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

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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.

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Acknowledgments

K.EA and MZ thank support from KEA’s European Research Council (ERC) Starting Grant 211166. MZ also thanks for support by Engineering and Physical Sciences Research Council (EPSRC) under Grant No. EP/J003387/1.

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Authors and Affiliations

  1. Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Katerina E. Aifantis

  2. Karlsruher Institut für Technologie, Institute for Applied Materials, 76131, Karlsruhe, Germany

    Daniel Weygand & Christian Motz

  3. Institute for Materials and Processes, The University of Edinburgh, Edinburgh, EH9 3JL, United Kingdom

    Nikolaos Nikitas & Michael Zaiser

Authors
  1. Katerina E. Aifantis
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  2. Daniel Weygand
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  3. Christian Motz
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  4. Nikolaos Nikitas
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  5. Michael Zaiser
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Correspondence to Katerina E. Aifantis.

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This author was an editor of this focus issue during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/jmr-editor-manuscripts/.

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Aifantis, K.E., Weygand, D., Motz, C. et al. Modeling microbending of thin films through discrete dislocation dynamics, continuum dislocation theory, and gradient plasticity. Journal of Materials Research 27, 612–618 (2012). https://doi.org/10.1557/jmr.2011.390

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  • DOI: https://doi.org/10.1557/jmr.2011.390

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