Continuum micro-mechanics of elastoplastic polycrystals

Continuum micro-mechanics of elastoplastic polycrystals

1965 | Rodney J Hill
Rodney J Hill's 1965 paper "Continuum Micro-Mechanics of Elastoplastic Polycrystals" presents a theoretical framework for analyzing the behavior of polycrystalline materials under plastic deformation. The paper introduces a self-consistent model to estimate the mechanical properties of an aggregate of elastoplastic crystals, based on the constitutive laws of individual crystals. The model is inspired by earlier work by Hershey, Kröner, and Budiansky, but differs in key aspects. The paper discusses the internal inhomogeneities of stress and strain in an arbitrarily deformed polycrystal, and evaluates the overall constitutive relations for the aggregate as a whole. The analysis considers the effects of plastic deformation on the aggregate, and introduces a method for determining the average strain concentration factor in grains with a given lattice orientation. The paper also explores the implications of plastic flow in the aggregate, and presents a self-consistent model for elastoplastic polycrystals. The analysis is based on a symbolic notation for curvilinear tensors, and includes detailed derivations of the constitutive relations for the aggregate. The paper concludes with a discussion of the implications of the model for the overall behavior of polycrystalline materials.Rodney J Hill's 1965 paper "Continuum Micro-Mechanics of Elastoplastic Polycrystals" presents a theoretical framework for analyzing the behavior of polycrystalline materials under plastic deformation. The paper introduces a self-consistent model to estimate the mechanical properties of an aggregate of elastoplastic crystals, based on the constitutive laws of individual crystals. The model is inspired by earlier work by Hershey, Kröner, and Budiansky, but differs in key aspects. The paper discusses the internal inhomogeneities of stress and strain in an arbitrarily deformed polycrystal, and evaluates the overall constitutive relations for the aggregate as a whole. The analysis considers the effects of plastic deformation on the aggregate, and introduces a method for determining the average strain concentration factor in grains with a given lattice orientation. The paper also explores the implications of plastic flow in the aggregate, and presents a self-consistent model for elastoplastic polycrystals. The analysis is based on a symbolic notation for curvilinear tensors, and includes detailed derivations of the constitutive relations for the aggregate. The paper concludes with a discussion of the implications of the model for the overall behavior of polycrystalline materials.
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[slides and audio] Continuum micro-mechanics of elastoplastic polycrystals