Modeling of micro- and macrosegregation and freckle formation in single-crystal nickel-base superalloy directional solid
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I.
INTRODUCTION
THE formation of freckles (or channel segregates) and macrosegregation in directional solidification of Ni-base superalloys has been the subject of numerous studies since the pioneering work of Giamei and Kear.[1] Copley et al.[2] suggested a criterion for freckle formation in steady columz nar growth that is based on a critical cooling rate, T (i.e., the product of imposed casting speed, R, and temperature gradient, G), below which freckles are likely to form (if G is below a certain critical value). Experiments on transparent model alloys and binary metallic alloys have shown that freckles are initiated by convective instabilities above or in the mushy zone (for example, References 3 through 5). Instabilities can develop in a positive thermal gradient when the segregated interdendritic liquid is less dense than the overlying bulk liquid of original composition. In the unstable mode, low-density liquid emanates from the mushy zone in the form of solutal plumes, or fingers, which are fed by flow of segregated liquid through the surrounding mush. This flow causes delayed growth and even remelting of dendrites, leading to the formation of a narrow, open channel in the mushy zone below each plume. The channel thus provides a self-sustaining path for feeding the plume. The channels eventually freeze and appear as chains of equiaxed grains (i.e., freckles) in the solidified superalloy. In the 1990s, there has been renewed interest in the ability to predict the formation of freckles and other defects in single-crystal, investment-cast Ni-base superalloys.[6–11] For example, in the most recent study by Pollock and MurM.C. SCHNEIDER, formerly Graduate Research Assistant, Department of Mechanical Engineering, University of Iowa, is with Software Development, Magma GmbH, Aachen, Germany, 52072. J.P. GU, Postdoctoral Researcher, and C. BECKERMANN, Professor, are with the Department of Mechanical Engineering, The University of Iowa, Iowa City, IA 52242-1527. W.J. BOETTINGER and U.R. KATTNER, Metallurgists, are with the Metallurgy Division, NIST, Gaithersburg, MD 20899. Manuscript submitted October 28, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A
phy,[11] detailed experiments were performed that indicate a strong correlation between the primary dendrite arm spacing and freckle formation for various SX alloys. For one alloy, the critical primary dendrite arm spacing was found to be 320 mm. The primary dendrite arm spacing, in turn, correlates well with the cooling rate (as subsequently discussed), thus confirming the criterion by Copley et al.[2] Another relationship, where l1 is proportional to G21/2 3 R21/4, produced a similar or slightly better criterion for freckle formation.[11] It was noted that accurate predictions using numerical models are still not possible, primarily due to the complex thermosolutal convection patterns. Clearly, such modeling requires an understanding of the complicated solute partitioning behavior during solidification of superalloys and its effect on liquid density, as well as
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