Quantifying elastic energy effects on interfacial energy in the Kim-Kim-Suzuki phase-field model with different interpolation schemes

Phase-field modeling is a microstructure-level simulation technique often used in the Integrated Computational Materials Engineering (ICME) approach to materials design. To perform quantitatively accurate phase-field simulations for this application, potential sources of error in model parameters such as interfacial energy must be fully understood. To this end, the interfacial energy of the Kim-Kim-Suzuki phase-field model coupled with elastic energy was investigated as a function of interface thickness for two different schemes to interpolate mechanical properties between phases: elastic misfit strain interpolation and elastic energy interpolation. Variations in interfacial energy were quantified for bicrystal and misfitting precipitate configurations. The interfacial energy deviates from its nominal value in the absence of elastic energy, and the deviation increases with increasing interface thickness. The deviation was positive for elastic energy interpolation and negative for misfit strain interpolation, and the magnitude of the deviation was greater for elastic energy interpolation. The order parameter profile through the interface is modified for both interpolation schemes, leading to an increase in the contribution to interfacial energy from the gradient and double-well terms in the free energy functional. There is also an excess elastic energy in the interfacial region for both interpolation schemes that contributes to the change in interfacial energy between phases. A criterion to aid in choosing interface thickness for the KKS model was introduced and validated for cubic materials with dilatational eigenstrain.