Turbulent fracture surfaces: A footprint of damage percolation?

TL;DR

This paper identifies a characteristic length scale in fracture surfaces that distinguishes between uncorrelated mono-affine behavior and correlated multi-fractal patterns, linking surface geometry to damage percolation and turbulence.

Contribution

It introduces a method to extract a length scale from fracture surface correlations and unifies the understanding of surface morphology across different scales.

Findings

Above the length scale, fracture surfaces are mono-affine and uncorrelated.

Below the length scale, surfaces exhibit multi-fractal, turbulent-like correlations.

The results support a model where large-scale features are from elastic line propagation, and small-scale features from damage cavity merging.

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.