In an aggregate under moderate loads, plastic deformation is considered to occur in favorably oriented crystals on single active slip systems. The residual stresses, due to the slip strains, are expressed in terms of the slip strains by an equivalent problem in elasticity. The resolved shear stresses, owing to the combined effects of the slip strains and the external load, are in turn related to the slip strains by material property. The slip-strain distribution can thus be determined, and the stress distribution follows. Analytical solutions are obtained for a cyclic load of constant amplitude, under certain simplifying assumptions. They agree closely with rigorous, numerical incremental calculations for a specific case. For materials that strain-harden against reverse slip in each infinitesimal region, decreasing hysteresis loops occur with cyclic loading, and the present results corroborate the essential features of an earlier analysis by Orowan.

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