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Modeling microbending of thin films through discrete dislocation dynamics, continuum dislocation theory, and gradient plasticity

Published online by Cambridge University Press:  14 December 2011

Katerina E. Aifantis ,
Daniel Weygand ,
Christian Motz ,
Nikolaos Nikitas  and
Michael Zaiser
Katerina E. Aifantis*
Affiliation:
Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Daniel Weygand
Affiliation:
Karlsruher Institut für Technologie, Institute for Applied Materials, 76131 Karlsruhe, Germany
Christian Motz
Affiliation:
Karlsruher Institut für Technologie, Institute for Applied Materials, 76131 Karlsruhe, Germany
Nikolaos Nikitas
Affiliation:
Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH9 3JL, United Kingdom
Michael Zaiser
Affiliation:
Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH9 3JL, United Kingdom
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

Constitutive models that describe crystal microplasticity in a continuum framework can be envisaged as average representations of the dynamics of dislocation systems. Thus, their performance needs to be assessed not only by their ability to correctly represent stress–strain characteristics on the specimen scale but also by their ability to correctly represent the evolution of internal stress and strain patterns. Three-dimensional discrete dislocation dynamics (3D DDD) simulations provide complete knowledge of this evolution, and averages over ensembles of statistically equivalent simulations can therefore be used to assess the performance of continuum models. In this study, we consider the bending of a free-standing thin film. From a continuum mechanics point of view, this is a one-dimensional (1D) problem as stress and strain fields vary only in one dimension. From a dislocation plasticity point of view, on the other hand, the spatial degrees of freedom associated with the bending and piling up of dislocations are essential. We compare the results of 3D DDD simulations with those obtained from a simple 1D gradient plasticity model and a more complex dislocation-based continuum model. Both models correctly reproduce the nontrivial strain patterns predicted by 3D DDD for the microbending problem.

Keywords

MicrostructureDislocationsGrain boundaries
Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 3: Focus Issue: Advances in Mechanics of One-Dimensional Micro/Nanomaterials , 14 February 2012 , pp. 612 - 618
Copyright
Copyright © Materials Research Society 2011

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