  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.
