Dislocation equilibrium positions on either side of a grain boundary in the presence of precipitates

The equilibrium positions of edge dislocations in a bicrystal are determined under the combined influence of a grain boundary, inter-dislocation interactions, and misfitting elliptical precipitates. The grain boundary is represented by a disclination dipole array, and the elliptical precipitates are modeled as Eshelby inclusions. The superposition principle of linear elasticity is utilized to calculate the total stress field and equilibrium states are obtained from minima of the total elastic energy using the Peach-Koehler framework. Two precipitate configurations are considered: co-quadrant and opposite-quadrant. In the co-quadrant configuration, the equilibrium lies in the far-field due to precipitate attraction, with a near-field local minimum state arising only within a limited, misorientation-dependent range of eigenstrain. In the opposite-quadrant configuration, the equilibrium shifts toward the precipitate and the near-field equilibrium is suppressed. The misorientation angle governs initial local minima states, while dislocation offset and precipitate size modify the transition conditions. When the precipitate lies close to the dislocation, its stress field dominates the equilibrium.