Fundamental Considerations in Micromechanical Modeling of Polycrystalline Metals at Finite Strain

Abstract

Issues germane to the theoretical foundations of micromechanical modeling and analysis of metals at finite strain are investigated. Established concepts and results are concisely reviewed and integrated, and some new relationships, both general and specific, are obtained. The proof, by Hill and Havner (1982), that plastic potentials for individual crystal deformation depend solely upon Green elasticity of the underlying crystal lattice is presented afresh and extended to polycrystalline metals, using the averaging theorem of Hill (1972) and the aggregate model of Havner (1974). A specialization of the general theory for individual crystals is emphasized, corresponding to a postulated constitutive inequality that is invariant under change in strain measure and a saddle potential function for nominal stress rate. For the polycrystalline aggregate model, in addition to plastic potential laws, other macroscopic relationships are derived making use of the recent analysis in Hill (1984), Various equations for incremental work are presented that involve open questions requiring further research.