Flow of interdendritic liquid and permeability in pb-20 Wt Pct Sn alloys
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I.
INTRODUCTION
FORalmost two decades studies have shown that the flow of interdendritic fluid, caused mainly by solidification shrinkage and the effect of gravity on fluid of variable density within the mushy zone, is mainly responsible for macrosegregation in cast alloys. 1-13 Thermal and compositional variations within the mushy zone cause variations in the mass density and hence convection of the interdendritic liquid. Figure 1 shows an example of quantitative results that can be obtained by modeling the interdendritic fluid flow. In this example solidification of the ingot proceeds upward. The liquidus and solidus isotherms are concave, and thus the gravity induced flow is downward and toward the center of ingot, where there is a reversal of flow. The segregation which results is strongly positive at the center of the ingot because the solute-rich interdendritic liquid has flowed to the center during solidification. In an ingot, such as that shown in Figure 1, another important effect can occur. "Freckles" form in the center of the ingot, if the velocity of the interdendritic liquid is in the same direction and its magnitude is greater than that of the isotherms. When this happens there is local remelting within the mushy zone and the opening of channels through which the interdendritic liquid flows against little resistance. Figure 2 is a micrograph of a Pb-20 wt pct Sn alloy. The light and dark areas in the micrograph are, respectively, the eutectic and the primary phase constituents of the alloy. The two large islands of the eutectic constituents, where preferential flow took place, are clearly viewed as the freckles in this micrograph. Permeability is a key parameter in the modeling of macrosegregation and the prediction of freckles; yet there are relatively few data available. Perhaps the first to measure permeabilities were Piwonka and Flemings 14 who reported permeability in A1-4.5 wt pct Cu alloys with equiaxial den-
dritic structures. In some of their experiments molten lead was forced through the dendrite interstices of partially solidified alloys, and the permeability was calculated from the rate of flow of the lead and the applied pressure. They also measured the flow of nitrogen through the porous networks which were developed by first displacing the interdendritic liquid with the nitrogen. From their results, Piwonka and Flemings 14showed that permeability, K, varied with volume fraction liquid, gL, as
where A is a constant. Equation [1] represented their data for 0 < gL 0.3, permeability increased more strongly with gL. The permeability in equiaxial A1-Si alloys was measured by Apelian et a1.15 In their experiments, the interdendritic liquid was forced out from the partially solid alloys with an inert gas. The resulting porous solid was then placed in a
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R. NASSER-RAFI is Process Engineer, Precision Castparts Corp., Portland, OR 97206; R. DESHMUKH is Member of Research Staff, Eng
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