Failure due to fatigue in fiber bundles and solids

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold (σc) 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 σ. We solve this dynamics of failure analytically and show that the average failure time τ of the bundle decreases exponentially as →σσc from below and τ=0 for σ>~σc. 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 the Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress σ less than the bundle's strength σc ̃ \~ (beyond which it fails instantly). The average failure time τ is again seen to decrease exponentially as →σσc ̃ \~ from below 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.