Elastic field by a dislocation loop in an anisotropic elastic half-space with general boundary conditions and its application in nanoindentation of single crystals

Abstract

The elastic displacement and stress fields induced by a dislocation loop of polygonal shape within an anisotropic homogeneous half-space with general boundary conditions on the flat surface z = 0 are obtained by employing the corresponding point-force Green's functions. We first study in detail the effects of the eight sets of boundary conditions on the elastic fields of dislocation loops. We then identify the elastic fields of dislocation loops corresponding to three of the eight sets of boundary conditions. These are the traction-free, completely, and partially sticking contact between the indenter and the indented single crystals, which are employed to establish the distribution dislocation loop model for simulating nanoindentation of single crystals. It is the first time that significant differences in the magnitude of sink-in and pile-up of the indented profile, and of the residual stress components, corresponding to different frictional boundary conditions, are observed, which could serve as benchmark in future nanoindentation study.