterization of fracture 1mm Exponent q q The Chinese University of Hong-Kong, September 2008 Preliminary results (G. Pallarès, B. Nowakowski et al., 08)

  32. 4- Statistical characterization of fracture log(P(f)) dzzP(Dh) z≈0.47 Dh/(dz)z log(f) The Chinese University of Hong-Kong, September 2008 Exceptions… Sandstone fracture surfaces (Ponson at al. 07) (Boffa et al. 99)

  33. 4- Statistical characterization of fracture • Linear elastic material The Chinese University of Hong-Kong, September 2008 Exceptions… « Model » material : sintered glass beads (Coll. H. Auradou, J.-P. Hulin & P. Vié 06) Porosity 3 to 25% Grain size 50 to 200 mm Vitreous grain boundaries

  34. 4- Statistical characterization of fracture 1/z Structure 2D (Ponson et al. 06) Roughness at scales > Grain size 2 independent exponents ζ=0.4± 0.05 β=0.5± 0.05 z=ζ/β=0.8 ±0.05 + « Universal » structure function

  35. Not convincing for paper… at length scales < heterogeneity size… What about sandstone and sintered glass? The Chinese University of Hong-Kong, September 2008 Summary • Cracks propagating through disordered media • are rough self-affine (5 decades) • universal roughness exponents : • z’ ≈0.6 • z≈0.8, b ≈0.6 • proceed through avalanches HOW TO MAKE SENSE OF ALL THIS????????

More Related