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This thesis aims at theoretical and computational modeling of the continuum dislocation theory coupled with its internal elastic field. In this continuum description, the space-time evolution of the dislocation density is governed by a set of hyperbolic partial differential equations. These PDEs must be complemented by elastic equilibrium equations in order to obtain the velocity field that drives dislocation motion on slip planes. Simultaneously, the plastic eigenstrain tensor that serves as a known field in equilibrium equations should be updated by the motion of dislocations according to Orowan's law. Therefore, a stress- dislocation coupled process is involved when a crystal undergoes elastoplastic deformation. The solutions of equilibrium equation and dislocation density evolution equation are tested by a few examples in order to make sure appropriate computational schemes are selected for each. A coupled numerical scheme is proposed, where resolved shear stress and Orowan's law are two passages that connect these two sets of PDEs. The numerical implementation of this scheme is illustrated by an example that simulates the recovery process of a dislocated cubic crystal. The simulated result demonstrates the possibility to couple macroscopic(stress) and microscopic(dislocation density tensor) physical quantity to obtain crystal mechanical response.
crystal plasticity, dislocation, dislocation density tensor, dislocation evolution equation
Date of Defense
November 7, 2011.
A Thesis submitted to the Department of Scientiﬁc Computing in partial fulfillment of the requirements for the degree of Master of Science.
Includes bibliographical references.
Anter El-Azab, Professor Directing Thesis; Tomasz Plewa, Committee Member; Xiaoqiang Wang, Committee Member.
Florida State University
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