Dislocations in nonlinear nonlocal media: Martensitic embryo formation

A model is developed for determining the stress and strain fields of an arr ay of slip dislocation defects in a two-dimensional elastic medium with a h ighly nonlinear and nonlocal energy functional. The medium serves as a mode l for an elastic system in the vicinity of a martensitic structural phase t ransformation, in the high-temperature regime where the metastable product phase first acquires local stability. The dislocation array is a model of a candidate site for heterogeneous nucleation of martensite. The slip disloc ation defects are included in the continuum by means of a static, external "topological" field superimposed on the conventional elastic displacement f ield. The results indicate that a fully transformed martensitic region of m esoscopic size is stabilized by the nonlinear elastic field of the dislocat ions at temperatures substantially higher than the equilibrium temperature T-0, consistent with the Kaufman-Cohen "preexisting embryo" hypothesis.