Prediction of grain structures in various solidification processes
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I.
INTRODUCTION
THE grain structure of as-cast components is one of the important features that a metallurgist has to control. As an example, Figure 1 shows the grain structure of a gas turbine blade which has been solidified under directional heat flow conditions. This nickel-base superalloy starts to solidify at the contact with the copper chill under the form of very fine grains (bottom of the blade). From this "outerequiaxed zone,"t~,2Jthe grains which have one of their (100} crystallographic orientations best aligned with the heat flow direction (vertical direction in this case) grow preferentially at the expense of less favorably oriented grains. This mechanism of grain selection is due to the {100) preferential growth of dendrites which compose the grains? .2] Accordingly, as the columnar grains grow upward, their density in a transverse section decreases. This grain selection mechanism, which has been known for several decades, is currently used in industry to produce single-crystal turbine blades;t3.71 in this case, a specially designed narrow channel inserted between the chill surface and the bottom of the blade allows only one grain to emerge at the top of this "selector." Once the thermal gradient in the remaining liquid becomes small, equiaxed grains can nucleate and grow at the expense of columnar grains, thus leading to the socalled "columnar-to-equiaxed" transition (CET). Such a transition is clearly visible in Figure 1. M. RAPPAZ, Professor, Ch.-A. GANDIN, Postdoctoral Fellow, and J.-L. DESBIOLLES, Staff Member, are with the Laboratoire de Metallurgie Physique, D~partement des Matrriaux, Ecole Polytec,hnique Frdrrale de Lausanne, CH-1015 Lausanne, Switzerland. Ph. THEVOZ, Executive Director, is with Calcom SA, PSE, CH-1015 Lausanne, Switzerland. This article is based on a presentation made at the "Analysis and Modeling of Solidification" symposium as part of the 1994 Fall meeting of TMS in Rosemont, Illinois, October 2-6, 1994, under the auspices of the TMS Solidification Committee. METALLURGICALAND MATERIALSTRANSACTIONSA
The formation and competition of grains during solidification can be studied using different techniques. Metallographic inspection of cast parts such as the one shown in Figure 1 is certainly instructive but does not bring much insight into the mechanisms that lead to such structures. In situ microscopy observation of the solidification of transparent organic alloys without doubt has been a major source of information.[4,5,61With the advent of powerful computers and sophisticated numerical techniques, physical models which integrate nucleation and growth mechanisms have been developed for the simulation of grain structure formation. At first, analytical models similar to the wellknown Avrami transformation law were developed for equiaxed grain structures. These so-called deterministic models, which have been reviewed in Reference 8, suffer from several limitations: they are based on average entities, they do not provide any view of the mierostructure, they do not consider prefe
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