An integrated model for dendritic and planar interface growth and morphological transition in rapid solidification
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I. INTRODUCTION
THERMAL spray deposition and melt spinning are important rapid solidification processes, in which thin layers of molten material are brought in contact with colder substrates. Because of small thickness and good thermal contact between the melt and the substrate, a large rate of melt cooling is achieved, leading to significant melt undercooling before solidification. In most cases, crystals are nucleated heterogeneously on the substrate surface, which is followed by columnar growth. Several heat-transfer and solidification models have been developed to simulate such solidification processes.[1,2] These studies have considered pure metals and have incorporated nonequilibrium crystalline growth kinetics into a heat-transfer model to study the effect of process conditions on rapid solidification characteristics. A planar solid/liquid interface is generally assumed. Recently, numerical models that can solve simultaneously the heat and mass diffusion equations with a planar interface subject to nonequilibrium crystalline growth kinetics of alloys have also been developed.[3–6] Several attempts have also been made to model the rapid dendritic solidification in spray deposition and melt spinning,[7,8,9] an important issue there being the treatment of the dendrite tip conditions. Flood and Hunt[7] are probably the first to treat the tip movement using a predetermined relationship between the tip velocity and melt undercooling based on the dendrite model of Burden and Hunt.[10] Because G.-X. WANG, formerly Senior Research Scientist, Center for Thermal Spray Research and Process Modeling Laboratory, State University of New York at Stony Brook, is Assistant Professor, Department of Mechanical Engineering, The University of Akron, Akron, OH 44325-3903. V. PRASAD, Professor, and S. SAMPATH, Associate Professor, are with the Center for Thermal Spray Research and Process Modeling Laboratory, State University of New York at Stony Brook, Stony Brook, NY 11794-2300. Manuscript submitted September 1, 1998.
METALLURGICAL AND MATERIALS TRANSACTIONS A
Burden and Hunt’s model is valid only for small undercooling and low growth velocity, more advanced dendrite growth models were proposed later.[8,9] They employ the velocitytemperature relationship obtained from more sophisticated dendrite growth models such as the Kurz, Giovanola, and Trivedi (KGT) model[11] for constrained dendritic growth and the Lipton, Kurz, and Trivedi (LKT) model[12] for free dendrite growth. It should be noted that both KGT and LKT models are derived based on the assumptions of steady-state dendrite growth and idealized thermal conditions. In the KGT model, a constant thermal gradient is assumed across the tip/melt interface. The LKT model, on the other hand, treats an isolated dendrite growing into an undercooled melt with a zero solid temperature gradient and all of the latent heat transferred to the melt. In melt quenching such as thermal spray and melt spinning, however, thermal conditions continuously change during the solidification. A larg
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