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A Statistical Formulation of Viscoplastic Behavior in Heterogeneous Polycrystals

Textures and Microstructures
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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.

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