A Statistical Formulation of Viscoplastic Behavior in Heterogeneous Polycrystals

Abstract

A formulation for viscoplastic behavior of heterogeneous polycrystals is presented based upon the familiar constructs of statistical continuum theory. The non‐local interaction law is derived which relates properties of the local velocity field to correlation functions of the local microstructure. It is demonstrated that correlation functions, based upon the two‐point orientation coherence function, are required in a theory which considers first‐order deviations from Taylor′s 1938 uniform strain (rate) assumption. The evolution of the coherence function with deformation is also briefly considered.