We show that a length scale ξ can be extracted from the spatial correlations of the "steep cliffs" that appear on a fracture surface. Above ξ, the slope amplitudes are uncorrelated and the fracture surface is monoaffine. Below ξ, long-range spatial correlations lead to a multifractal behavior of the surface, reminiscent of turbulent flows. Our results support a unifying conjecture for the geometry of fracture surfaces: for scales larger than ξ, the surface is the trace left by an elastic line propagating in a random medium, while for scales smaller than ξ, the highly correlated patterns on the surface result from the merging of interacting damage cavities.
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Vernède et al. (2015) studied this question.
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