Turbulent fracture surfaces: A footprint of damage percolation?

Abstract: We show that a length scale xi can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above xi, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below xi, long-range spatial correlation lead to a multi-fractal behavior of the surface, reminiscent of turbulent flows. Our results support a unifying conjecture for the geometry of fracture surfaces: for scales > \xi the surface is the trace left by an elastic line propagating in a random medium, while for scales < \xi the highly correlated patterns on the surface result from the merging of interacting damage cavities.