Table of Contents
Textures and Microstructures
Volume 11 (1989), Issue 1, Pages 57-71
http://dx.doi.org/10.1155/TSM.11.57

A Statistical Formulation of Viscoplastic Behavior in Heterogeneous Polycrystals

1Department of Mechanical Engineering, Yale University, New Haven, Connecticut 06520-2157, USA
2Laboratoire de Physique et Mécanique des Matériaux, Université de Metz, Metz 57000, France

Received 10 February 1989

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.