3D equilibrium shapes of periodically arranged anisotropic precipitates with elastic misfit

A numerical procedure for simulating the equilibrium shapes of precipitates in two phase materials, such as Ni-base alloys is presented. Assuming a periodic arrangement of precipitates a unit cell is analyzed to take particle interaction in 3D into account. Using the concept of generalized driving forces as the source of morphological evolution, a necessary condition for an equilibrium shape is derived. In the derivation of the driving force, elastic strain energy arising from the elastic misfit of the two phases and interface energy is considered. Both phases are assumed to be linear elastic but anisotropic and different from each other. The periodic cell problem is numerically solved with a Boundary Element Method. Numerical simulation for material parameters which mimic Ni-base alloys show the influence of particle size, stiffness ratio of the two phases, volume fraction and external load on the resulting equilibrium shapes