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

Abstract

Abstract 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. Acknowledgements Thanks are due to Dr Anter El Azab for enabling access to his paper (El Azab Citation2003) prior to publication and for discussion concerning the relation between his and the present approach. J.K. wishes to express his gratitude for the financial support by grants GAČR 106/00/1109 and VZ J-00021. Notes † Compare also equation (Equation54) below.