Screw dislocation in a thin film with surface effects

We use conformal mapping techniques to derive a semi-analytical solution to the problem of a (straight) screw dislocation embedded in a thin solid film. The surfaces of the film are assumed to incorporate surface effects which result in deformation-dependent tractions imposed on the surfaces of the film. A number of examples are used to illustrate the stress distribution in the film and the image force acting on the dislocation. We show that in the absence of surface effects significant errors are induced in the determination of both the stress field in the film and the mobility of the dislocation, in particular as the dislocation approaches each of the film's surfaces or as the film becomes thinner. In fact, we demonstrate that the incorporation of surface effects with either positive or negative (surface) shear modulus can either relieve or intensify the stress concentration on the surfaces of the film. We find also that the dislocation tends to move towards a surface which possesses a smaller surface shear modulus and a smaller distance to the dislocation. Moreover, we show that when the thickness of the film exceeds ten times the (smaller) distance between the film's surfaces and the dislocation, the film can be treated essentially as a half-space without inducing large errors in the determination of the stress field in the film and the image force imposed on the dislocation.