Phase-field modeling of recrystallization nucleation and grain boundaries in polycrystals

Solid-state recrystallization in polycrystalline materials involves complex interactions between crystal nucleation and grain boundary migration, which significantly affect microstructure evolution and material properties. Modeling this coupled behavior is challenging due to its inherent multiscale nature. This work presents a phase-field model that captures the coupled dynamics of recrystallization nucleation and grain boundary evolution. The model integrates mesoscale boundary migration with microscale nucleation in a thermodynamically consistent framework. Based on Landau theory, a variational formulation is used to derive the governing equations, accounting for multiple energy contributions. To handle nonlinearities and multiscale coupling, a space- and time-dependent Lagrange multiplier is introduced to improve energy stability. Time discretization combines the Crank–Nicolson and Adams–Bashforth methods, while spatial derivatives are solved using Fourier spectral method with $O(NlogN)$ complexity. The energy stability of our model is rigorously analyzed. Numerical results demonstrate its accuracy, efficiency, and robustness in reproducing recrystallization pathways and nucleation–boundary interactions. This framework offers a stable and scalable tool for simulating microstructure evolution and understanding multiscale coupling in complex crystalline systems.