Simulation and analysis of $\gamma$-Ni cellular growth during laser powder deposition of Ni-based superalloys

Cellular or dendritic microstructures that result as a function of additive manufacturing solidification conditions in a Ni-based melt pool are simulated in the present work using three-dimensional phase-field simulations. A macroscopic thermal model is used to obtain the temperature gradient $G$ and the solidification velocity $V$ which are provided as inputs to the phase-field model. We extract the cell spacings, cell core compositions, and cell tip as well as mushy zone temperatures from the simulated microstructures as a function of $V$. Cell spacings are compared with different scaling laws that correlate to the solidification conditions and approximated by $G^{-m}{V}^{-n}$. Cell core compositions are compared with the analytical solutions of a dendrite growth theory and found to be in good agreement. Through analysis of the mushy zone, we extract a characteristic bridging plane, where the primary $\gamma$ phase coalesces across the intercellular liquid channels at a $\gamma$ fraction between 0.6 and 0.7. The temperature and the $\gamma$ fraction in this plane are found to decrease with increasing $V$. The simulated microstructural features are significant as they can be used as inputs for the simulation of subsequent heat treatment processes.