Abstract

It is shown that the force dF exerted on a line element νdσ of a dislocation with Burgers vector f by a stress τ is given by dF=-ν×(f.τ)dσ. An analogy is drawn between the behavior of a closed line dislocation in a stress field and the behavior of a closed current-carrying loop in a field of magnetic induction. Then formulas for the stress components caused at any point of an infinite elastically isotropic crystal by a line element of a general Burgers dislocation are deduced from Burger's expressions for the displacements (see Sec. III(C)). These formulas bear a close analogy to the Biot-Savart formula of electromagnetic theory. Both of these results taken together constitute a complete system for the investigation of the mutual interaction of dislocations in an infinite elastically isotropic crystal.