Prediction of grain structures in various solidification processes

Grain structure formation during solidification can be simulated via the use of stochastic models providing the physical mechanisms of nucleation and dendrite growth are accounted for. With this goal in mind, a physically based cellular automaton (CA) model has been coupled with finite element (FE) heat flow computations and implemented into the code 3-MOS. The CA enmeshment of the solidifying domain with small square cells is first generated automatically from the FE mesh. Within each time-step, the variation of enthalpy at each node of the FE mesh is calculated using an implicit scheme and a Newton-type linearization method. After interpolation of the explicit temperature and of the enthalpy variation at the cell location, the nucleation and growth of grains are simulated using the CA algorithm. This algorithm accounts for the heterogeneous nucleation in the bulk and at the surface of the ingot, for the growth and preferential growth directions of the dendrites, and for microsegregation. The variations of volume fraction of solid at the cell location are then summed up at the FE nodes in order to find the new temperatures. This CAFE model, which allows the prediction and the visualization of grain structures during and after solidification, is applied to various solidification processes: the investment casting of turbine blades, the continuous casting of rods, and the laser remelting or welding of plates. Because the CAFE model is yet two-dimensional (2-D), the simulation results are compared in a qualitative way with experimental findings.