Generation of a dipole of misfit dislocations in an axisymmetrical precipitate embedded in a semi-infinite matrix

The strain relaxation of an axisymmetrical precipitate embedded in a semi-infinite matrix with a planar free-surface has been theoretically investigated through the generation in the structure of a dislocation dipole. An energy variation calculation has been performed and the formation of the dipole composed of two misfit edge dislocations has been characterised in the interface. It is found that, contrary to the case where the inclusion is embedded in an infinite-size matrix, there exists near the free-surface a preferential plane selected for the dipole formation in the interface which corresponds to the plane perpendicular to the free surface and containing the inclusion centre. A stability diagram of the structure with respect to the dipole formation in the interface has been provided as a function of the misfit strain and the distance of the inclusion from the free-surface, for different values of the inclusion radius.