Surface effects on image stresses and dislocation pile-ups in anisotropic bi-crystals

Based on the image decomposition method and the Leknitskii-Eshelby-Stroh (LES) formalism, the effects of surface conditions and misorientation on the dislocation image stress and dislocation distributions in double-ended discrete dislocation pile-ups are studied in a new bi-crystal surface layer configuration. This new configuration contains a stiff layer of finite thickness adjacent to the free surface, which influences the dislocation image stress. The numerical method is first applied to different half-space and bi-crystal configurations for Ni. It is shown that the stiff layer significantly modifies the profile of the dislocation image stress compared to a free or rigid surface. A size effect on the dislocation image stress is found when considering two parallel free surfaces. In addition, the effect of each free surface is individually analyzed. Meanwhile, a grain size effect is also found when considering two parallel grain boundaries. In a second application, the numerical study of a double-ended dislocation pile-up model is proposed, terminating on a grain boundary on one side and on a stiff layer adjacent to a free surface on the other side. The effects of surface conditions, grain boundary and critical stress on dislocation distributions in the double dislocation pile-up are analyzed both at loading and unloading in the case of Ni bi-crystals.