A phase-field model for evolving microstructures with strong elastic inhomogeneity

An efficient phase-field model is proposed to study the coherent microstructure evolution in elastically anisotropic systems with significant elastic modulus inhomogeneity. It combines an iterative approach for obtaining the elastic displacement fields and a semi-implicit Fourier-spectral method for solving the time-dependent Cahn-Hilliard equation. Each iteration in our iterative numerical simulation has a one-to-one correspondence to a given order of approximation in Khachatuyran's perturbation method. A unique feature of this approach is its ability to control the accuracy by choosing the appropriate order of approximation. We examine shape dependence of isolated particles as well as the morphological dependence of a phase-separated multi-particle system on the degree of elastic inhomogeneity in elastically anisotropic systems. It is shown that although prior calculations using first-order approximations correctly predicted the qualitative dependence of a two-phase morphology on elastic inhomogeneity, the local stress distributions and thus the driving force for microstructure evolution such as coarsening were in serious error quantitatively for systems with strong elastic inhomogeneity.