Part IX - Papers - Macrosegregation: Part I

General expressions are given to describe macro-segregation in castings and ingots which results from mass flow of solute-rich liquid to feed solidification and thermal contractions. Analytical solutions are given for solidification with planar isotherms (unidirectional and bidirectional heat flow). These solutions describe inverse segregation and centerline segregation. Numerical examples are given for A1-4.5 pct Cu alloy. In 1540, Vannoccio Biringuccio published one of the first references to macrosegregation, describing the problem of exudation and inverse segregation in the manufacture of bronze gun barrels.' Since then, a great many studies of macrosegregation have been reported. Recent work of particular engineering interest includes that of Marburg 2 and others:" on centerline segregation and other types of segregation in large steel ingots, and work of Adams,5 Scheil, 6 and Kirkaldy and youdelis7 on inverse segregation in nonferrous ingots. In most studies on this subject, the various types of macrosegregation have been treated as separate phenomena. For example, quite different mechanisms have been proposed for formation of centerline segregation, negative cone of segregation, inverse segregation, banding, and so forth. In this, and in several papers to follow, it is proposed that these as well as other types of macrosegregation result from the same basic mechanism and can be quantitatively described by the same basic equation. It has often been suggested that some types of segregation (such as centerline segregation and banding) occur as a result of buildup of solute at the tips of growing dendrites.2-4 ,8-10 As example, banding can be induced in centrifugal castings by mechanical vibration, and Northcott 10 suggests this might be due to the influence of the vibration on the boundary layer at the dendrite tips of the growing dendrites. However, in view of the extremely small boundary layer known to exist at the tips of the dendrites,11,12 any interpretation of macrosegregation based on this boundary layer is clearly incorrect. Note that experiment has shown that significant buildup of solute does not occur at dendrite tips in ingot solidification, but even if such buildup occurred the thickness of the enriched zone would only be the order of D/U where D is liquid diffusion coefficient and U is dendrite tip velocity. For usual casting or ingot solidification this solute-enriched layer is 10"3 cm, far too small to account, for example, for centerline segregation.11'12 It has also been suggested that convection in the bulk liquid (ahead of the advancing dendrites) might cause segregation by sweeping away the solute-rich boundary layer in front of the dendrites.3 However, since there is no significant boundary layer, this explanation must be incorrect. The convection might directly cause segregation by penetrating between the dendrite arms, and presumably in a rimming steel ingot it is sufficiently vigorous to cause some segregation in this way. Centerline segregation, however, cannot be interpreted as resulting from this convection since a sharply segregated zone is usually found near the centerline, with the bulk of the ingot being nearly of nominal composition. If convection in the bulk liquid were the direct cause, a gradual change in ingot composition over the entire cross section would be expected. It is known that sudden changes in convection of the bulk liquid during solidification can result in banding,14 but it is not clear that the banding results directly from the effect of convection on solute distribution. Changes in convection also affect thermal conditions in the liquid-solid region of a solidifying ingot. It will be seen later in this paper, and in a paper to follow, that macrosegregation is strongly influenced by these thermal changes. Recognizing that in some cases of ingot solidification (as in solidification of rimming steels) convection in the bulk liquid may have a direct effect on solute distribution, we neglect it in this paper and in the several to follow. We then derive general expressions describing macrosegregation which results from the mechanism of interdendritic flow of solute-rich liquid