A Multi-phase-field Approach for Solidification with Non-negligible Volumetric Expansion—Application to Graphite Growth in Nodular Cast Iron

Multi-phase field models have become powerful tools for prediction of microstructure evolution in technical alloys. Coupling to CALPHAD databases provides complex multicomponent multiphase thermodynamic data and diffusion matrices. Although many thermodynamic databases contain volume data, this information is by now hardly used for solidification, since a comprehensive modelling of volumetric expansion based on solid- and fluid-mechanics exceeds present computational capacities. A novel multicomponent multi-phase-field approach is presented which handles volumetric expansion in a simplified way. It assumes that temporary pressure caused by local expansion is instantaneously released by matter transport on a time scale much faster than diffusion. The new approach neglects any mechanical and kinetic aspects of expansion, but allows for a change in total volume and for thermodynamically consistent volume fractions. Moreover, expansion-driven matter fluxes and associated advective solute transport are considered. Application is illustrated by the example of spheroidal graphite growth in a hypoeutectic cast iron alloy.