Crack localization and the interplay between stress enhancement and thermal noise

Santanu Sinha,Subhadeep Roy,Alex Hansen

doi:10.1016/j.physa.2021.125782

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 nucleates 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 which 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.

Highlights

Growth of fractures under external stress in heterogeneous materials, such as concrete or fiber-reinforced composites, depends on the interplay between material disorder and local stress concentration throughout the failure process
The thermal noise initiates a creep failure process to break the system over time even if the applied stress is less than the critical value
We observed that the presence of thermal fluctuations makes the failure events spatially uncorrelated and non-localized even if the strength of system disorder is low

Summary

Introduction

Growth of fractures under external stress in heterogeneous materials, such as concrete or fiber-reinforced composites, depends on the interplay between material disorder and local stress concentration throughout the failure process. Introducing thermal fluctuations by probabilistic noise, thermally activated failures have been investigated widely with this model for the global load sharing case [15,16,17,18,19,20] These studies have explained the time-dependent strain rate and showed how the temperature plays a crucial role in the creep lifetime. We introduce the thermal noise in the model by a probabilistic algorithm that is based on the elastic energy and the breaking energy of a fiber These two disorders compete with the inhomogeneous stress distributions that is caused by the local load sharing process and create non-trivial failure dynamics.

Model description

Results

Localized vs non-localized fracture growth

Boundary between the random and localized failure

Conclusions