On the phase field model for microstructure evolution during selective laser melting of powder bed including diffusion-induced stresses

Abstract

In this paper, we develop a phase field model for microstructure evolution in laser powder-bed additive manufacturing processes, which allows for the effect of elastic stresses due to diffusion of atomic defects (vacancy and interstitial atom) generated at the moving liquid-solid interface. The governing equations of the model including a time-dependent Ginsburg-Landau equation for the phase field with additional stress term, a diffusion-drift Cahn–Hilliard like equation describing atomic defect dynamics, an energy balance equation for the temperature change, and finally the mechanical equilibrium equation for the elastic displacement fields are derived within a thermodynamic framework based on entropy generation guaranteeing thermodynamic consistency. The most simple 1D and isothermal equilibrium situation is considered to study phenomenon of diffusion-flexural instability with the atomic defect clustering and periodic distributions of defects. The effect of this instability on the exfoliation of deposited thin layers on a substrate is also discussed.