Numerical analysis of the fungibility of disclination dipole by dislocation array or dislocation monopole

Disclinations have been discovered and applied to a wide variety of materials, underscoring the importance of their analysis. Previous studies have demonstrated that a disclination dipole can be represented by a dislocation array in a deformation schematic and by a dislocation monopole in a stress state. Based on these observations, we propose that the elastic field of a disclination dipole can be substituted with that of a dislocation array or dislocation monopole, allowing the development of the disclination theory grounded in dislocation theory. In this study, we conducted a quantitative analysis of the elastic strain–energy of disclination dipoles, dislocation arrays, and dislocation monopoles using linear elasticity theory and molecular dynamics (MD) simulation. While linear elasticity theory facilitates a quantitative evaluation of the elastic field, it fails to account for out-of-plane deformation of the material. Therefore, MD analysis, which considers out-of-plane deformation, was employed to obtain versatile results applicable to a broader range of materials. Our findings from both theoretical analyses indicate that, in terms of strain–energy, a disclination dipole with a large separation can be represented by a dislocation array, whereas a dipole with a small separation can be represented by a dislocation monopole. This study newly performs strain–energy analysis of dislocations and disclinations using these two theoretical approaches.