Eutectic reaction and nonconstant material parameters in micro-macrosegregation modeling

Abstract

Recently, the authors presented a general framework for the calculation of the local solidification path in micro-macrosegregation computations (Reference 1). For a volume element whose overall solute content is not necessarily constant, the problems of solute diffusion in the primary solid phase and of remelting were addressed. In handling the eutectic reaction, the mass fraction and the solute profile in the primary phase at the beginning of the eutectic reaction were assumed to be “frozen.” In the present study, this restriction has been relaxed, as the solute diffusion in the primary phase occurring during the eutectic reaction is taken into account as well as that taking place for temperatures between the liquidus and the eutectic. It is shown that there is a potential for dissolving the secondary phase, which is controlled by diffusion in the primary phase. Other extensions of the former modeling concept made in the present study are to allow different densities of the liquid and solid phases, nonlinear phase diagram characteristics, and a temperature and/or solute concentration-dependent solute diffusivity in the primary phase. Assuming that the variations of enthalpy and of average solute concentration are known from the solution of the macroscopic continuity equations, modeling examples focusing on the extensions of the former model have been carried out.