Prediction of Columnar to Equiaxed Transition during Diffusion-Controlled Dendritic Alloy Solidification
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INTRODUCTION
CASTINGS of metallic alloys may exhibit either wholly columnar or entirely equiaxed grain structures, depending on the alloy composition and the solidification conditions. Another more complex structure, which is often observed in chill castings, is composed of both kinds of grains. This mixed mode of solidification occurs if equiaxed grains can nucleate and grow in the bulk liquid ahead of the advancing columnar front, resulting in a transition from a columnar zone to a central equiaxed zone in some as-cast structures. [~,2,3] The prediction of the columnar to equiaxed transition (CET) is of great interest for the evaluation and design of the mechanical properties of solidified products. To this aim, it is necessary to understand the CET mechanisms and to develop a model to quantify important features of the composite structure, such as the relative size of the two zones. As suggested by many previous studies, the CET, caused by the competition between columnar and equiaxed growth, is primarily governed by such casting parameters as the alloy composition, pouring superheat, nuclei density present in the melt, cooling capacity at the metal/mold interface, and melt convection. Qualitatively, it can be anticipated than the CET occurs earlier when an alloy has a higher solute level, lower pouring temperature, smaller thermal gradient, higher nuclei density present in the melt, and more vigorous melt convection. However, quantitative predictions of the CET require a more thorough understanding and a full account of all physical mechanisms involved. For small specimens of almost uniform temperature, experimental observations indicate that nucleation and growth of the equiaxed grains ahead of the columnar front are the most important mechanisms for causing the CET. t41 For sizable castings, the temperature field significantly affects the competitive columnar and equiaxed solidification, since columnar growth is constrained by the C.Y. WANG, Graduate Student and Research Assistant, and C. BECKERMANN, Associate Professor, are with the Department of Mechanical Engineering, University of Iowa, Iowa City, IA 52242. Manuscript submitted March 12, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
movement of the isotherms, and equiaxed growth ahead of the columnar front in turn alters the temperature field through the release of latent heat. The complications of these multiple mechanisms have hindered the mathematical modeling of the CET phenomenon. Only recently have efforts been made to theoretically model the CET. Hunt t51first developed an analytical model by considering steady-state columnar and equiaxed growth. The model qualitatively reveals the influences of alloy composition, nuclei density, and cooling rate on the CET. Subsequently, Flood and Hunt t6,71extended the work to model dynamically the CET in a one-dimensional (l-D) ingot. They incorporated grain nucleation and growth principles into a heat-flow calculation, and simulated the CET as a Stefan-like discontinuity interface. Although their work
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