Computation of solidification paths in multiphase alloys with back-diffusion

Mathematical modeling of microsegregation in multicomponent alloys is a considerable challenge since solidification implies generally the formation of many different solid phases, each one changing the dynamics of phase transformation as the morphology becomes very complex and the kinetics phenomena more diverse. Before sophisticated models based on the resolution of partial differential mass conservation equations can give reliable predictions in multiphase alloys, there is a need to calculate solidification paths based on the incremental mass conservation equation and the back-diffusion parameters. The incremental mass balance proposed in this contribution was written without considering a specific migration mechanism. This decoupling allowed an easy integration of a microsegregation model enabling the evaluation of back-diffusion parameters. In this paper, Ohnaka’s microsegregation model was chosen because it allows a simple and elegant inclusion of the cross interdiffusion coefficients in the calculation of back-diffusion parameters. The model assumes that complete mixing prevails in the liquid phase and that equilibrium conditions can be applied for a sub-system having a composition defined according to the mobility of species and a set of empirical parameters. A large range of solidification paths lying between Scheil and global equilibrium conditions can be calculated and used to explain experimental observations. The model was applied on a ternary Al–Mg–Mn alloy for comparison purposes, with the software DICTRA. An excellent agreement between the two models was obtained using similar assumptions. The scheme was also applied on AA6111 and allowed us to understand large deviations observed between the amounts of secondary phases obtained with DSC experiments and those predicted by Scheil or equilibrium conditions.