Screw dislocation near interface in gradient elasticity

A gradient elasticity theory described elsewhere has been employed to consider a straight screw dislocation near a flat interface separating two elastic media with different elastic constants and gradient coefficients. We have derived, in integral form, solutions for the dislocation stress fields and for the "image" force which acts upon the dislocation due to the interface. It has been shown that both stress components remain continuous at the interface, in contract to the well-known classical solution having a component which undergoes a jump discontinuity there. Far from the interface and the dislocation lines (at distances > > 10root c), gradient and classical solutions coincide. We have also dispensed with the classical singularity of the elastic "image" force acting upon a dislocation due to the interface, and shown that this force remains finite there. In fact, we have found an additional short-range elastic interaction between the dislocation and the interface due to a difference in the gradient coefficients of the media in contact. The appropriate additional "image" force acting upon the dislocation, is finite and maximum at the interface. Under the action of this force, the dislocation tends to penetrate into the medium having the larger gradient coefficient. In the general case where both the elastic constants mu sub i and the gradient coefficients c sub i are different for the bonded media, the total "image" force manifests quite different behavior near the interface depending on the ratios mu sub 2 / mu sub 1 and c sub 2 /c sub 1 , while its long-range component remains as in the classical theory of elasticity.