3D inhomogeneous, misfitting second phase particles-equilibrium shapes and morphological development

A 3D simulation of equilibrium shapes of precipitates forming from diffusive phase transitions is presented. The concept of generalized forces is used to take elastic and interfacial energy into consideration when calculating the equilibrium morphologies. By using shape optimization techniques an efficient iterative scheme for finding equilibrium morphologies is presented. A first step towards simulating the temporal evolution of the microstructure is undertaken, by proposing a simple generalized evolution law. The numerical simulations underline the importance of elastic strain energy in the developing of certain microstructures, such as convex, concave, prolate and oblate cuboids. It is elaborated that particle size together with stiffness ratio between particle and matrix play an significant role