Failure due to fatigue in fiber bundles and solids

TL;DR

This paper models fatigue failure in fiber bundles, showing failure time decreases exponentially with stress and revealing power-law avalanche distributions, aligning with experimental fatigue observations in solids.

Contribution

It provides an analytical and numerical study of fatigue failure in fiber bundles, introducing noise-induced failure dynamics and comparing with Griffith crack nucleation.

Findings

Failure time decreases exponentially with increasing stress.

Avalanche size distribution follows a power law decay.

Results align with experimental fatigue behavior in solids.

Abstract

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold beyond which all fail simultaneously in absence of noise. At finite noise, the bundle acquires a fatigue behavior due to the noise-induced failure probability at any stress. We solve this dynamics of failure analytically and show that the average failure time of the bundle decreases exponentially as the stress increases. We also determine the avalanche size distribution during such failure and find a power law decay. We compare this fatigue behavior with that obtained phenomenologically for the nucleation of Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress less than the bundle's strength (beyond which it fails instantly). The average failure time is again seen to decrease exponentially as the stress increases and the avalanche size distribution shows similar power law decay. These results are also in broad agreement with experimental observations on fatigue in solids. We believe, these observations regarding the failure time are useful for quantum breakdown phenomena in disordered systems.