Pair interaction of coaxial circular prismatic dislocation loops in elastic solids with spherical surfaces

In the present work, the pair interaction of coaxial circular prismatic dislocation loops (PDLs) arbitrary placed in elastic solids with free spherical surfaces is considered. The analytical solutions for the pair interaction energies of PDLs in an elastic sphere, an elastic medium with a spherical pore and a spherical layer are given in the form of double power series and illustrated by energy maps built in the space of the normalized PDL radii and axial positions. The results can be used for analyzing the theoretical models of stress relaxation processes in bulk and hollow core-shell nanoparticles and pentagonal particles, which occur through the formation of dislocation ensembles.