Abstract
Cellular automata (CA) models of as-solidified grain structure, originally developed and applied to casting, have become a common means of predicting grain structure resulting from Additive Manufacturing (AM) processes. The majority of these models are based on the decentered octahedron approach, which attempts to correct for the effect of grid anisotropy on the prediction of competitive solidification of dendritic grains. However, AM solidification occurs under cooling rates (๐ฬ ) and thermal gradients (๐บ) that are orders of magnitude larger than those encountered in casting, and no systematic investigation on the effect of the CA model cell size (๐ฅ๐ฅ) and time step (๐ฅ๐ก) on AM microstructure predictions has been performed. In this study, such an investigation is first performed via simulation of individual grains of various crystallographic orientations with a fixed, unidirectional ๐บ, showing that CA prediction of the steady-state undercooling matched the expected values based on the interfacial response function at small ๐บ and deviated from the expected values at large ๐บ. Simulation of competitive growth of multiple grains showed a weakening of the predicted texture as ๐บ and ๐ฅ๐ฅ became large. Simulation of solidification under AM conditions, where ๐บ and ๐ฬ vary spatially across the melt pools, showed that not only does grain selection weaken and deviate from expectations at large ๐ฅ๐ฅ, but grains with crystallographic โจ1 0 0โฉ aligned with the grid directions are more adversely affected by the temperature field discontinuities than grains with other crystallographic orientations. Despite the fact that the exact grain competition results depended on ๐ฅ๐ก, the overall texture development was notably less sensitive to ๐ฅ๐ก than ๐ฅ๐ฅ, provided that a reasonable value of ๐ฅ๐ก is selected based on the ratio of ๐ฅ๐ฅ to the maximum local solidification velocity in the simulation domain. Finally, from the directional solidification and AM simulation results, an analysis of computational cost compared to simulation resolution is performed based on an equation derived to quantify the relatively inaccuracy in grain selection based on the model and temperature field inputs. From this analysis, it is concluded that there is a need for algorithmic improvements to improve CA grain competition accuracy for large ๐บ processing conditions as sufficiently small ๐ฅ๐ฅ to resolve the necessary competition is intractable for many AM processing conditions.
