Cellular Automaton Finite Difference Modeling of Morphological Evolution during Alloy Solidification

"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 predict the development of solidification structures within real components of complex geometry, where significant constraint of the thermal and solutal fields may exist. Such cases present complex boundaries and large domain sizes, which may preclude the effective use of more conventional methods. In this work, a model is presented which couples a two-dimensional alternate-direction-implicit finite-difference diffusion solution with a cellular automaton growth algorithm to simulate morphological evolution in alloys solidifying under directional growth conditions. Temperature, composition, and interface curvature are incorporated into a local growth potential which is used by the automaton, allowing the interface to evolve. Alloy solidification is simulated over a range of experimental conditions, producing various structures. Issues addressed include morphological instability, primary spacing selection, interface curvature, microsegregation, and tip conditions.IntroductionThe development of dendritic structure plays an essential role in alloy solidification. Virtually every microstructural feature, within a cast alloy component, is related to the interface morphology present during solidification. Conventional solidification theory, describing dendrite tip kinetics and mushy zone phenomena, provides a means for estimating overall microstructural parameters for an alloy solidified under steady-state conditions. Microstructural prediction for actual components, which are finite in size and complex in geometry, requires a description of the evolution of the interface morphology under transient conditions and geometrical constraint and an understanding of how the structure propagates through the mold. Any useful simulation tool must be equipped to handle these circumstances within the limits of computational feasibility."