Modeling of microporosity, macroporosity, and pipe-shrinkage formation during the solidification of alloys using a mushy-zone refinement method: Applications to aluminum alloys

Abstract

A microporosity model, based on the solution of Darcy’s equation and microsegregation of gas, has been developed for arbitrary two- (2-D) and three-dimensional (3-D) geometry and coupled for the first time with macroporosity and pipe-shrinkage predictions. In order to accurately calculate the pressure drop within the mushy zone, a dynamic refinement technique has been implemented: a fine and regular finite volume (FV) grid is superimposed onto the finite-element (FE) mesh used for the heat-flow computations. For each time-step, the cells, which fall in the mushy zone, are activated, and the governing equations of microporosity formation are solved only within this domain, with appropriate boundary conditions. For that purpose, it is necessary to identify automatically the various liquid regions that may appear during solidification: open regions of liquid are connected to a free surface where a pressure is imposed, partially closed liquid regions are connected to an open region via the mushy zone, and closed regions are totally surrounded by the solid and/or mold. For partially closed liquid pockets, it is shown that an integral boundary condition applies before macroporosity appears. Finally, pipe shrinkage (i.e., shrinkage appearing at a free surface) is obtained by integration of the calculated interdendritic fluid flow over the open-region boundaries, thus ensuring that the total shrinkage (microporosity plus macroporosity and pipe shrinkage) respects the overall mass balance. This very general approach is applied to Al-Cu and Al-Si alloys.