Primary dendrite distribution and disorder during directional solidification of Pb-Sb alloys
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INTRODUCTION
IN order to achieve uniformity in the mechanical properties of materials, it is important to avoid any inhomogeneity in the spatial distribution of dendritic microstructures that are formed during solidification processing. This is especially true in directionally solidified superalloy gas turbine engine components, such as turbine blades and vanes. An extensive body of literature[1–5] exists on the dependence of the average primary spacing on the composition, growth speed, and thermal gradients, for the dendritic morphologies. The average primary dendrite spacing has generally been measured as 冪A/(N ⫺ 1), where N is the number of dendrites in a given area of A on a cross section that is transverse to the growth direction. This technique inherently assumes a square distribution of dendrites. However, an analysis of the nearest and higher-order spacing distribution of dendrites indicated their arrangement to be closer to a hexagonal pattern.[6] While cellular arrays have been extensively studied for their spacing distribution during initial transient growth and during steady-state growth using analytical techniques such as minimum spanning trees (MSTs)[7,8,9] and Voronoi polygons,[7,8,9] similar studies for dendritic arrays have not been carried out. The purpose of this study was to examine the influence of interdendritic convection on the distribution of primary dendrites during initial transient growth and during the subsequent steady-state directional solidification of binary metallic alloys. During directional solidification of metallic alloys, with the melt on top and solid below, the thermal profile is expected to cause stability against convection. However, the solutal profile in the mushy zone and in the JUN HUI and R. TIWARI, Graduate Students, X. WU, Research Associate, and S.N. TEWARI, Professor, are with the Chemical Engineering Department, Cleveland State University, Cleveland, OH 46115. Contact e-mail: [email protected] R. TRIVEDI, Professor, is with the Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011. Manuscript submitted January 31, 2002. METALLURGICAL AND MATERIALS TRANSACTIONS A
overlying melt immediately ahead of the dendritic array would be expected to be stable only if the solute enrichment increases the melt density, as is the case with the Al-Cu alloy. In the hypoeutectic Pb-Sb alloys, the solute enrichment decreases the melt density, which causes convection in the mushy zone.[10] Two alloy compositions, Pb-5.8 wt pct Sb and Pb-2.2 wt pct Sb, were selected to achieve varying degrees of thermosolutal convection in the mushy zone. The dendritic array for the Pb-5.8 wt pct Sb alloy is expected to be more permeable than that for the Pb-2.2 wt pct Sb for similar growth conditions, because of its larger interdendritic liquid fraction (the interdendritic eutectic volume fraction is approximately 0.38 for the Pb-5.8 wt pct Sb, vs 0.09 for the Pb-2.2 wt pct Sb). Therefore, the 5.8 wt pct Sb alloy would be subject to more interdendritic convection
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