Assessment of Interpolation Schemes of Elasticity at Particle-Matrix Interface in the Phase-Field Method

Phase-field method is effective simulation technique for modeling the coherent microstructure evolution in elastically anisotropic systems. For binary system, the influence of the elastic effect is mainly seen on the interface. For the mechanical properties of interface, the interpolation of mechanical properties for two phases is required. Therefore the interfacial energy is affected by elastic energy differently according to the interpolation schemes. In this study, comparison of three existing interpolation schemes including Khachaturyan's strain interpolation scheme (KHS), Voight-Taylor's elastic energy interpolation scheme (VTS) and steinbach-apel's interpolation scheme (SAS) is discussed. We represent the elastic energy density and stress and strain for the binary system using three interpolation schemes and discuss which is suitable scheme for morphological evolution. Three models coupled with different interpolation schemes are implemented in MOOSE(Multiphysics Object Oriented Simulation Environment) framework.