A quantitative phase-field model for two-phase elastically inhomogeneous systems

Abstract Solid-state phase transformations are influenced by strains that are generated internally or applied externally. The stress state, composition, and microstructure evolution, which together determine the properties of solid materials can be studied using phase-field models coupled with micro-elasticity theory in the small strain limit. This coupling has been implemented using various schemes in literature. In a previous article (Durga et al., 2013), the authors evaluated three main existing schemes for a two-phase system and concluded that these schemes are not quantitative for inhomogeneous anisotropic elastic properties of the two phases. The stress states predicted by these models deviate from the expected values due to the generation of extra interfacial energy, which is an artefact of the models resulting from interfacial conditions different from local mechanical equilibrium conditions. In this work, we propose a new scheme with interfacial conditions consistent with those of the analytical results applicable to a general system where shear strains may be present. Using analytical solutions for composition and stress evolution, we validate this model for 2D and 3D systems with planar interface in the presence of misfit between phases and applied strains, and a 2D system with an elliptical second-phase particle. This extended scheme can now be applied to simulate quantitatively the microstructural evolution with coupled chemical and mechanical behaviour in any 2D or 3D two-phase system subject to internal or external strains irrespective of interface curvature.