Super-Arrhenius dynamics for sub-critical crack growth in disordered brittle media

TL;DR

This paper investigates how material disorder affects thermally activated crack growth in brittle media, revealing a super-Arrhenius law where disorder increases lifetime and decreases crack velocity.

Contribution

It introduces a model incorporating disorder via a rupture threshold distribution and derives analytical predictions aligned with numerical results.

Findings

Disorder inhibits crack growth velocity.

Material lifetime follows a super-Arrhenius law.

Disorder increases the effective activation temperature.

Abstract

Taking into account stress fluctuations due to thermal noise, we study thermally activated irreversible crack growth in disordered media. The influence of material disorder on sub-critical growth of a single crack in two-dimensional brittle elastic material is described through the introduction of a rupture threshold distribution. We derive analytical predictions for crack growth velocity and material lifetime in agreement with direct numerical calculations. It is claimed that crack growth process is inhibited by disorder: velocity decreases and lifetime increases with disorder. More precisely, lifetime is shown to follow a super-Arrhenius law, with an effective temperature theta - theta_d, where theta is related to the thermodynamical temperature and theta_d to the disorder variance.