The stress field of a general circular Volterra dislocation loop: analytical and numerical approaches

A closed-form analytical solution for the stress field of a circular Volterra dislocation loop, having glide and prismatic components, is obtained. Assuming linear elasticity and infinite isotropic material, the stress field is found by line integration of the Peach-Koehler equation for a circular dislocation loop. The field equations are expressed in terms of complete elliptic integrals of the first and second kinds. The general loop solution is, from the principle of superposition, the additive sum of the prismatic and glide solutions. Finally, the obtained stress solution is compared with the stress calculation results from segmented loops (six to 24 segments) having the same radius. Such comparisons are useful as a benchmarking measure for newly emerging dislocation dynamics codes which discretize a curved dislocation line in some form or another.