Theory of Dislocation Cells: The Dislocation Quadrupole

Abstract

The prototype of all dislocation cells composed of dislocations with two mutually perpendicular Burgers vectors is the terminated quadrupole. It consists of two similar, mutually perpendicular, rectangular glide dislocation loops which interpenetrate such that their edge dislocation segments are parallel to each other and that each of the two pairs of like-handed screw dislocation segments form a cross of fourfold symmetry. The stress components of the terminated quadrupole have been computed numerically and have been presented in the form of contour maps in, or parallel to, the midplane of the quadrupoles as well as in a cut parallel to the prism axis of the quadrupole. It is found that the intensity of the stresses falls with distance from the cell as 1/r5 for medium short or squat quadrupoles, and as 1/r4 for very elongated quadrupoles.