Discrete dislocation modeling of fatigue crack growth in single crystals
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A framework for the analysis of crack growth under cyclic loading conditions in crystalline solids is discussed where plastic flow arises from the motion of large numbers of discrete dislocations and the fracture properties are embedded in a cohesive surface constitutive relation. The formulation is the same as used to analyze crack growth under monotonic loading conditions, differing only in the remote loading being a cyclic function of time. Fatigue, i.e. crack growth in cyclic loading at a driving force for which the crack remains stationary under monotonic loading, emerges as a consequence of the evolution of internal stresses associated with the irreversibility of the dislocation motion. A fatigue threshold, Paris law behavior, striations and the accelerated growth of short cracks are outcomes of the calculations.