An efficient method for computing microstructural evolution of elastically homogeneous media

A boundary integral method is introduced to study the dynamics of the morphological evolution of a three-dimensional, coherent precipitate in an infinite, elastic matrix. The precipitate evolves diffusionally in which the precipitate-matrix interface satisfies a generalized Gibbs-Thomson boundary condition, accounting for surface energy, elastic and interface kinetic energy. Elastically homogeneous systems, where the precipitate and matrix phases are taken to have the same elastic stiffness tensor of general anisotropy, are considered. A computationally efficient approach, which only involves surface integration, is developed to determine the elastic strain energy due to a misfit strain between the phases. The convergence rate of the numerical method is obtained, and the method is applied to simulate the evolution of a single precipitate in a cubic system. Results show that the number and the stability of equilibrium shapes of the precipitate change as the ratio between the elastic and surface energies is larger than a critical value. For ratios below the critical value, there is unique stable equilibrium shape of cubic symmetry; for a range of values beyond the critical value, at least two kinds of equilibrium shapes exist: one retains cubic symmetry and is metastable, and the other is tetragonal symmetric and more stable.