International audienceA three-dimensional (3-D) model for the prediction of dendritic grain structures formed during solidification is presented. This model is built on the basis of a 3-D cellular automaton (CA) algorithm. The simulation domain is subdivided into a regular lattice of cubic cells. Using physically based rules for the simulation of nucleation and growth phenomena, a state index associated with each cell is switched from zero (liquid state) to a positive value (mushy and solid state) as solidification proceeds. Because these physical phenomena are related to the temperature field, the cell grid is superimposed to a coarser finite element (FE) mesh used for the solution of the heat flow equation. Two coupling modes between the microscopic CA and macroscopic FE calculations have been designed. In a so-called “weak” coupling mode, the temperature of each cell is simply interpolated from the temperature of the FE nodes using a unique solidification path at the macroscopic scale. In a “full” coupling mode, the enthalpy field is also interpolated from the FE nodes to the CA cells and a fraction of solid increment is computed for each mushy cell using a truncated Scheil microsegregation model. These fractions of solid increments are then fed back to the FE nodes in order to update the new temperature field, thus accounting for a more realistic release of the latent heat (i.e., the solidification path is no longer unique). Special dynamic allocation techniques have been designed in order to minimize the computation costs and memory size associated with a very large number of cells (typically 107 to 108). The potentiality of the CAFE model is demonstrated through the predictions of typical grain structures formed during the investment casting and continuous casting processes

This article is based on a presentation made at the “Analysis and Modeling of Solidification” symposium as part of the 1994 Fall meeting of TMS in Rosemont, Illinois, October 2–6, 1994, under the auspices of the TMS Solidification Committee.International audienceGrain structure formation during solidification can be simulatedvia 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 code3- 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

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