A three-dimensional continuum theory of dislocation systems: Kinematics and mean-field formulation

Thomas Hochrainer (1) , Michael Zaiser (2) , Peter Gumbsch (3, 4)

1 IZBS - Institut für Zuverlässigkeit von Bauteilen und Systemen
2 Center for Materials Science and Engineering
3 Institut fuer Zuverlaessigkeit von Bauteilen und Systemen
4 Fraunhofer IWM - Fraunhofer Institute for Mechanics of Materials

We propose a dislocation density measure which is able to account for the evolution of systems of three-dimensionally curved dislocations. The definition and evolution equation of this measure arise as direct generalisations of the definition and kinematic evolution equation of the classical dislocation density tensor. The evolution of this measure allows to determine the plastic distortion rate in a natural fashion and therefore yields a kinematically closed dislocation-based theory of plasticity. A self-consistent theory is built upon the measure which accounts for both the long range interactions of dislocations and their short range self-interaction which is incorporated via a line tension approximation. A two-dimensional kinematic example visualises the definitions and their relations to the classical theory.

Mots clés: Physical Sciences

Thomas Hochrainer, Michael Zaiser, Peter Gumbsch. A three-dimensional continuum theory of dislocation systems: Kinematics and mean-field formulation. Philosophical Magazine, 2007, 87 (08-09), pp.1261-1282. ⟨10.1080/14786430600930218⟩. ⟨hal-00513758⟩