In the two previous sections, the statistical scaling properties of fracture surfaces in heterogeneous materials were shown to obey Family-Viseck scaling, characterized by two set of critical exponents, namely ζ=0.75, β =0.6 and Z= ζ/β=1.2 in glass, metallic alloys, mortar and wood, and ζ=0.4, β =0.5 and Z= ζ/β=0.8 in sandstone and packing of sintered glass beads.x of these anisotropic self-affine regimes was found to coincide with the size of the process zone where damage cavities can be observed (see Figure). Moreover, in silica glass, the size of the process zone and x were found to decay both as the logarithm of the crack growth velocity (see Figure). In packing of sintered glass beads, the scaling properties were observed from 100µm (microstructure scale) to 10mm, i.e. at scales three orders of magnitudes larger than the size of the process zone (about 100 nm as in homogeneous glass). This leads us to conjecture that the two series of critical exponents are obtained whether fracture surfaces are observed at scales below or above the size of the process zone /1/.
To uncover the origin of these two distinct universality classes we focused more specifically on the range of length-scales over which the scaling properties are observed. In metallic alloys and oxide glasses, the cut-off length
Top: Damage cavities in metallic alloys from /2/. Center: Same for Aluminosilicate glass from /3/ The process zone is found to be about 100µm in metallic alloys and 100nm in oxide glasses to be compared to the self-affine cutoff length ξ ~ 100µm and ξ ~ 100nm respectively. In silica glass, the size of the process zone Rc and ξ were found to decay both as the logarithm of the crack growth velocity v (Bottom, from /1/)