Microstructural evolution in orthotropic elastic media

We consider the problem of microstructural evolution in binary alloys in tw o dimensions. The microstructure consists of arbitrarily shaped precipitate s embedded in a matrix. Both the precipitates and the matrix are taken to b e elastically anisotropic, with different elastic constants. The interfacia l energy at the precipitate-matrix interfaces is also taken to be anisotrop ic, This is an extension of the inhomogeneous isotrpic problem considered b y H.-J, Jou et nl. (1997, J. Comput. Phys. 131, 109). Evolution occurs via diffusion among the precipitates such that the total (elastic plus interfac ial) energy decreases; this is accounted for by a modified Gibbs-Thomson bo undary condition at the interfaces. The coupled diffusion and elasticity eq uations are reformulated using boundary integrals. An efficient preconditio ner for the elasticity problem is developed based on a small scale analysis of the equations. The solution to the coupled elasticity-diffusion problem is implemented in parallel. Precipitate evolution is tracked by special no n-stiff time stepping algorithms that guarantee agreement between physical and numerical equilibria. Results show that small elastic inhomogeneities i n cubic systems can have a strong effect on precipitate evolution, For exam ple, in systems where the elastic constants of the precipitates are smaller than those of the matrix, the particles move toward each other. where the rate of approach depends on the degree of inhomogeneity. Anisotropic surfac e energy can either enhance or reduce this effect, depending on the relativ e orientations of the anisotropies. Simulations of the evolution of multipl e precipitates indicate that the elastic constants and surface energy contr ol precipitate morphology and strongly influence nearest neighbor interacti ons. However, for the parameter ranges considered, the overall evolution of systems with large numbers of precipitates is primarily driven by the over all reduction in surface energy. Finally, we consider a problem related to the microstructure of fully orthotropic geological materials. (C) 2000 Acad emic Press.