Continuum modeling of dislocation plasticity: Theory, numerical implementation, and validation by discrete dislocation s
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mas Hochrainer Department of Scientific Computing, Florida State University, Tallahassee, Florida 32310
Michael Zaiser The University of Edinburgh, Center for Materials Science and Engineering, Edinburgh EH93JL, United Kingdom
Peter Gumbsch Karlsruher Institut für Technologie, IZBS—Institut für Zuverlässigkeit von Bauteilen und Systemen, 76131 Karlsruhe, Germany; and Fraunhofer IWM, 79108 Freiburg, Germany (Received 2 July 2010; accepted 2 December 2010)
Miniaturization of components and devices calls for an increased effort on physically motivated continuum theories, which can predict size-dependent plasticity by accounting for length scales associated with the dislocation microstructure. An important recent development has been the formulation of a Continuum Dislocation Dynamics theory (CDD) that provides a kinematically consistent continuum description of the dynamics of curved dislocation systems [T. Hochrainer, et al., Philos. Mag. 87, 1261 (2007)]. In this work, we present a brief overview of dislocation-based continuum plasticity models. We illustrate the implementation of CDD by a numerical example, bending of a thin film, and compare with results obtained by three-dimensional discrete dislocation dynamics (DDD) simulation.
I. INTRODUCTION
The development of advanced materials for high-end applications is driven by continuous progress in the synthesis and control of the materials microstructure on submicrometer and nanometer scales. Several pioneering studies have shown that, when confined to submicrometer dimensions, many materials exhibit unexpected and useful properties different from their macroscale behavior.7 As an example, nanostructured bulk metals and thin film structures may exhibit extraordinary strength and fatigue resistance. Even for traditional materials, the general trend toward miniaturization of components and systems makes predictive modeling of their mechanical performance on the micro- and nanoscale an engineering problem of growing importance, because components of submicrometer size behave differently from their macroscopic counterparts. The challenge of developing predictive models for the size-dependent mechanical response of materials on small scales has led to an increased effort on developing dislocation-based continuum theories of plasticity. Although discrete dislocation dynamics (DDD) simulations (e.g., Refs. 5, 10, 15, 32, 35, 46, 47, 48) provide an alternative approach to continuum models, DDD cannot a)
Address all correspondence to this author. e-mail: [email protected] This paper has been selected as an Invited Feature Paper. DOI: 10.1557/jmr.2010.92 J. Mater. Res., Vol. 26, No. 5, Mar 14, 2011
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be easily incorporated into the engineering “toolbox” for component design and assessment, because there still exists no standard approach for simulating systems with general geometries and boundary conditions (BCs). In the context of continuum dislocation dynamics, on the other hand, DDD simulations can play an importan
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