Title: Simulation and analysis of $γ$-Ni cellular growth during laser powder deposition of Ni-based superalloys,
Abstract: 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.