A two-dimensional model for the description of the columnar-to-equiaxed transition in competing gray and white iron eute
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I. INTRODUCTION
IT is well known that one of the most important types of casting alloys, cast iron, can solidify in two different forms: gray or white iron. After solidification (before solidstate transformations occur), gray iron is a eutectic microstructure composed of g-iron (austenite) and graphite, which are the phases at thermodynamic equilibrium. White iron is a metastable eutectic structure consisting of austenite and Fe3C. Due to differences in growth kinetics, gray iron forms at low cooling rates, whereas white iron is favored by fast cooling conditions. The iron carbon phase diagram illustrated in Figure 1 and the kinetics diagram of Figure 2 illustrate the difference in thermodynamic equilibrium and growth kinetics of the two eutectic structures. Depending on solidification conditions, the gray and white iron eutectics can exhibit either a fully columnar morphology (i.e., grown directionally from the walls of the mold) or an entirely equiaxed structure, consisting of grains randomly nucleated in the bulk. More often, both morphologies form in the casting, resulting in a transition from an outer columnar zone to a central equiaxed region. Since the physical properties of white and gray iron are very different, being able to predict the microstructure as a A. JACOT, Senior Scientist, is with Research and Development, Calcom S.A., Parc Scientifique, CH-1015 Lausanne, Switzerland. D. MAIJER, Research Associate, and S.L. COCKCROFT, Associate Professor, are with the Department of Metals and Materials Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4. Manuscript submitted May 7, 1999.
METALLURGICAL AND MATERIALS TRANSACTIONS A
function of the casting conditions is of considerable practical interest. However, predicting the proportion of white and gray iron for a wide range of cooling conditions is a complex task. First, it requires an accurate description of the nucleation and growth phenomena of the two types of eutectic. Second, the model must account for the competition that occurs between the columnar and equiaxed morphologies and correctly predict the location of the possible transition. Finally, the microstructural model has to be coupled with a macroscopic heat-flow calculation in order to predict the microstructural distribution at the scale of the casting. Models describing the solidification of white and gray iron have been proposed by several authors.[2–8] The approach generally taken[2,5–8] consists of coupling a finite-difference or a finite-element (FE) method, which provides a solution of the heat-diffusion problem, with a microscopic deterministic model describing the equiaxed solidification of cast iron. Although these models correctly predict the proportions of white and gray iron in the cases presented, they are restricted to situations where the grain structure is entirely equiaxed. The columnar-to-equiaxed transition (CET) has been modeled in one-,[9,10] two-[11–14] and three-[15] dimensional problems. Some CET models[9] are based on the assumption of a steady-s
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