Three-dimensional phase field modeling of columnar to equiaxed transition in directional solidification of Inconel 718 alloy

Understanding the columnar to equiaxed transition (CET) is vital in production of materials with superior properties using casting, welding, and additive manufacturing processes. In this study, a three dimensional (3D) phase field-lattice Boltzmann (PF-LB) model was developed to simulate the CET in directional solidification of Inconel 718 alloy. The phase field (PF) method was used to determine the solid/liquid transition. The solute diffusion equation was solved by the lattice Boltzmann method (LBM), due to its suitability for parallel pro-cessing and its simplicity in terms of modeling complex boundaries. A CET solidification map was developed for different temperature gradients and growth rates and the evolution of dendrites for equiaxed, columnar, and mixed regimes was studied. The resulting microstructure for different growth regimes was demonstrated and discussed in terms of grain size and orientation. In addition, the variation of maximum solute concentration along the sample height was investigated. It was found that while initial grain size does not affect the average grain size for equiaxed growth, it affects the PDAS for columnar growth significantly. A model was proposed to predict the primary dendrite arm spacing for columnar growth in a wide range of temperature gradient, solidification rate, and initial grain size. The novelty of this model is in the inclusion of the effect of initial grain size, which is important in processes that involve melting and solidification on a preexisting substrate, such as welding and additive manufacturing.