Application of alloy solidification theory to cellular automata modeling of near-rapid constrained solidification

To utilize the full potential of additive manufacturing routes for metallic part production, understanding how microstructure and texture develop as functions of alloying additions and process conditions is critical. Use of cellular automata (CA) with alloy solidification theory can provide a useful augmentation to experimental microstructure observations, as it can accurately and efficiently reproduce nucleation and growth of cubic crystal structures common to binary and ternary alloy solidification. We apply CA to model constrained solidification under thermal gradient magnitudes and solidification velocities representative of those commonly encountered along the melt pool boundary in Laser Engineered Net Shaping (LENS®), a specific alloy-based additive process. Various sets of alloying elements, quantities, and nucleation parameters are used to show the model's ability to predict realistic trends in nucleation and growth of single phase β-Ti alloys. 2D and 3D model implementations are qualitatively and quantitatively compared, and alloy composition (element and quantity) is shown to play a critical role on the columnar to equiaxed transition (CET) through changes to the interfacial response function. Simulation results are further used to define a parameter that correlates with the CET over a range of imposed conditions, linking alloy solidification theory to the CA prediction of microstructure. This CA model can serve as a useful tool when designing sets of alloying additions that would produce given microstructures, while coupled application of this CA to process scale simulations of additive process temperature fields will facilitate design of both specific alloy compositions and sets of process conditions for microstructure control.