An analysis of the melt flow permeability for evolving hypoeutectic Al-Si mushy zone microstructures by phase field simulations

Abstract

The evolution of 3D microstructures during solidification has been simulated by the phase field method for a hypoeutectic Al-Si-Mg casting alloy at the scale of a representative volume element (RVE) for isotropic and anisotropic thermal conditions. The corresponding evolution of the melt flow permeability is derived by solving the Navier-Stokes equation on this RVE, i.e. determining the flow for an applied pressure gradient. To characterize the microstructures their interfacial area density and their tortuosity were calculated. The solid fraction was used to track the progress of solidification. The predicted permeabilities of the microstructures can be fitted to a Carman-Kozeny equation amended by a parameter that accounts for the closure of open flow channels, i.e. the complete encapsulation of residual melt. Good agreement was found except for the solidification morphology resulting from anisotropic conditions. In this case, the permeability for the flow in the direction of the thermal gradient deviated at higher solid fractions. The reasons for this deviation are investigated and discussed. Overall, we demonstrate that effective melt flow permeabilities can be derived from microstructure simulations. It leads to a parameterized Carman-Kozeny relationship for the evolving permeability during solidification calibrated by microstructure simulations. This relation can be used in macroscopic casting simulations.