Microstructure evolution in three-dimensional inhomogeneous elastic media

A new, three-dimensional boundary integral method is used to study the evolution of an isolated precipitate growing by diffusion in an infinite, elastic matrix. An adaptive surface mesh is used to accurately and efficiently discretize the precipitate boundaries in three dimensions. The model accounts for diffusion, surface energy, interface kinetics and elastic energy, which are coupled through a modified Gibbs-Thomson boundary condition at the precipitate-matrix interface. The precipitate and matrix phases are taken to have different elastic-stiffness tensors, and there is a mismatch strain between the phases. Both isotropic and anisotropic elasticity are investigated. In this article, the coarsening and growth of a single precipitate are simulated under various conditions. For isotropic elasticity, coarsened shapes are found to be consistent with the equilibrium-shape analysis of Johnson and Cahn. Growth shapes are found to become rapidly nonlinear and to develop regions of high curvature. In elastically anisotropic systems, coarsened shapes are found to be consistent with the equilibrium-shape calculations of Mueller and Gross. Simulations of coarsening in which the cubic axes of the precipitate are different from those of the matrix suggest that there may be more than one local minima in the energy, so that the observed shapes depend on the growth path. Finally, non-convex precipitate morphologies are seen for the growth of soft Ni₃Al precipitates in a Ni matrix, consistent with experimental observations. In the case of a hard Ni₃Si precipitate grown under the same conditions, we find self-similar growth of a convex shape.