Numerical method for the evolution of multi-phase systems with non-equilibrium, stressed planar interfaces

A numerical model for the solution of the coupled elasticity and binary diffusion equations in one dimension is developed for a stressed, multiphase, diffusion couple using a two-grid, finite difference method. Associated with the coherent interfaces are interfacial kinetic barriers that can impede the transfer of mass from one phase to another and permit the interfaces to deviate from local equilibrium. Stresses arise from composition independent misfit strains and applied tractions. Numerical calculations show that the interfacial kinetic barriers retard the growth of the intermediate phase in the absence of stress effects. Misfit strains can alter the sign, as well as the magnitude, of the evolution of the intermediate phase and introduce multiple linearly stable equilibrium states for a given temperature, alloy composition, and mechanical loading condition.