Continuum dislocation dynamics: Towards a physical theory of crystal plasticity

Journal of the Mechanics and Physics of Solids, Volume 63,  2014, Pages 167–178.

Thomas Hochrainera, , , Stefan Sandfelda, 1, Michael Zaiserb, 1, Peter Gumbscha, c

 a Institute for Applied Materials IAM, Karlsruhe Institute of Technology KIT, Engelbert-Arnold-Str. 4, 76131 Karlsruhe, Germany and

b The University of Edinburgh, Center for Materials Science and Engineering, King’s Buildings, Sanderson Building, Edinburgh EH93JL, United Kingdom and

c Fraunhofer IWM, Wöhlerstr. 11, 79108 Freiburg, Germany.



The plastic deformation of metals is the result of the motion and interaction of dislocations, line defects of the crystalline structure. Continuum models of plasticity, however, remain largely phenomenological to date, usually do not consider dislocation motion, and fail when materials behavior becomes size dependent. In this work we present a novel plasticity theory based on systematic physical averages of the kinematics and dynamics of dislocation systems. We demonstrate that this theory can predict microstructure evolution and size effects in accordance with experiments and discrete dislocation simulations. The theory is based on only four internal variables per slip system and features physical boundary conditions, dislocation pile ups, dislocation curvature, dislocation multiplication and dislocation loss. The presented theory therefore marks a major step towards a physically based theory of crystal plasticity.

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