Development of thermal strain in the coherent mushy zone during solidification of aluminum alloys
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8/10/04
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Development of Thermal Strain in the Coherent Mushy Zone during Solidification of Aluminum Alloys AAGE STANGELAND, ASBJØRN MO, ØYVIND NIELSEN, DMITRY ESKIN, and MOHAMMED M’HAMDI A constitutive equation for thermal strain in the mushy zone during solidification of aluminum alloys has been determined based on a two-phase volume-averaged description of the mushy zone. The change of linear dimensions in the horizontal plane of cast samples during solidification is investigated experimentally. The temperature when the solid part of the mushy zone starts to contract, and the total contraction of the solid part of the mushy zone, are determined experimentally. The constitutive model for thermal strain in the mushy zone reflects that there is no thermal strain in the solid part of the mushy zone at a low solid fraction and that the thermal strain in the mushy zone approaches thermal contraction in fully solid as the solid fraction increases towards one. The parameters in the constitutive model for thermal strain in the mushy zone are determined by combining experimental results with thermomechanical simulations of the experiments. The heat-transfer coefficients and the parameters in the model are tuned to make the simulations reproduce the experimentally determined temperature field and contraction. Al-Cu alloys with Cu concentrations from 0.3 to 9 wt pct Cu and an Al-7 wt pct Si-0.3 wt pct Mg alloy are tested both with and without grain refinement and at various cooling rates. The solid fractions when the alloys start to contract (gth s ) are in the range of 0.48 to 0.97. A lower solute concentration, grain refinement, and higher cooling rate increase gsth.
I. INTRODUCTION
HOT tearing is one of the major defects that can occur during solidification of alloys. This defect is believed to be a result of inadequate melt feeding initiating tears and severe deformation leading to the opening and propagation of the tears. This type of defect appears at the end of the solidification when the solid fraction is high.[1] Two main mechanisms associated with hot tearing are the solidification shrinkage leading to interdendritic melt flow[2] and the thermally induced deformation caused by nonuniform cooling contraction of the casting.[3,4] While solidification shrinkage is the volume change associated with the phase transformation from liquid to solid, thermally induced deformation is associated with the change in solid density with decreasing temperature. A mathematical model addressing these phenomena (i.e., shrinkage-driven melt flow and thermally induced deformation) in an isotropic mushy zone was recently proposed by Mo and co-workers.[3,5] This model is based upon general volume-averaged conservation equations.[6] A main challenge in such modeling is to establish reliable constitutive relations for the mushy-zone permeability and rheology. Concerning the latter, the approach in Reference 5 includes a constitutive model that treats the mush as a viscoplastic porous medium saturated with liquid,[7] a
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