Phase field modeling of melting and solidification dynamics in metallic powders during the bed fusion process

Abstract

In this study, we introduce a phase field model designed to represent the intricate physical dynamics inherent in selective laser melting processes. Our approach employs a phase-field model to simulate the liquid–solid phase transitions, fluid flow, and thermal conductivity with precision. This model is founded on the variational principle, aiming to minimize the free energy functional, thereby guaranteeing the dissipation of energy. We have developed a complex model that integrates a series of phase field equations, which address the evolution of interfaces and the dynamics of phase transitions. The model also encompasses the Navier–Stokes equations to depict fluid motion and an energy equation to trace the temperature distribution. Critical to the effectiveness of this model is the consideration of the coupling relations among these equations, ensuring a holistic representation of the phenomena. The discretization of the model is achieved through the semi-implicit Crank–Nicolson scheme, which confirms the unconditional energy stability of the system. We have subjected the model to a series of numerical tests, which have validated its capability to accurately capture the evolution of interface morphology, temperature fields, and flow patterns. The results demonstrate numerical stability and efficiency. A central achievement of this research is the establishment of a rigorous proof of unconditional energy stability within the phase-field model tailored for selective laser melting processes. The numerical results affirm the physical accuracy and numerical dependability of the proposed model, which lays a foundation for future simulation endeavors.