Simulation and Experimental Investigation of Grain Selection during Columnar Growth

"The grain selection mechanism which occurs during the growth of columnar dendritic structures is routinely used in the investment casting industry to produce directionally solidified (DS) and single crystal turbine blades. However, the evolution of the grain density with increasing distance from the chill has rarely been correlated with the evolution of the grain texture. This contribution presents a three-dimensional (3-D) stochastic modeling approach which permits the computation of grain maps, pole figures and grain density evolutions in DS superalloys. These predictions are compared with measurements resulting from an automatic indexing technique of Electron Back-Scattered diffraction Patterns. This 3-D stochastic model, which applies to uniform temperature situations, has to be extended to the dendritic growth in a thermal gradient. As a preliminary step, a 2-D Cellular Automaton (CA) has been coupled recently to Finite Element (FE) heat flow computations in order to predict the grain structures in complex shape investment cast part. The application of this CAFE model to the investment casting of a turbine blade is presented. Considering these results, the extension of the CAFE algorithm to three dimensions is discussed.INTRODUCTIONThe selection of columnar grains during the directional solidification of alloys plays a key role during the investment casting of directionally solidified (DS) and single crystal (SC) components for aerospace applications [I]. This selection mechanism, leading to a competition of the dendritic network propagation at grain boundaries, has been the subject of many investigations. In particular, the study of Walton and Chalmers [2] is remarkable since it provides a link between the evolutions of the density and of the texture of columnar grains with increasing distance from the mold wall. Since this original work of Walton and Chalmers, two new tools have become available, which enable one to revisit the problem of grain selection in much greater depth. The first one is a fully automatic indexing technique of Electron Back-Scattered diffraction Patterns (EBSPs) [3-6] which directly gives the crystallographic orientation of the solid at any location of the specimen. Pole figures, orientation distributions, misorientations between grains can be visualized very easily with this technique. This information can be directly compared with the results of a second tool: a three-dimensional (3-D) stochastic model (SM) describing the nucleation and growth of grains in a uniform temperature field [6-9]. In order to extend this model to non-uniform temperature situations, a preliminary 2-D model has been developed [10]. It is based on a Cellular Automaton (CA) algorithm coupled with Finite Element (FE) heat flow computations. Since the details of both the automatic indexing technique of EBSPs and the simulation tools have already been published [3-10], only a brief summary is given here."