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Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

Published online by Cambridge University Press:  29 January 2016

Alireza Ebrahimi
Affiliation:
Universität Bremen, Am Biologischen Garten 2, 28359 Bremen, Germany
Thomas Hochrainer
Affiliation:
Universität Bremen, Am Biologischen Garten 2, 28359 Bremen, Germany
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Abstract

A persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.

In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus® in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

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Copyright
Copyright © Materials Research Society 2016 

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Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam
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