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A theory of subgrain dislocation structures

Ortiz, M. and Repetto, E. A. and Stainier, L. (2000) A theory of subgrain dislocation structures. Journal of the Mechanics and Physics of Solids, 48 (10). pp. 2077-2114. ISSN 0022-5096. https://resolver.caltech.edu/CaltechAUTHORS:20171213-085512032

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Abstract

We develop a micromechanical theory of dislocation structures and finite deformation single crystal plasticity based on the direct generation of deformation microstructures and the computation of the attendant effective behavior. Specifically, we aim at describing the lamellar dislocation structures which develop at large strains under monotonic loading. These microstructures are regarded as instances of sequential lamination and treated accordingly. The present approach is based on the explicit construction of microstructures by recursive lamination and their subsequent equilibration in order to relax the incremental constitutive description of the material. The microstructures are permitted to evolve in complexity and fineness with increasing macroscopic deformation. The dislocation structures are deduced from the plastic deformation gradient field by recourse to Kröner's formula for the dislocation density tensor. The theory is rendered nonlocal by the consideration of the self-energy of the dislocations. Selected examples demonstrate the ability of the theory to generate complex microstructures, determine the softening effect which those microstructures have on the effective behavior of the crystal, and account for the dependence of the effective behavior on the size of the crystalline sample, or size effect. In this last regard, the theory predicts the effective behavior of the crystal to stiffen with decreasing sample size, in keeping with experiment. In contrast to strain-gradient theories of plasticity, the size effect occurs for nominally uniform macroscopic deformations. Also in contrast to strain-gradient theories, the dimensions of the microstructure depend sensitively on the loading geometry, the extent of macroscopic deformation and the size of the sample.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/S0022-5096(99)00104-0DOIArticle
ORCID:
AuthorORCID
Ortiz, M.0000-0001-5877-4824
Stainier, L.0000-0001-6719-6616
Additional Information:© 2000 Elsevier. Received 1 April 1999; received in revised form 6 December 1999. The support of the Department of Energy through Caltech's ASCI Center of Excellence for Simulating Dynamic Response of Materials is gratefully acknowledged. LS also wishes to gratefully acknowledge the support from the Belgian Scientific Research Fund (FNRS).
Group:GALCIT
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Fonds National de la Recherche Scientifique (FNRS)UNSPECIFIED
Subject Keywords:A. Microstructures; A. Dislocations; B. Constitutive behavior; B. Crystal plasticity; C. Energy methods
Issue or Number:10
Record Number:CaltechAUTHORS:20171213-085512032
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171213-085512032
Official Citation:M. Ortiz, E.A. Repetto, L. Stainier, A theory of subgrain dislocation structures, In Journal of the Mechanics and Physics of Solids, Volume 48, Issue 10, 2000, Pages 2077-2114, ISSN 0022-5096, https://doi.org/10.1016/S0022-5096(99)00104-0. (http://www.sciencedirect.com/science/article/pii/S0022509699001040)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83854
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:16 Dec 2017 00:38
Last Modified:23 Nov 2020 20:26

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