Thermal strain in the mushy zone for aluminum alloys
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NTRODUCTION
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 that initiates tears and 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] 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 et al.[3,5] This model is based upon general volumeaveraged conservation equations.[6] One challenge in such a modeling is to establish reliable constitutive relations for thermally induced deformations. Thermal strain is the driving force for thermally induced deformations. While the thermal strain can easily be related to the density variation with temperature in a one-phase continuum, the situation is more complicated in the twophase mushy zone (Figure 1). At low solid fractions, the bonds between the individual dendrites are relatively weak or even nonexistent. The dendrites can therefore contract with decreasing temperature without affecting the positions of their individual mass centers. Such solid-phase volume change would be accompanied by unlimited liquid feeding. Consequently there will be no thermal strain transmitted
AAGE STANGELAND, Scientist, formerly with SINTEF Materials and Chemistry, N-0314 Oslo, Norway, and the University of Oslo, N-0316, Oslo, Norway, is now with The Bellona Foundation, N-0505 Oslo, Norway. ASBJØRN MO, Professor, is with SINTEF Materials and Chemistry, N-0314 Oslo, Norway, and the University of Oslo, N-0316, Oslo, Norway. Contact e-mail: [email protected] DMITRY ESKIN, Senior Scientist, is with the Netherlands Institute for Metals Research, 2628CD, Delft, The Netherlands. Manuscript submitted February 23, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
through the mushy zone—i.e., there will be no macroscopic thermal strain imposed onto the mushy zone.* At high solid *Macroscopic thermal strain rate is in this study the volume-averaged thermal strain rate calculated based on volume-averaged velocity gradients.
fractions, on the other hand, there is reason to believe that dendrites will coalesce or tangle,[7,8] meaning that a change in the solid density would be reflected in a nonzero macroscopic thermal strain as in the one-phase continuum. In this work, the critical solid fraction when the macroscopic thermal strain becomes nonzero is referred to as the solid fraction at onset of contraction, gsth. A constitutive equation for thermal strain in the mushy zone has recently been established,[9] and the parameters in this relation were determined for binary Al-Cu alloys. The purpose of the current study is to determine the parameters in the constitut
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