Two-dimensional scaling properties of experimental fracture surfaces

TL;DR

This study investigates the 2D scaling properties of fracture surfaces, revealing anisotropic scaling invariance with universal exponents in different materials, and suggests analogies with out-of-equilibrium statistical physics models.

Contribution

It provides the first detailed analysis of 2D scaling invariance in fracture surfaces, identifying universal anisotropic exponents and linking fracture morphology to statistical physics models.

Findings

Scaling invariance is anisotropic on fracture surfaces.

Two universal scaling exponents are identified for different directions.

The 2D structure function resembles models from out-of-equilibrium physics.

Abstract

The morphology of fracture surfaces encodes the various complex damage and fracture processes occurring at the microstructure scale that have lead to the failure of a given heterogeneous material. Understanding how to decipher this morphology is therefore of fundamental interest. This has been extensively investigated over these two last decades. It has been established that 1D profiles of these fracture surfaces exhibit properties of scaling invariance. In this paper, we present deeper analysis and investigate the 2D scaling properties of these fracture surfaces. We showed that the properties of scaling invariance are anisotropic and evidenced the existence of two peculiar directions on the post-mortem fracture surface caracterized by two different scaling exponents: the direction of the crack growth and the direction of the crack front. These two exponents were found to be universal, independent of the crack growth velocity, in both silica glass and aluminum alloy, archetype of brittle and ductile material respectively. Moreover, the 2D structure function that fully characterizes the scaling properties of the fracture surface was shown to take a peculiar form similar to the one predicted by some models issued from out-of-equilibrium statistical physics. This suggest some promising analogies between dynamic phase transition models and the stability of a crack front pinned/unpinned by the heterogenities of the material.