A closed-form analytical solution for the resolved shear stress field of an elongated rectangular dislocation loop was obtained. The stress field played a significant role in the modelling of dislocation patterns. Assuming linear isotropic elasticity, the stress fields for loops with infinitesimal and finite heights were derived. In the first case, the integration of the stress field of infinitesimal loops was applied. In the second case, a summation of the stress fields of the 4 straight dislocation segments which constituted the loop were used. The stress solution for the loop with a finite height was compared with the much simpler analytical formula for the stress field of a loop with infinitesimal height, and the range of validity of the infinitesimal-height approximation was determined.

The Stress Field of Rectangular Prismatic Dislocation Loops. S.Verecký, J.Kratochvíl, F.Kroupa: Physica Status Solidi A, 2002, 191[2], 418-26