Modelling of microsegregation in ternary alloys: Application to the solidification of Al-Mg-Si

Abstract

A fast numerical model has been developed for the quantitative prediction of microsegregation during solidification of ternary alloys. Considering a small volume of uniform temperature, the back-diffusion equations in the primary solid phase are solved in a 1-dimensional configuration using an implicit finite difference formulation with a Landau transformation onto a fixed [0,1] interval. The other phases which may precipitate during solidification are supposed to be stoichiometric and at equilibrium while the liquid is in a state of complete mixing. These calculations are coupled with phase diagram data through the use of mapping files: the liquidus surface, the monovariant lines and all the pertaining information are mapped through calls to Thermo-Calc, prior to starting the microsegregation calculation itself. This very efficient microsegregation model can thus be coupled directly to macrosegregation computations performed at the scale of a whole casting: from the average enthalpy and concentrations variations computed at each mesh point of a casting during one time step, this microsegregation model is capable of predicting the variations of temperature, of the volume fractions of the various phases, of the liquid concentrations and of the average density. The efficiency of this coupling between microsegregation calculation and thermodynamic mapping files is demonstrated in the particular case of the Al-Mg-Si system.