This preprint was accepted October 30, 2006
ABSTRACT: The stress field of non-singular screw dislocation is investigated in the second order approximation by means of the translational gauge approach of the Einstein-type. The stresses of second order around the screw dislocation are classically known for the hollow circular cylinder with traction-free external and internal boundaries. The inner boundary surrounds the dislocation's core, which is not captured by the conventional solution. The present gauge approach enables the classically known quadratic stresses be continued inside the core. The corresponding gauge equation is chosen in the Hilbert--Einstein form. The gauge equation plays a role of non-conventional incompatibility law, and the stress function method is used for its solution. The modified stress potential is obtained as a sum of two parts: conventional, say, `background' and a short-ranged gauge contribution. The latter just causes additional stresses localized within the dislocation's core. The asymptotic properties of the resulting stresses are studied. Since the gauge contributions are short-ranged, the background stress field dominates at the distances sufficiently large with respect to the core. The outer cylinder's boundary is traction-free. At sufficiently moderate distances, the second order stresses acquire regular continuation within the core region, and the cut-off at the core is absent. Expressions for the asymptotically far stresses provide us self-consistently with new length parameters of the unconventional origin. These lengths are given by means of the elastic moduli and could characterize an exteriority of the dislocation core.[Full text: (.ps.gz)]