Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture

TL;DR

This study explores the fractal geometry of bursts during creep rupture in a fiber bundle model, revealing universal fractal properties of burst perimeters and their relation to crack growth dynamics.

Contribution

It uncovers the fractal nature of burst fronts and proposes their classification within a universality class of loop-erased self-avoiding walks.

Findings

Burst perimeters have a universal fractal dimension of 1.25.

Burst growth dynamics reflect a transition from 1 to 1.25 in fractal dimension.

Burst geometries are consistent with loop-erased self-avoiding random walks.

Abstract

We investigate the geometrical structure of breaking bursts generated during the creep rupture of heterogeneous materials. Based on a fiber bundle model with localized load sharing we show that bursts are compact geometrical objects, however, their external frontier has a fractal structure which reflects their growth dynamics. The perimeter fractal dimension of bursts proved to have the universal value 1.25 independent of the external load and of the amount of disorder in the system. We conjecture that according to their geometrical features breaking bursts fall in the universality class of loop-erased self-avoiding random walks with perimeter fractal dimension 5/4 similar to the avalanches of Abelian sand pile models. The fractal dimension of the growing crack front along which bursts occur proved to increase from 1 to 1.25 as bursts gradually cover the entire front.