A theory of slip band spacing in fatigued materials has been developed based on a criterion of minimum strain energy accumulation within slip bands. A two-dimensional, quasi-monotonic, dipole pile-up model is employed for this purpose. Multiple parallel, equally spaced, mutally interacting slip bands are considered. Each slip band is modeled as an accumulation of dipoles. Partially irreversible slip processes with stochastic fluctuations are allowed in the model. It is shown that for a given imposed plastic work, there exists a unique configuration (number and spacing) of the bands that has the minimum internal energy stored within all bands. An expression for the optimum slip band spacing in polycrystalline materials has been derived based on all experimentally determinable parameters. The effects of plastic strain amplitude, temperature and environment on this optimum slip band spacing are assessed. There is reasonably good agreement between theory and experiment.
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