Roughness and multiscaling of planar crack fronts

TL;DR

This study numerically investigates the roughness and multiscaling behavior of planar crack fronts, revealing the influence of disorder correlation length and Larkin length on different scaling regimes.

Contribution

It introduces a detailed analysis of the interplay between disorder correlation length and Larkin length in crack front roughness within a long-range elastic string model.

Findings

Multiscaling occurs below the disorder correlation length for strong disorder.

Asymptotic roughness exponent of approximately 0.39 is observed at large scales.

Different scaling regimes are separated by the Larkin length and disorder correlation length.

Abstract

We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $\xi$. The problem is shown to have two important length scales, $\xi$ and the Larkin length $L_c$. Multiscaling of the crack front is observed for scales below $\xi$, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent $\zeta \approx 0.39$ is recovered for scales larger than both $\xi$ and $L_c$. If $L_c > \xi$, these regimes are separated by a third regime characterized by the Larkin exponent $\zeta_L \approx 0.5$. We discuss the experimental implications of our results.