Three dislocations confinement in a layer within a semi-infinite size matrix

An edge dislocation is considered in the centre of a two-dimensional layer embedded in a semi-infinite size matrix of different elastic coefficients. The possibility of introducing by gliding two supplementary edge dislocations of the same Burgers vector as the central one (or at least of the same sign), from the layer-matrix interfaces into the layer, has been investigated theoretically from both Peach–Koehler force and energy-based analyses. The stable equilibrium positions of the two dislocations, symmetrically positioned with respect to the layer axis, and the energy conditions for the dislocation introduction in the layer from the interfaces have been determined versus the ratio of the shear moduli of the matrix and the layer. Despite the repulsive nature of the forces that dislocations exert on each other when their Burgers vectors have the same sign, it is found that the introduction into the layer of the two gliding dislocations, symmetrically positioned with respect to the layer axis, can be energetically favourable at stable symmetrical equilibrium positions when the matrix is harder than the layer, with a shear modulus ratio greater than a critical value. This study thus underlines a shear modulus effect on the dislocation confinement in the layer.