The theoretical behavior of a polycrystalline solid as related to certain general concepts of continuum plasticity

Abstract

This paper is directed toward establishing general characteristics of continuum stress-plastic strain relations from Schmid's Law of plastic slip in individual crystal grains. To this end certain theoretical results obtained by Lin are reaffirmed through a rigorous derivation, and the principle of maximum plastic work is extended to small elastic-plastic strains in an isotropic polycrystalline aggregate. It is shown that the macroscopic incremental plastic strain vector over a unit volume of a fine-grained solid is strictly normal to a yield surface in macrostress space only if the individual crystals are elastically isotropic. The resulting equations for polycrystalline solids are contrasted with those obtained from certain stability postulates and thermodynamic foundations in continuum plasticity, and general features of similarity are discussed.