TearSim: A two-phase model addressing hot tearing formation during aluminum direct chill casting
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in aluminum direct-chill (DC) casting start to develop in the mushy zone at a stage where the solid fraction is close to one.[1,2] There are two transport phenomena associated with this cracking problem,[3] namely, the interdendritic melt flow associated with the solidification shrinkage[4,5] and the thermally induced deformation caused by nonuniform cooling contraction of the casting.[1,6,7] Closely linked to the latter phenomenon are the constraints on the kinematic behavior imposed by the entirely solidified material close to the mushy zone. In References 8 and 9, shrinkage-driven melt flow and thermally induced deformations were systematized in a two-phase continuum model for the coherent part (defined in Section II) of an isotropic mushy zone. This model is based upon volume averaged conservation equations,[10] and thus quantifies volume averaged velocities and stresses in both the liquid and solid phases. The two-phase model was further developed to address hot tearing formation in aluminum ingots during the DC casting start-up and quasistationary phases.[11] This approach unifies the two-phase model[8,9] in which the coherent mushy zone is considered as a viscoplastic porous medium saturated with liquid,[12–15] with the ‘‘classical’’ approach to thermally induced deformations in one-phase solid materials using the linear kinematics approximation.[16] It is particularly emphasized that this model accounts for the possible viscoplastic volume change (dilatation/compression) of the coherent mushy zone solid skeleton, reflecting thus on the continuum scale ‘‘opening/closing’’ of the dendrite network by thermally induced deformations. Moreover, the conservation equations are formulated in such a way that both the two-phase coherent mush and the one-phase elastic-viscoplastic material at the lower temperatures are handled in the same model. MOHAMMED M’HAMDI, Senior Scientist, is with SINTEF Materials Technology, N-0314 Oslo, Norway. Contact e-mail: mohammed. [email protected] ASBJØRN MO, Professor, is with SINTEF Materials Technology and the University of Oslo, N-0316, Oslo, Norway. HALLVARD G. FJÆR, Principal Scientist, is with the Institute for Energy Technology, N-2007 Kjeller, Norway. Manuscript submitted January 28, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
Similar to the classical approach to thermally induced deformations, the governing equations are solved with input from prior heat-transfer and solidification path calculations. A one-dimensional solution of the two-phase equations with some relevance for DC casting was presented in Reference 11, and a two-dimensional (2-D) solution was preliminarily presented in Reference 17. The purpose of the present article is to give a more thorough presentation of this modeling tool, referred to as TearSim, including a comparison of modeling results to experimental results obtained in fullscale DC castings.[18] Based on ideas presented elsewhere,[5,19–21] a hot tearing criterion is then proposed to which two-phase quantities calculated by TearSim are input. The first part
