Dislocations in Materials with Couple Stress

The stress-fields of long straight screw and edge dislocations in a linear isotropic and centre-symmetric second-grade elastic material are obtained. For a screw along the axis of a circular cylinder the displacement and stress fields are identical with those of classical elasticity. This also holds for the torsional correction in a cylinder of finite length. In the case of an edge dislocation in an infinite medium, the displacement and stress-fields are different from the classical fields, although their asymptotic form at large distances is the same. This result is true both for general second-grade materials and for the special case of materials with couple-stress studied by Mindlin and Tiersten. The asymptotic form of the hyperstress components is also obtained. There is considerable difference in the stress-fields in the vicinity of the dislocation core between materials with couple stress and classical elastic materials, ranging in some of the cases considered up to an order of magnitude increase in some of the stress components. The departure from classical behaviour is capable of persisting to greater distances from the centre of the dislocation line for second grade materials than for Mindlin-Tiersten materials. 1