Solidification of a ternary metal alloy: A comparison of experimental measurements and model predictions in a Pb-Sb-Sn s
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INTRODUCTION
THE macroscopic maldistribution of alloy constituents during solidification, commonly called macrosegregation, is a defect that occurs in real metal processing systems. This nonuniformity of species distribution, especially when it forms a high composition gradient, can lead to areas of high stress concentration, which contribute to cracking during extrusion or forging of wrought alloys or when an as-cast piece is severely loaded in service.[1,2] Macrosegregation studies in binary systems have become quite common since the introduction of single-domain numerical models, which feature one set of conservation equations and boundary conditions for an entire, fixed computational domain containing solid, liquid, and multiphase regions. These models have been successfully used to predict general macrosegregation and flow patterns in several binary alloys. A complete review has been presented by Prescott and Incropera.[3] Most applications of these models have involved the solidification of binary alloys. While the study of binary mixtures is an obvious starting place, where one can examine a simple, well-defined system and more easily discern the basic transport phenomena involved in alloy casting, most commercial alloys contain more than two components. Frequently, these alloys have amounts of two or more solutes significant enough to affect the convective flows that lead to macrosegregation and other defects. The formation of secondary and tertiary solid phases, including eutectic and peritectic reactions, also may occur in comMATTHEW JOHN M. KRANE, formerly Graduate Research Assistant, School of Mechanical Engineering, is Assistant Professor, School of Materials Engineering, Purdue University. FRANK P. INCROPERA, Professor and Head, School of Mechanical Engineering, and DAVID R. GASKELL, Professor, School of Materials Engineering, are with Purdue University, West Lafayette, IN 47907. Manuscript submitted May 1, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
mercial metal alloys and should be treated using appropriate thermodynamic models. The first analytical study of macrosegregation during the solidification of a multicomponent alloy was conducted by Mehrabian and Flemings.[4] Their analysis developed a three-component Scheil formulation for the partition of the components and invoked several simplifying assumptions, including modeling freezing only on the primary liquidus surface and along the binary eutectic troughs, ignoring the effect of solidification at the invariant points. The authors analyzed the effects of the initial composition and distance from the chilled surface on the formation of intermetallic compounds and primary phases of aluminum-rich Al-CuNi systems. Picking initial concentrations in the Al-rich corner, on or near the twofold saturation line between primary Al and NiAl3 regions, the authors calculated negative and positive segregation near the chilled surface for Ni and Cu, respectively. Because the melt is stably stratified, the system was dominated by solidification shrinkage
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