A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification
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7/8/03
10:03 PM
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A Solutal Interaction Mechanism for the Columnarto-Equiaxed Transition in Alloy Solidification M.A. MARTORANO, C. BECKERMANN, and Ch.-A. GANDIN A multiphase/multiscale model is used to predict the columnar-to-equiaxed transition (CET) during solidification of binary alloys. The model consists of averaged energy and species conservation equations, coupled with nucleation and growth laws for dendritic structures. A new mechanism for the CET is proposed based on solutal interactions between the equiaxed grains and the advancing columnar front— as opposed to the commonly used mechanical blocking criterion. The resulting differences in the CET prediction are demonstrated for cases where a steady state can be assumed, and a revised isotherm velocity (VT) vs temperature gradient (G) map for the CET is presented. The model is validated by predicting the CET in previously performed unsteady, unidirectional solidification experiments involving Al-Si alloys of three different compositions. Good agreement is obtained between measured and predicted cooling curves. A parametric study is performed to investigate the dependence of the CET position on the nucleation undercooling and the density of nuclei in the equiaxed zone. Nucleation undercoolings are determined that provide the best agreement between measured and calculated CET positions. It is found that for all three alloy compositions, the nucleation undercoolings are very close to the maximum columnar dendrite tip undercoolings, indicating that the origin of the equiaxed grains may not be heterogeneous nucleation, but rather a breakdown or fragmentation of the columnar dendrites.
I. INTRODUCTION
A CHANGE from an outer columnar to an inner equiaxed grain structure is a common occurrence in metal alloy castings, and numerous mechanisms for the columnar-to-equiaxed transition (CET) have been proposed based on experimental evidence.[1] Mathematical modeling of the CET during alloy solidification, however, has had limited success owing to the complex interplay of macroscopic phenomena, such as heat transfer and fluid flow, and microscopic phenomena, such as nucleation and dendritic growth. All previous CET models, as well as the present study, neglect or oversimplify the treatment of melt convection and movement of free equiaxed grains. Usually, equiaxed grains are assumed to nucleate and grow in the constitutionally undercooled liquid ahead of the advancing columnar front, as originally proposed by Winegard and Chalmers.[2] The CET occurs when the advance of the columnar front is blocked by the equiaxed grains. The CET models can be classified as stochastic or deterministic. Stochastic models aim to follow the nucleation and growth of each individual grain.[3,4,5] No assumptions are made regarding the grain morphology. The evolution of the shape of the envelope of each grain is computed as a function of the local thermal environment. The CET may then be determined based on whether the average final grain shape in a portion of a casting appears mor
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