Non- and Quasi-Equilibrium Multi-Phase Field Methods Coupled with CALPHAD Database for Rapid-Solidification Microstructural Evolution in Laser Powder Bed Additive Manufacturing Condition

Abstract

A solidification microstructure is formed under high cooling rates and temperature gradients in powder-based additive manufacturing. In this study, a non-equilibrium multi-phase field method (MPFM), based on a finite interface dissipation model, coupled with the Calculation of Phase Diagram (CALPHAD) database, was developed for a multicomponent Ni alloy. A quasi-equilibrium MPFM was also developed for comparison. Two-dimensional equiaxed microstructural evolution for the Ni (Bal.)-Al-Co-Cr-Mo-Ta-Ti-W-C alloy was performed at various cooling rates. The temperature-γ fraction profiles obtained under 105 K/s using non- and quasi-equilibrium MPFMs were in good agreement with each other. Over 106 K/s, the differences between the non- and quasi-equilibrium methods grew as the cooling rate increased. The non-equilibrium solidification was strengthened over a cooling rate of 106 K/s. Columnar-solidification microstructural evolution was performed at cooling rates of 5 × 105 K/s to 1 × 107 K/s at various temperature gradient values under a constant interface velocity (0.1 m/s). The results show that, as the cooling rate increased, the cell space decreased in both methods, and the non-equilibrium MPFM was verified by comparing with the quasi-equilibrium MPFM. Our results show that the non-equilibrium MPFM showed the ability to simulate the solidification microstructure in powder bed fusion additive manufacturing.

Keywords

• additive manufacturing
• rapid solidification
• microstructural evolution
• non-equilibrium
• quasi-equilibrium
• multi-phase field method