A Statistical Theory of Polycrystalline Plasticity

The plasticity and viscoplasticity of polycrystalline materials are studied analytically in terms of lattice dislocations, with the principal effects attributed to non-extended obstacles. Non-equilibrium statistical mecha­nics is used to describe the evolution of the dislocation structures during loading and unloading processes. A plausible variation in the probability density function for mobile dislocations for such processes is suggested. The proposed material model is in good qualitative agreement with several observed phenomena that previously could not be quantified on the basis of the dislocation theory. Numerical examples illustrate the effect of the rate of loading, the variations in the recovery effect as it relates to the extent of load reversal, and a means for treating materials that exhibit a yield plateau. In the limit, the proposed model yields results for inviscid plasticity