Multi-scale simulation of dendrite growth for direct energy deposition of nickel-based superalloys

Highlights

• A multiscale model was developed for direct energy deposition process.

• A power-law function of Λ~R^−1.31 between the PDAS and the cooling rate is obtained.

• A circuitous relationship between the PDAS and $G^{-0.5}{V_s}^{-0.25}$ is found.

• A PDAS map for additive manufacturing of metals is obtained.

Abstract

In this study, a multi-scale model that integrates a macro-scale transient three-dimensional mass and heat transfer model and a micro-scale thin-interface phase-field model is developed to simulate the solidification behavior of the molten pool and the dendritic growth behavior for direct energy deposition process. Both the longitudinal molten pool morphology and the primary dendritic arm spacing (PDAS, Λ) of the columnar dendrites are validated by experiments. As revealed from the macro-scale simulation, the solidification velocity V_s and the temperature gradient G are coupled with an opposite trend, and the cooling rate R decreases along the solid/liquid interface from the top to the bottom of the molten pool. The micro-scale simulation shows that a power-law function (Λ ∝ R^−1.31) with a scaling factor much larger than a traditional directional solidification (Λ ∝ R^−0.5). Moreover, contrary to Hunt's and Kurz-Fisher's linear models, a circuitous relationship between Λ and $G^{-0.5}{V_s}^{-0.25}$ is found to be clustered within a narrow region. The coupled solidification parameters along the solidification interface with an asymptotic increase of G near the bottom of the molten pool contribute to the above PDAS observations.