Crack Localization and the Interplay between Stress Enhancement and Thermal Noise

TL;DR

This paper investigates how thermal noise and stress influence failure patterns in a disordered fiber bundle model, revealing a transition from uncorrelated to localized failure as stress and temperature vary.

Contribution

It introduces a model combining thermal fluctuations with stress enhancement, identifying the conditions for localized versus random failure in disordered systems.

Findings

Failure becomes spatially uncorrelated at low stress and finite temperature.

Localized cracks grow when applied stress exceeds a temperature-dependent threshold.

The failure transition boundary depends on temperature and stress, with higher temperatures raising the failure threshold.

Abstract

We study the competition between thermal fluctuations and stress enhancement in the failure process of a disordered system by using a local load sharing fiber bundle model. The thermal noise is introduced by defining a failure probability that constitutes the temperature and elastic energy of the fibers. We observe that at a finite temperature and low disorder strength, the failure process, which nucleate in the absence of any thermal fluctuation, becomes spatially uncorrelated when the applied stress is sufficiently low. The dynamics of the model in this limit lies closely to the universality class of ordinary percolation. When applied stress is increased beyond a threshold value, localized fractures appear in the system that grow with time. We identify the boundary between the localized and random failure process in the space of temperature and applied stress, and find that the threshold of stress corresponding to the onset of localized crack growth increases with the increase of temperature.