Development of a freckle predictor via rayleigh number method for single-crystal nickel-base superalloy castings
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I. INTRODUCTION
FRECKLES (or channel segregates) have been the subject of intense research efforts for about 30 years,[1,2] due to their importance as a defect in alloy casting and the interesting fluid-mechanical phenomena associated with their formation.[3] Freckles are chains of small equiaxed grains in an alloy otherwise solidified with a columnar structure. In particular, in directionally solidified single-crystal superalloy parts, freckles are generally a cause of rejection. Solidification experiments with transparent model alloys and binary metallic alloys have shown that freckles are initiated by convective instabilities in the high-liquid-fraction region of the mushy zone near the primary dendrite tips (for a review, refer to Hellawell et al.).[4] During upward directional solidification into a positive temperature gradient, the melt inside the mushy zone can become gravitationally unstable due to chemical segregation of alloy elements at the scale of the dendrite arms. Such microsegregation can cause the local melt density to decrease during solidification if light alloy elements are preferentially rejected into the melt (for a partition coefficient less than unity) or if heavy alloy elements are preferentially incorporated into the solid C. BECKERMANN, Professor, is with the Department of Mechanical Engineering, The University of Iowa, Iowa City, IA 52242-1527. J.P. GU, formerly Postdoctoral Researcher, Department of Mechanical Engineering, The University of Iowa, is Engineer with PCC Structurals Inc., Portland, OR 97206-0898. W.J. BOETTINGER, Metallurgist, is with the Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. Manuscript submitted January 25, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
(for a partition coefficient greater than unity). If the melt overcomes the retarding frictional force in the porousmedium-like mushy zone, convection cells form. Since the mass diffusivity of the liquid is much lower than its heat diffusivity, the segregated melt retains its composition as it flows upward through the mush into regions of higher temperature. There, the melt causes delayed growth and localized remelting of solid, such that pencil-shaped channels, devoid of solid, form in the mushy zone. Low-density, highly segregated liquid emanates from the channels as solutal plumes or fingers flowing upward into the superheated liquid. Hence, the channels provide self-sustaining paths for feeding the plumes. At the lateral boundary of the channels, higher-order dendrite arms can become detached from the main trunk, most likely by a local remelting process. These dendrite fragments either (1) remain in the channels and grow into the equiaxed grains later observed as freckle chains or (2) are advected out of the channels by the flow and, if not remelted completely, may form spurious grains inside the columnar structure or even cause a columnar-to-equiaxed transition.[1,4–6] Clearly, the onset of freckling depends on the complicated interplay of the stabilizing therm
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