A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection

Abstract

A combined cellular automaton-finite difference (CA-FD) model has been developed to simulate solute diffusion controlled solidification of binary alloys. Constitutional and curvature undercooling were both solved to determine the growth velocity of the solid/liquid interface. A modified decentered square/octahedron (in two or three dimensions) growth technique was implemented in the cellular automaton to account for the effect of crystallographic anisotropy. The resulting model is capable of simulating the growth of equiaxed and columnar dendritic grains in 2D and 3D, with the <100> directions either aligned or inclined with the grid. The algorithm used can also be used on coarser grids, with a concomitant loss in resolution, allowing simulation of sufficiently large numbers of dendrites in 3D to investigate the distribution of spacings, as well as average behavior. Simulations were performed for directional solidification with a range of withdrawal velocities and nucleation conditions, but a constant thermal gradient. The simulations capture the full microstructural development and primary spacing selection by both branching and overgrowth mechanisms. The model illustrates that there is a range of possible stable spacings, and that the final spacing is history dependent. It was also found that a minimum deviation from the steady state dendrite spacing is required before the spacing adjustment mechanisms are activated. The influence of perturbing the withdrawal velocity upon the stability of the spacing was also investigated. It was found that perturbations significantly reduce the range of stable primary dendrite spacing.