A general formalism was presented for incorporating dislocations into phase-field methods, 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 was paid to the treatment of dislocation cores after the discretization of real and reciprocal space required by the computer implementation of any phase-field methods. In particular, a method based upon 2 length scales was proposed in order to account for dislocation cores which were much smaller than the grid spacing. The method was illustrated by simulation of the motion of a dislocation loop in a microstructure representing a late-stage γ/γ’ microstructure.

Phase Field Methods and Dislocations. D.Rodney, Y.Le Bouar, A.Finel: Acta Materialia, 2003, 51[1], 17-30