A discrete model for the prediction of subsequent yield surfaces in polycrystalline plasticity

Abstract

A discrete model suitable for the analysis of polycrystalline aggregate response under macroscopically uniform, quasi-static loading is developed, with particular emphasis on the characteristics of subsequent yield surfaces in stress or strain space. Internal stress and deformation states are determined from approximating, piecewise linear infinitesimal displacement fields within crystal grains, based upon broadly defined constitutive behavior which permits inclusion of cubic or hexagonal crystal anisotropy and relatively general hardening laws over crystallographic slip systems. Appropriate aggregate matrices are established as symmetric, positivedefinite, and internal fields corresponding to the solution of the discrete model are proved to be unique. It is further shown that the final calculation of incremental crystal shears can be posed as a quadratic programming problem.