An integral representation was presented for the stress function of a stress field produced by a dislocation loop of arbitrary shape in an anisotropic crystal. The derivation of the stress function was supposed to be easily comprehensible. As an application, an integral form of interaction energy between two dislocation loops was shown and the interaction energy was estimated numerically. Dislocation loops, C and C0, were located on the same crystal plane (111). The Burgers vectors of C and C0 were supposed to be the same, and parallel to the [111] direction. The length of the Burgers vector was b. As an example, the radii of the loops C and C0 were assumed to be 5b and 2b, respectively. The distance between centers of the circular dislocation loops was r. Parameters h and r determined the position of the small dislocation loop, C0. As an example, elastic constants were take to be C11 = 2.30, C12 = 1.35 and C44 = 1.17; which corresponded to those of body-centered cubic iron. The stress function was derived from the equation for the stress field by solving Poisson’s equation. In the case of anisotropic crystals, the interaction energy was expressed by the summation of four double integrals over C and C0. The negative interaction energy meant that the force acting on the dislocation loops C and C0 was attractive. The interaction energy gradually decreased with increasing distance between the two dislocation loops. Because of the elastic anisotropy, the interaction energy depended upon the angle, h. The energy difference unexpectedly did not necessarily decrease with increasing distance, r. In the present calculations, the largest energy difference was 0.0180, for the case of r = 12b.

Interaction Energy Between Dislocation Loops in an Anisotropic Crystal: Application of Elasticity Theory. K.Ohsawa, M.Yagi, H.Koizumi, E.Kuramoto: Journal of Nuclear Materials, 2011, 417[1-3], 1071-3