Mushy zone rheology and hot tearing in aluminium DC casting

Mo and co-workers recently formulated a two-phase (solid+liquid) model in which the two main mechanisms associated with hot tearing formation during solidification and subsequent cooling, namely shrinkage-driven melt flow and thermally induced deformation, are addressed simultaneously. The volume-averaged mass and momentum conservation equations are formulated for the coherent part of an equiaxed mushy zone. In the fully solidified (one-phase) region of the solution domain, the modelling equations simplify to those applied in the "classical" approach to thermally induced deformations. The constitutive model in the mushy zone treats the solid phase as a viscoplastic porous medium saturated with liquid, and the possibility of volume change, i.e., densification and dilatation of the semi-solid material, is taken into account. The evolution of the temperature field with time and a unique solidification path are input to the model. In the present article, the modelling equations are solved numerically for the start-up phase of direct chill casting of an axisymmetric aluminium extrusion ingot. Output of the model are the strains and stresses in the coherent mush as well as in the fully solidified ingot regions, and the mushy zone liquid flow and associated pressure. The latter quantity is a central parameter in a hot tearing criterion recently proposed by Rappaz and co-workers. They related hot tearing to the formation of pores deep in the mush, and thereby to the pressure drop associated with the melt flow to feed the solidification shrinkage and the possible solid dilatation associated with the thermally induced volume change. The main focus of the present article is to present some modelling studies estimating the effect of such solid phase dilatation on the liquid pressure and thereby on the hot tearing susceptibility. The interaction between the mushy zone liquid flow and solid deformation is also discussed.