Topography of a crack. Fracture surface images processed to highlight the steepest cliffs of (left to right) aluminum, mortar, and ceramic in frames that are 3, 20, and 8mm wide, respectively. The steepest cliffs are white and appear to have a pattern rather than being entirely random.
Turbulent Fracture Surfaces: A Footprint of Damage Percolation?
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.