Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Correlated Percolation in the Damage Zone

TL;DR

This paper explains the universal roughness of brittle fracture surfaces through a correlated percolation process in the damage zone, supported by a fuse model and mean-field theory, aligning with observed experimental values.

Contribution

It introduces a model linking fracture surface roughness to correlated percolation in damage zones, providing theoretical predictions consistent with empirical data.

Findings

Correlation length exponent nu ≈ 1.35 in 2D fuse model

Roughness exponent zeta ≈ 0.75 in 2D model

In 3D, nu=2 predicts zeta=0.80, matching observations

Abstract

We suggest that the observed large-scale universal roughness of brittle fracture surfaces is due to the fracture process being a correlated percolation process in a self-generated quadratic damage gradient. We use the quasi-static two-dimensional fuse model as a paradigm of a fracture model. We measure for this model, that exhibits a correlated percolation process, the correlation length exponent nu approximately equal to 1.35 and conjecture it to be equal to that of uncorrelated percolation, 4/3. We then show that the roughness exponent in the fuse model is zeta = 2 nu/(1+2 nu)= 8/11. This is in accordance with the numerical value zeta=0.75. As for three-dimensional brittle fractures, a mean-field theory gives nu=2, leading to zeta=4/5 in full accordance with the universally observed value zeta =0.80.