title: Turbulent fracture surfaces: a footprint of damage percolation?
abstract: 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.
authors.affiliation: Tortoise Analytics, 75005 Paris, France.
authors.forename: Stéphane
authors.initials: S
authors.lastname: Vernède
authors.affiliation: Institut Jean le Rond d'Alembert (UMR 7190), CNRS-Université Pierre et Marie Curie, 75005 Paris, France.
authors.forename: Laurent
authors.initials: L
authors.lastname: Ponson
authors.affiliation: Capital Fund Management, 23 rue de l'Université, 75007 Paris, France.
authors.forename: Jean-Philippe
authors.initials: JP
authors.lastname: Bouchaud