CELLULAR-AUTOMATON MODELING OF MORPHOLOGICAL EVOLUTION DURING ALLOY SOLIDIFICATION.
Ralph. E. Napolitano, Jr., Georgia Institute of Technology, Atlanta, Georgia;
(currently of Metallurgy Division, NIST).
Morphological evolution of a dendritic growth front in a binary alloy is simulated using a cellular automaton approach to establish the feasibility of modeling such growth with a local rule-based scheme. The motivation for this work is derived from the need to understand and predict the development of solidification structures within components of complex geometry, where significant constraint of the thermal and solutal fields may exist. In these cases, local transients and anomalies may preclude the effective use of more conventional methods of microstructural prediction. The model utilizes a two-dimensional alternate-direction-implicit finite-difference technique for calculation of the solute field. A uniform temperature gradient and a constant isotherm velocity are assumed, describing the conditions within a small representative volume element of a casting. Local temperature, composition, and interface curvature are incorporated into a growth function which is utilized by the automaton in a probabilistic fashion, allowing the interface to evolve. Alloy solidification is simulated over a range of experimental conditions, giving rise to planar, cellular, and dendritic growth, and comparisons with analytical solutions are made where possible. The model is shown to predict growth mode transitions, thermal and solutal interfacial conditions, and microsegregation. Finally, the model is applied to several cases where geometric constraint is significant. Despite several limitations which are identified, the potential usefulness of the approach is demonstrated.