Modeling of binary alloy solidification under conditions representative of Additive Manufacturing

Understanding the interplay among process parameters, microstructure, and presence of defects is critical to optimizing Additive Manufacturing (AM) routes for producing specialty alloy parts with unique geometry, properties, and compositional features. However, since it is not feasible to obtain experimental results for every possible set of AM process, process conditions, and alloy composition, computational modeling is becoming an increasingly important tool for understanding key physical processes, with the hope of developing a framework for AM materials design. One such physical process of interest is the dendritic solidification within grains; we implement a Cellular Automata (CA) model for coupled solute transport and growth of cellular and dendritic beta-Ti alloy colonies under thermal conditions typically encountered in AM processes. Quantitative agreement with analytical models of the undercooling-solidification velocity relationship was achieved, as well as qualitative agreement with trends in primary dendrite arm spacing (PDAS), secondary arm development, and compositional profile with changes in solidification conditions. The roles of solute diffusivity, interfacial energy, and alloying addition are considered as well. Under rapid solidification conditions, extension to include local nonequilibrium for solute allowed for the modeling of solute trapping along dendrite stems as well as qualitative representation of the dendritic to banded morphology transition. To quantitatively reproduce non-equilibrium solidification at the dendritic colony scale and more accurately estimate rapid solidification microstructures, use of multiple grids or more complex CA rules would be in order.