Since the pioneering work of Mandelbrot et al [1], the statistical characterization of fracture surfaces is nowadays a very active field of research. The fracture surfaces of various materials show surprising scaling properties (see [2-3] for reviews) and especially self-affine scaling invariance over a wide range of length scales. Indeed, the fracture surfaces obtained in materials as different as metallic alloys [4-7], ceramics [8-9], glass [10-11], quasi-crystals [12-13], rocks [14-15], mortar [16-17], sea ice [18], and wood [19-20] exhibit self-affine scaling properties characterized by a local roughness exponent ζ≈0.8 and this in spite of huge differences in the fracture mechanisms. It was therefore suggested that this local roughness exponent ζ, measured along the direction of crack front, might have a universal value [21], i.e., a value independent of the fracture mode and of the material. However, quite recently, significantly different values of the local roughness Exponent ζ have been measured due to the anisotropy and the heterogeneity of the material structure [7,21-23], the kinetics of crack growth [24] or the possible multifractal character of the crack surfaces [25]. On the other hand, fracture surfaces were shown to exhibit anisotropic scaling morphological features, characterized by two different roughness exponents whether observed along the direction of crack front or crack growth [10,12-13]. This anisotropic scaling was shown to take a universal specific form independent of the considered material, the failure mode and the crack growth velocity [12-13]. Finally, recent experiments in sandstone [26-27], artificial rock [28] and granular packing of sintered glass beads [11,29], which are materials exhibiting a brittle failure, have shown self-affine scaling properties, especially at large length scales, characterized by a roughness exponent measured along the direction of crack front closer to 0.4-0.5. These latter experimental results deserve some more thinking especially since the measured roughness indexes (0.4-0.5) are significantly smaller than 0.8 and hence they suggest the existence of a second universality class for failure problems.
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