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The slip band formed in a grain on the material surface is a preferential site for crack initiation during low strain fatigue of polycrystalline metals. The forward and reverse plastic flow within the slip band is modeled in the present study by dislocations with different signs moving on two closely located layers, and it is assumed that their movement is irreversible. Based on the model, the monotonic buildup of dislocation dipoles piled up at the grain boundary is systematically derived using the theory of continuously distributed dislocations. This buildup is associated with the progress of extrusion or intrusion. The number of stress cycles up to the initiation of a crack of the grain size order is defined as the cycle when the stored strain energy of accumulated dislocations reaches a critical value. The relation between the initiation life and the plastic strain range derived theoretically is in agreement with a Coffin-Manson type law, and that between the fatigue strength and the grain size is expressed in an equation of the Petch type.
Tanaka et al. (Sun,) studied this question.