Elastic fields due to dislocations in anisotropic bi- and tri-materials: Applications to discrete dislocation pile-ups at grain boundaries

Abstract

Elastic fields due to single dislocations and dislocation pile-ups are computed in heterogeneous media like bi-materials, half-spaces and tri-materials thanks to the Leknitskii–Eshelby–Stroh formalism for twodimensional anisotropic elasticity. The tri-material configuration allows to consider grain boundary regions with finite thickness and specific stiffness. The effects of these parameters are first studied in the case of a single dislocation in a Ni bicrystal. Image forces may arise because of both dissimilar grain orientations and the presence of a finite grain boundary region. In particular, it is shown that the Peach– Koehler force projected along the dislocation glide direction can exhibit a change of sign with the dislocation position. Therefore, an equilibrium position in the absence of applied stress can be found by coupling an attractive compliant grain boundary region with a repulsive orientation of the adjacent crystal, or a repulsive stiff grain boundary region with an attractive orientation. Regarding dislocation pile-ups, it is shown that the resolved shear stress scales approximately with the inverse of the square root distance from the leading dislocation in the pile-up. This scaling law remains valid in anisotropic elasticity for the chosen heterogeneous media. Both the grain boundary stiffness and grains misorientation influence pileup length and resolved shear stress, but the effect of misorientation is clearly seen to be predominant. In the case where the leading dislocation is unlocked, the resolved shear stress at a given position in the neighboring grain is reduced when the grain boundary stiffness is increased due to the pushing back of dislocations from the grain boundary.