Modeling the Interaction between Vacancies and Grain Boundaries during Ductile Fracture

The experimental results in previous studies have indicated that during the ductile fracture of pure metals, vacancies aggregate and form voids at grain boundaries. However, the physical mechanism underlying this phenomenon remains not fully understood. This study derives the equilibrium distribution of vacancies analytically by following thermodynamics and the micromechanics of crystal defects. This derivation suggests that vacancies cluster in regions under hydrostatic compression to minimize the elastic strain energy. Subsequently, a finite element model is developed for examining more general scenarios of interaction between vacancies and grain boundaries. This model is first verified and validated through comparison with some available analytical solutions, demonstrating consistency between finite element simulation results and analytical solutions within a specified numerical accuracy. A systematic numerical study is then conducted to investigate the mechanism that might govern the micromechanical interaction between grain boundaries and the profuse vacancies typically generated during plastic deformation. The simulation results indicate that the reduction in total elastic strain energy can indeed drive vacancies toward grain boundaries, potentially facilitating void nucleation in ductile fracture.