Two-phase modeling directed toward hot tearing formation in aluminum direct chill casting

Abstract

The two-phase mass and momentum conservation equations governing shrinkage-driven melt flow and thermally induced deformation are formulated for the aluminum direct chill (DC) casting process. Two main mechanisms associated with hot tearing formation during solidification and subsequent cooling are thus addressed simultaneously in the same mathematical model. The approach unifies the two-phase mushy zone model outlined by Farup and Mo, the constitutive relations that treat the mushy zone as a viscoplastic porous medium saturated with liquid outlined by Martin et al., and the “classical” mechanics approach to thermally induced deformations in solid (one-phase) materials using the linear kinematics approximation. A temperature field and a unique solidification path are considered as input to the model. The governing equations are solved for a one-dimensional (1-D) situation with some relevance to the DC casting process. The importance of taking into account the transfer of momentum from the liquid phase to the solid phase is then demonstrated through modeling examples. Furthermore, the modeling results indicate that the constitutive law governing the viscoplastic behavior of the solid skeleton of the mushy zone should take into account that the solid skeleton can be compressed/dilated as well as stress space anisotropy. Calculated peak values for liquid pressure and solid stress turn out to correlate to the hot tearing susceptibility measured in casting trials in the sense that trials having the largest cracks are those for which the highest pressures and stresses are computed.