Modelling of Microsegregation

Abstract

A numerical model has been developed for the quantitative prediction of microsegregation during solidification of ternary alloys. Due to the computational efficiency of the algorithm, this model can be incorporated into macrosegregation calculations performed at the scale of a whole casting. Solidification and possible remelting are calculated for an open system, i.e., for a small volume element whose average solute contents are not necessarily constant during the casting. Assuming uniform temperature in this small volume element, the variations of average enthalpy and solute contents are assumed to be known functions of time resulting from the average continuity equations solved at the macroscopic scale. This microsegregation model developed for globulitic grain structures considers the diffusion of the solute elements in one dimension with a front-tracking procedure for the primary solid-liquid interface. Solute back-diffusion in the primary phase occurring during the various stages of solidification (primary, eutectic valley and ternary eutectic solidification) are taken into account through an implicit finite difference formulation with a Landau transformation for the mapping of the variable solid comain onto a fixed [0,1] interval. Complete solute mixing in the liquid is assumed and the solid phases different from the primary phase are supposed to be stoechiometric and the most stable. This model also allows the consideration of different specific masses for the liquid and solid, temperature-dependent solute diffusivities in the primary phase and non-linear phase diagram. A coupling with phase diagram calculations obtained ith the Thermo-Cale software [1] has been performed through mapping files. At each microscopic time step, liquidus slopes and partition coefficients of each involved phase are bilinearly interpolated from this file, resulting in an accurate and efficient microsegregation calculation. This model is applied to the case of an Al-Mg-Si alloy. From the enthalpy and average solute content evolutions, it allows to obtain the calculated concentration profiles of the solute elements and the solidification path of the alloy, including the formation of the primary phase, the solidification along a monovariant line and the precipitation of ternary eutectic. The new liquid concentrations, the new temperature, the new average specific mass and the new fraction of each phase calculated by the present model are the input of the next macrosegregation calculation step. Homogenisation treatment of low-concentration alloys can also be predicted by mapping the solvus surfaces of the phase diagram in a similar way. This approach can be extended to more complex alloy systems but direct access to Thermo-Cale [1] should be made in order to avoid too large mapping files.