A phase field model for the simulation of grain growth in materials containing finely dispersed incoherent second-phase particles

A phase field model is presented for simulating grain growth in materials containing small incoherent second-phase particles that are constant in time. The model of [L.-Q. Chen, W. Yang, Phys. Rev. B 50 (1994) 15752] for grain growth in single phase materials, that represents a polycrystalline microstructure with a set of phase field variables (eta)i(r,t), has been modified to incorporate the presence of second-phase particles by adding an extra term (epsilon)(phi)(sigma)i(eta)2ito the free energy expression, with (phi) a spatially dependent parameter that equals one inside the particles, and zero elsewhere and (epsilon)a positive constant. The interaction between a particle and a diffuse interphase is analyzed from an energetic point of view and the effect of pinning particles on the shape and the evolution of an initially spherical grain is studied for two-dimensional and three-dimensional systems.