The stress field of a dislocation lying in a plate

Abstract

The stress field of an edge dislocation lying in the midplane of an isotropic plate of thickness 2a with free surfaces is calculated. The Burgers vector b lies in the plane of the plate. The field is calculated as the sum of two terms: the stresses of the dislocation in an infinite medium together with an array of images which annul the tangential tractions, and the stresses which annul the normal tractions and are derived from a stress function given by a convergent Fourier integral. The long-range bending of the beam depends only on the integral and agrees with Eshelby’s result. The energy of interaction with a similar dislocation at a distance Xa can be expressed by a Fourier integral alone. If this integral is evaluated by the method of residues, the asymptotic form for large X is given by the poles of the integrand with the smallest positive real parts. These do not lie on the imaginary axis; the asymptotic form, therefore, shows damped oscillations ∼3.0075bD sin(1.3843X+0.1175) exp(−3.7488X). The first minimum occurs at X?2.4.