Scale-free phase field theory of dislocations.
According to recent experimental and numerical investigations, if a characteristic length (such as grain size) of a specimen is in the submicron size regime, several new interesting phenomena emerge during the deformation. Since in such systems boundaries play a crucial role, to model the plastic response it is crucial to determine the dislocation distribution near the boundaries. In this Letter, a phase-field-type continuum theory of the time evolution of an ensemble of parallel edge dislocations with identical Burgers vectors, corresponding to the dislocation geometry near internal boundaries, is presented. Since the dislocation-dislocation interaction is scale free (1/r), apart from the average dislocation spacing the theory cannot contain any length scale parameter. As shown, the continuum theory suggested is able to recover the dislocation distribution near boundaries obtained by discrete dislocation dynamics simulations.