J.-L. Desbiolles

Modeling of equiaxed microstructure formation in casting

A general micro/macroscopic model of solidification for 2-D or 3-D castings, valid for both dendritic and eutectic equiaxed alloys, is presented. At the macroscopic level, the heat diffusion equation is solved with an enthalpy formulation using a standard FEM implicit scheme. However, instead of using a unique relationship between temperature and enthalpy (i.e., a unique solidification path), the specific heat and latent heat contributions, whose sum equals the variation of enthalpy at a given node, are calculated using a microscopic model of solidification. This model takes into account nucleation of new grains within the undercooled melt, the kinetics of the dendrite tips or of the eutectic front, and a solute balance at the scale of the grain in the case of dendritic alloys. The coupling between macroscopic and microscopic aspects is carried out using two time-steps, one at the macroscopic level for the implicit calculation of heat flow, and the other, much finer, for the microscopic calculations of nucleation and growth. This micro/macroscopic approach has been applied to one-dimensional and axisymmetric castings of Al-7 pct Si alloys. The calculated recalescences and grain sizes are compared with values measured for one-dimensional ingots cast under well-controlled conditions. Furthermore, the influence of casting conditions on temperature field, undercooling, grain size, and microstructural spacings is shown to be predicted correctly from axisymmetric calculations with regard to the expected experimental behavior.

Prediction of grain structures in various solidification processes

Grain 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.

Modeling of percolation of globular-equiaxed grains in Al-Cu alloys

A new mesoscopic model able to describe percolation of globular-equiaxed grains, highly relevant for hot tearing formation in castings, has been developed. This model is inspired from the granular model of Sistaninia et al. [1-5] that considers polyhedral grains based on a Voronoi tessellation of space. In the new mesoscopic model, the set of tetrahedra that define the grains are further subdivided into smaller tetrahedra called columns and solute diffusion is considered in both the solid and liquid phases. This allows to obtain smoother shapes of the grains and to better describe a progressive coalescence of the grains. In addition, it gives the possibility of having liquid pockets in the last-stage solidification (which is not possible in the case of polyhedral grains) and thus correctly describe the solid fraction at which the grain structure is percolated. The shape of the grains has first been validated with a multiphase-field method. The relevant microstructural features, such as the percolation state of an Al-Cu alloy, were then deduced from the model. This information will then be used to refine the 3D granular models of Sistaninia et al. [1-5] which account for stress development and liquid feeding, in order to create more advanced predictive tools for hot tearing formation.