SOME SCALING PROPERTIES OF FRACTURE SURFACES 99th Statistical Mechanics Conference, May 2008 D. Bonamy, L. Ponson, E. Bouchaud GROUPE FRACTURE CEA-Saclay, France

Scale of the material heterogeneities Include the basic mechanisms into a statistical description Macroscopic scale Mechanics of materials 99th Statistical Mechanics Conference, May 2008

No easy averaging at a crack tip:  Strong stress gradient  The most brittle link breaks first  Rare events statistics No «equivalent effective homogeneous» material  (r) r c 00 00

  Fractography Fracture surface = trace of the propagating crack front 99th Statistical Mechanics Conference, May 2008

1- Scaling properties of fracture surfaces 2- Crack line propagating through a random microstructure 3- Conclusion OUTLINE 99th Statistical Mechanics Conference, May 2008

Aluminum alloy  =0.77 3nm  0.1mm 1- Scaling properties…  = 0.77 z  h max (z) Profiles perpendicular to the direction of crack propagation 99th Statistical Mechanics Conference, May 2008

 = 0.78 Ti 3 Al-based alloy  = nm  0.5mm 1- Scaling properties… 99th Statistical Mechanics Conference, May 2008

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

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

Béton (Profilométrie) Glass (AFM) Aluminum alloy (SEM+Stereo) Quasi-crystals (STM) Δh 2D (Δz, Δx) = ( A ) 1/2 AB ΔxΔx ΔzΔz 130mm  = 0.75  = 0.6 z =  /  ~ 1.2  h/  x   z/  x 1/ z 1- Scaling properties… h (Å) Coll. D.B., L.P., L. Barbier, P. Ebert

Mortar (Profilometry) Glass (AFM) Aluminum alloy (SEM+Stereo) Quasi-crystals (STM) Δh 2D (Δz, Δx) = ( A ) 1/2 AB ΔxΔx ΔzΔz 130mm  = 0.75  = 0.6 z =  /  ~ 1.2  h/  x   z/  x 1/ z Mortar 1- Scaling properties… (Coll. S. Morel & G. Mourot) h (Å) Coll. D.B., L.P., L. Barbier, P. Ebert

Mortar (Profilometry) Glass (AFM) Metallic alloy (SEM+Stereo) Quasi-crystals (STM) AB ΔxΔx ΔzΔz 130mm 1- Scaling properties…  z/  x 1/z ( l z / l x ) 1/  (  z/ l z )/(  x/ l x ) 1/ z  h/  x  (  h/ l x )/(  x/ l x )  Universal structure function Very different length scales h (Å) Coll. D.B.,L.P.,L. Barbier,P. Ebert

General result : anisotropic self-affine surface  independent of disorder Crack front= «elastic line» Fracture surface = trace left behind by the front J.-P. Bouchaud, EB, G. Lapasset, J. Planès (93) 2- Crack line…

D. Bonamy et al, PRL 2006  Linear elastic material  Weak distorsions z x f(x,z) KI0KI0 KI0KI0 h(x,z) 2- Crack line…  Family-Viscek structure function  Universal exponents  With values ζ=0.4, β=0.5 or logarithmic roughness Observed on sintered glass beads

What did we MISS ? Damage ! Amorphous silica Ti 3 Al-based alloy Roughness measurements performed within the damaged zone !   damaged zone size 99th Statistical Mechanics Conference, May Crack line…

2 classes of universality 1 Linear elastic region 2 Intermediate region: damage « perturbates » front (screening)  =0.75  = Conclusion Observation of both regimes on metallic alloys, mortar and silicate glasses 99th Statistical Mechanics Conference, May 2008

Disorder  line roughness Elastic restoring forces  rigidity of the line Undamaged material Transmission of stresses through long range undamaged material :long range interactions (1/r 2 )  very rigid line 3- Damage… Transmission of stresses through a « Swiss cheese »: Screening of elastic interactions  lower rigidity  Long range  Short range 99th Statistical Mechanics Conference, May 2008