Multiscale modeling of droplet deposition and solidification dendrite growth during DED-Arc additive manufacturing of a nickel-based superalloy

The evolutions of droplet morphology on the macroscale and solidification microstructure on the microscale, during direct energy deposition (DED)-Arc additive manufacturing of a nickel-based alloy, are simulated by developing a multiscale model based on the lattice Boltzmann and cellular automaton models. The macroscopic model is quantitatively validated by modeling the time-dependent phase interface position and temperature distribution for a classical Stefan problem of phase change in the multiphase system. In the simulation of droplet deposition, it is found that the contact line length between the deposited droplet and substrate is proportional to a defined overall factor, d_\rm D^2 \cdot \left| \bm u \right|^2\cdot \Delta T\cdot \left( 1+\cos \theta_0 \right), composed of droplet size (d_\rm D), impact velocity (\bm u), temperature difference (\Delta T), and intrinsic contact angle (\theta), respectively. The overall factor allows one to evaluate the contact line length prior to the experiment, which is significant for heat transfer efficiency and formability of the additive manufacturing products. The evolution of temperature distribution during multilayer droplet deposition is obtained, and the calculated cooling rate (\sim 800 K/s) and temperature gradient (\sim 1 K/m) accord well with the typical data in the literature. By mapping the macroscopic temperature field data into the microscopic model through multidimensional linear interpolation, the growth of dendrites during solidification of the pillar-shaped product is reproduced. Both the simulation and experimental results show that the solidification dendrites present coarse columnar patterns, with several millimeters in length extending multiple deposition layers. This work not only elucidates the complex interactions among droplet impact dynamics, convective heat transfer, solidification/melting, and wetting phenomena in droplet deposition, but also provides an alternative for the predictions of the DED-Arc additive manufacturing formability, as well as the evolution of convections, temperature, and solidification microstructure.