Prismatic dislocation loops in crystalline materials with empty and coated channels

This paper presents for the first time an analytical solution to the boundary-value problem in the theory of elasticity for a circular prismatic dislocation loop (PDL) coaxial to a hollow cylindrical channel in an elastically isotropic infinite matrix. The stress fields and energy of the PDL are calculated and analyzed in detail. Based on the solution, a theoretical model for the misfit stress relaxation through the formation of a misfit PDL around a misfitting nanotube embedded in an infinite matrix is suggested. The critical radii of the embedded nanotube are found and discussed. It is shown that, for thin nanotubes prepared by nanolayer growth on the initial channel surface, there are two critical inner radii of the nanotube, between which the formation of a misfit PDL is energetically favorable. •Circular prismatic dislocation loop coaxial to a hollow channel in a matrix.•Stress fields and energy of the loop are calculated and analyzed in detail.•Modeling the misfit stress relaxation in nanotube embedded to a matrix.•Critical radii of the embedded nanotube are found and discussed.