The morphological evolution of the microstructure in heterogeneous materials is of great interest in material design and mechanics of materials. For example, it is experimentally observed that second phase particles in Ni-based super alloys undergo shape changes from spheres to cuboids with round corners, to platelets aligned along crystallographic directions when super alloys are annealed at constant temperature. Phenomena like splitting of a single large particle into a group of small cuboids or a pair of γ’ precipitate doublets are also observed by experiments.
 
In this work, we present a sharp interface model and numerical tools considering the interaction between different physical phenomena: e.g. chemical equilibrium, mechanical stress and interfacial energy effect and study their influences on the equilibrium morphologies of misfit particles in phase-separated alloys. The geometry of the material interface is implicitly described by the level set approach and the morphological transformation of microstructures, such as merging and splitting, creating sharp cusps, can be accurately captured. The extended finite element method is developed to evaluate the elastic and chemical fields without requiring remeshing during the evolution process. We found that the equilibrium morphology of the heterogeneities is strongly dependent upon the elastic anisotropy of the system, the ratio of chemical and elastic energy, as well as the particle size.