Universality Classes in Constrained Crack Growth

TL;DR

This study extends the fiber bundle model to explore crack front dynamics, revealing two universality classes: pinned elastic line at large scales and percolation at small scales, with distinct roughness exponents and fractal properties.

Contribution

It identifies and characterizes two universality classes governing crack front motion across different scales, linking elastic line pinning and percolation phenomena.

Findings

Large-scale roughness exponent ~0.39

Small-scale roughness exponent ~2/3

Fractal dimension of crack front ~1.77

Abstract

Based on an extension of the fiber bundle model we investigate numerically the motion of the crack front through a weak plane separating a soft and an infinitely stiff block. We find that there are two regimes. At large scales the motion is consistent with the pinned elastic line model and we find a roughness exponent equal to 0.39 +/- 0.04 characterizing it. At smaller scales, coalescence of holes dominates the motion rather than pinning of the crack front. We find a roughness exponent consistent with 2/3, which is the gradient percolation value. The length of the crack front is fractal on these smaller scales. We determine its fractal dimension to be 1.77 +/- 0.02, consistent with the hull of percolation clusters, 7/4. This suggests that the crack front is described by two universality classes: on large scales, the pinned elastic line one and on small scales, the percolation universality class.