An efficient and energy stable framework for phase field simulations of grain growth in additive manufacturing

Phase field simulations play a key role in the understanding of microstructure evolution in additive manufacturing. However, they have been found extremely computationally expensive. One of the reasons is the small time step requirement to resolve the complex microstructure evolution during the rapid solidification process. This paper investigates the possibility of using a class of stabilized time integration algorithms to accelerate such phase field simulations by increasing the time steps, based on a phase field model dedicated to simulating the solidification of 316L stainless steel during additive manufacturing, particularly in a regime where the solid-liquid interface is moving fast and there is absolute interfacial stability with negligible composition variations. The specific computational framework, incorporating the finite element method and the stabilized time integration algorithms, was developed. A theoretical analysis on energy stability was conducted, based on a revisited energy law derived for the phase field model. The numerical results confirmed that the proposed framework can effectively enforce the numerical stability and a decreasing energy requirement for the phase field simulations with at least two orders-of-magnitude larger time steps over conventional explicit methods. 2D and 3D phase field simulations have been conducted with relevant physical and kinetic parameters for 316L stainless steel. This computational framework can be easily adapted for different phase field models and open numerous opportunities for efficient phase field simulations.