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We study theoretically the dynamical process of yielding in cyclicallysheared amorphous materials, within a thermal elastoplastic model and the softglassy rheology model. Within both models we find an initially slowaccumulation, over many cycles after the inception of shear, of low levels ofdamage in the form strain heterogeneity across the sample. This slow fatiguethen suddenly gives way to catastrophic yielding and material failure. Strongstrain localisation in the form of shear banding is key to the failuremechanism. We characterise in detail the dependence of the number of cyclesbefore failure on the amplitude of imposed strain, the working temperature, andthe degree to which the sample is annealed prior to shear. We discuss ourfinding with reference to existing experiments and particle simulations, andsuggest new ones to test our predictions.

Slow fatigue and highly delayed yielding via shear banding in oscillatory shear