A Statistical Formulation of Viscoplastic Behavior in Heterogeneous Polycrystals

A formulation for viscoplastic behavior of heterogeneous polycrystals is presented based upon thefamiliar constructs of statistical continuum theory. The non-local interaction law is derived whichrelates properties of the local velocity field to correlation functions of the local microstructure. It isdemonstrated that correlation functions, based upon the two-point orientation coherence function, arerequired 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.