Cellular Automaton Model for Quantitative Prediction of Microsegregation in Alloys

Microsegregation in alloys has a significant effect on the steel properties. Numerical simulations using cellular automaton (CA) models are often used to predict microsegregation behavior. However, the CA model has problems quantitatively predicting the microsegregation behavior owing to the inaccuracy of the calculation of the interface curvature. In this study, we developed a two-dimensional quantitative CA model that incorporates interface curvature calculations using the height function (HF) method, correction of mass-balance errors, and solid–liquid interface movements caused by solidification and melting. In a simple calculation of the curvature of circles using the HF method, we confirmed that the HF method could calculate the curvatures of circles of various radii with an error of less than 1%. In addition, we performed simulations of the unidirectional solidification of a single dendrite of an Fe–C alloy using two CA models that implemented curvature calculation models using the conventional and HF methods, and investigated the effects of both models on dendrite morphology. The development of secondary dendrite arms was observed only in the CA model that implemented the HF method, thereby confirming the effect of the curvature calculation on dendrite morphology. Finally, we performed simulations of the multidendrite growth of an Fe–C alloy under continuous cooling at different cooling rates using the CA model that implemented the HF method. Consequently, the solute concentration in the solid exhibited an appropriate distribution following the lever rule, and the microsegregation behavior based on the cooling rate was reasonably simulated.