Statistical Physics of Fracture Surfaces Morphology

TL;DR

This paper explores the statistical physics of fracture surface morphologies, highlighting the limitations of traditional models and proposing new models and analysis methods to better understand the complex scaling behaviors observed.

Contribution

It introduces models incorporating deviations from linear elasticity and novel symmetry-based analysis methods to better capture fracture surface multiscaling phenomena.

Findings

Models reproduce multiscaling in 1+1 dimensions.

Symmetry-based analysis organizes complex scaling properties.

Proposes experiments with preserved rotational symmetry.

Abstract

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.