3-Dimensional simulation of the grain formation in investment castings

International audienceA 3-dimensional (3-D) probabilistic model which has been developed previously for the prediction of grain structure formation during solidification is applied to thin superalloy plates produced using the investment-casting process. This model considers the random nucleation and orientation of nuclei formed at the mold surface and in the bulk of the liquid, the growth kinetics of the dendrite tips, and the preferential growth directions of the dendrite trunks and arms. In the present study, the grains are assumed to nucleate at the surface of the mold only. The computed grain structures, as observed in 2-dimensional (2-D) sections made parallel to the mold surface, are compared with experimental micrographs. The grain densities are then deduced as a function of the distance from the mold surface for both the experiment and the simulation. It is shown that these values are in good agreement, thus, providing validation of the grain formation mechanisms built into the 3-D probabilistic model. Finally, this model is further extended to more complex geometries and the 3-D computed grain structure of an equiaxed turbine-blade airfoil is compared with the experimental transverse section micrograph

A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures

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