Modeling of Macrosegregation and Solidification Grain Structures with a Coupled Cellular Automaton-Finite Element Model

Abstract

A coupled Cellular Automaton (CA)-Finite Element (FE) model is presented for the prediction of solidification grain structures coupled with the calculation of solid and liquid flow induced macrosegregation. The model is applied to simulate the solidification of a Pb-48wt%Sn alloy in a rectangular cavity cooled down from only one of its vertical boundaries. The algorithm and the numerical implementation of the coupling between the CA and FE methods are first validated by considering a single grain developing with no undercooling. Such a CAFE simulation is shown to retrieve the solution of a purely FE method simulation for which the grain structure is not accounted for. Several applications of the model are then presented to quantify the effects of the grain structure on the final macrosegregation map. In particular, the effect of the undercooling of the columnar front, the presence of equiaxed grains nucleated in the undercooled liquid, as well as the transport and sedimentation of equiaxed grains are investigated. Although good validation is reached when comparing computed and measured segregation profiles available in the literature for the chosen configuration, it is concluded that refined experimental data are required to further validate the predictions of a coupled CAFE model.

Methodological Progress for Computer Simulation of Solidification and Casting

“…The movement of the solid phase (for example, the transport and sedimentation of equiaxed grains) generates a movement of the liquid phase and the transport of all quantities that needs to be accounted for at the scales of the CA cell and the FE mesh. The model is applied to simulate the solidification of a Pb-48mass%Sn alloy 34,36) and a Ga-5mass%In binary alloy.…”

“…57,58) When the local undercooling is regarded only as the contribution of solutal undercooling, the growth kinetics is described by the KGT 59) or the LKT model. 60) Recently, the GGAN model 33,34) was developed by considering the contributions of solutal and curvature undercooling in the presence of fluid flow. It can calculate just a dendrite tip growth velocity as a function of both the intensity and the orientation of the fluid flow with respect to the dendrite growth direction.…”

“…It assumes an abrupt burst of nucleation as soon as a critical undercooling is reached. 32,[34][35][36] Another one is the continuous nucleation model which assumes a continuous temperature dependence of the nucleation density. Since several families of nucleation sites, all characterized by different critical undercoolings, usually coexist in the melt, this seems to be more realistic.…”

“…with combinations of the probabilistic and the deterministic approaches. Firstly, Gandin et al [29][30][31][32][33][34][35][36] developed mesoscopic-scale CA (in the order mm to cm), which can model the columar-to-equiaxed transition (CET) as well as the grain structure by solving each individual grain growth. This is done through a coupling with macroscopic heat and solute transport equations (deterministic approach).…”

“…Even in the presence of fluid flow, where each dendrite tip growth velocity is different due to both the effects of the intensity and the orientation of the fluid flow with respect to the dendrite growth direction, it results in the "irregular decentredquadrilateral" growth algorithm for a 2D case. [34][35][36]61) Recently, using the third algorithm, Gandin et al proposed the coupled Cellular Automaton-Finite Element (CA-FE) model, for the prediction of the interaction between the formation of the grain structure and the macrosegregation. This was additionally coupled with the calculation of a solid and liquid flow induced macrosegregation.…”