Influence of dendrite network defects on channel segregate growth
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Influence of Dendrite Network Defects on Channel Segregate Growth M. SIMPSON, M. YEREBAKAN, and M.C. FLEMINGS The recent interest in calculating interdendritic flow in solidifying ingots has been partly generated by the wish to predict where channel segregates (or A-segregates) might form. L2In such calculations channel segregates are assumed to be produced by interdendritic fluid flow dissolving channels in the primary dendrite network. Most commonly, formation of channel segregates is supposed to occur when the inequality given below is satisfied: 3 V0 " U/IU] 2 7> 1
[1]
where vo is the interdendritic flow velocity calculated using a packed bed theory assuming uniformly varying isotropic permeability, and u is the isotherm velocity defined by u = -VT(OT/Ot)/IVTF 2
Here VT is the temperature gradient. In this note we refine the analysis leading to [1] by examining the flow through a dendrite network with a small defect in it. This differs from the treatment of Reference 3 and subsequent work in which the dendrite network is assumed to act as a medium of uniform or uniformly varying permeability. The presence of the small defect turns out to make channel segregates grow much more readily than in a homogeneous medium. This can be easily understood: at a local defect in the dendrite network such as a grain boundary or a hot tear, the local interdendritic velocity can be substantially different from the average interdendritic velocity. This can lead to the conditions for channel segregate growth being satisfied at the defect, although they may not be satisfied elsewhere. To analyze the growth of channel segregates, we solve the equations governing their evolution in a simple case. Consider the section of the mushy zone in a solidifying casting M. SIMPSON and M. YEREBAKAN, both formerly with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, are now with, respectively, the Norton Research Corporation (Canada) Ltd., Niagara Falls, ON L2G 6S2, Canada. and Avarmetal. Kapaliqar~i Hart 49, lstanbul, Turkey. M.C. FLEMINGS is Chairman of the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. Manuscript submitted January 28, 1985. METALLURGICAL TRANSACTIONS A
Inferdendmhc
flow
J
J
Fig. 1 - - Small defect in the mushy zone of a solidifying ingot.
shown in Figure 1. This section is small enough that the pressure and temperature gradients VP and VT, the cooling rate, and the volume fraction liquid gL are essentially constant across it except in the vicinity of a small prolate ellipsoidal (needle-shaped) defect. There is a constant difference 6gL between the volume fraction liquid in the defect and the volume fraction liquid outside it. The needle-shaped region acts as a test for the growth of channel segregates. If 6gL increases with time, then the needle-shaped defect will become ever more pronounced (and hence will form a channel), whereas if 6& decreases, then the defect will fade away. The equations governing the flow o
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