It was shown that the gradient theory of elasticity, for the case of an edge dislocation, predicted a zero value for the elastic dilatation at the dislocation line. Other components of the elastic strain remained singular there. However, these singularities appeared within an extremely small region (of the order of 0.0001nm) around the dislocation line. All of the strain components were finite beyond this region. They approached zero as the boundary of the above region was approached, and attained maximum values (3 to 14%) within that region. The component of total displacement which was normal to the glide plane of the dislocation was finite at the dislocation line. This contrasted with the classical solution, which was singular there. Two characteristic distances arose naturally, as in the case of screw dislocations. One distance could be considered to be the radius of the dislocation core, and the other could be considered to be the radius of strong short-range interactions between dislocations. It was concluded that the gradient solution would be especially useful for modelling such interactions.

Edge Dislocation in Gradient Elasticity. M.J.Gutkin, E.C.Aifantis: Scripta Materialia, 1997, 36[1], 129-35