Near-eutectic alloys freeze with a macroscopically discrete solid-liquid interface at a temperature below the equilibrium eutectic temperature. The velocity dependence of the freezing temperature results from the microscale species diffusion for microstructures with coupled eutectic growth characteristic of a near-eutectic alloy composition. At solidification rates that are representative of gravity permanent mold and die casting processes, consideration of the nonequilibrium conditions at the interface affects the prediction of the macroscale thermal field, and it in turn affects microscale properties.
A phase-field formulation is presented to model the alloy solidification which implicitly links the interface temperature to the interface speed. The utility of the method is well-suited for complex evolving solid-liquid interfaces and the velocity-dependent freezing temperature is satisfied implicitly.
The dimensionless governing equations are solved numerically with a fixed-grid Galerkin finite element method. After demonstrating sufficient numerical accuracy, temperature, phase field, and interface position results are presented for a square domain and three-dimensional casting geometry. Limitations of the phase-field method are discussed, and the conjugate heat transfer problem is studied to address boundary condition issues.