Phase field methods and dislocations

We present a general formalism for incorporating dislocations in Phase Field methods (PFM) based on the elastic equivalence between a dislocation loop and a platelet inclusion of specific stress-free strain. Dislocations may be elastically and dynamically coupled to any other field such as a concentration field. Special attention is paid to the treatment of dislocation cores after the discretization of real and reciprocal space required by the computer implementation of any PFM. In particular, we propose a method based on two length scales to account for dislocation cores much smaller than the grid spacing. The method is illustrated through the simulation of the motion of a dislocation loop in a microstructure representative of a late-stage γ/γ′ microstructure.