The importance of being curved: bowing dislocations in a continuum description

Evolution equations for scalar density and orientation of fields of curved dislocations formulated in the framework of the continuum theory of moving dislocations serve as the starting point for development of a non-local dislocation-based constitutive relation for crystal plasticity, on the length scale intermediate between the phenomenological hardening laws of strain-gradient crystal plasticity and the explicit treatment of three-dimensional discrete dislocation dynamics. The key features of the proposed approach are the refined averaging in the continuum theory based on separation of single-valued dislocation fields, and the accounting for the line energy of the bowed dislocations which renders the theory non-local.

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