A theory of subgrain dislocation structures
type: Item
instance of: scholarly article
title: A theory of subgrain dislocation structures
zbMATH Open document ID: 1001.74007
DOI: 10.1016/S0022-5096(99)00104-0
author: E. A. Repetto
author: M. Ortiz
author: L. Stainier
published in: Journal of the Mechanics and Physics of Solids
publication date: 2001-01-17T00:00:00Z
review text: The authors construct a micromechanical theory of dislocations and finite-deformation single-crystal plasticity on the basis of a direct generalization of deformation microstructures and the computation of the attendant effective behavior. The final purpose is the description of lamellar dislocation structures that develop at large strains under monotonic loading. The authors use a constructive approach in that they exploit an explicit construction of microstructures by recursive lamination and their subsequent equilibration in order to relax the incremental constitutive description of the material. Dislocation structures are related to the plastic deformation gradient via the Nye-Kroener's formula for dislocation density tensor. Nonlocality is introduced by accounting for the self-energy of dislocations. Applications of the theory are given to the generation of complex microstructures. Among the predictions obtained is the effective behavior of crystal to stiffen with decreasing sample size in accordance with experimental observations. The present theory differs from the fashionable strain-gradient theories of plasticity in that the said size effect occurs for nominally uniform macroscopic deformations, and the dimension of microstructures depend sensitively on the loading geometry, the extent of macroscopic deformation, and the size of the sample. An interesting remark concerns the obtained expression for the configurational force which relates it to the orientation of dislocation walls. Also, recursive algorithms are given explicitly.
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74E15
zbMATH DE Number: 1513352
zbMATH Keywords: micromechanical theory of dislocations
zbMATH Keywords: finite-deformation single-crystal plasticity
zbMATH Keywords: lamellar dislocation structures
zbMATH Keywords: large strains
zbMATH Keywords: monotonic loading
zbMATH Keywords: recursive lamination
zbMATH Keywords: plastic deformation gradient
zbMATH Keywords: Nye-Kroener's formula
zbMATH Keywords: dislocation density tensor
zbMATH Keywords: effective behavior
zbMATH Keywords: size effect
zbMATH Keywords: configurational force
reviewed by: Gérard A. Maugin
MaRDI profile type: Publication
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full work available at URL: s0022-5096(99)00104-0
OpenAlex ID: W2007645219
description: scientific article; zbMATH DE number 1513352