The behaviour of a screw dislocation around a circular surface crack was analyzed by using the conformal mapping method. The effects of the crack length and radius of curvature, upon the shielding effect and strain energy, were examined in detail. It was found that, for a dislocation at a fixed distance from the crack tip and located on a plane that was tangential to the crack surface at the tip, there existed a critical crack length which corresponded to the maximum shielding effect of the dislocation upon the circular surface crack. The critical length increased with crack radius of curvature, and approached infinity as the crack became planar. The shielding effect vanished as the crack disappeared. It increased rapidly for crack lengths up the critical length, regardless of the crack radius of curvature. Upon reaching the maximum, it decreased slightly at higher radii of curvature but decreased significantly at lower radii of curvature as the crack became longer. The shielding was more pronounced for higher radii of curvature than for lower radii, and the difference increased with crack length. A surface micro-crack therefore initially propagated in a rather brittle manner but then became more ductile. When the crack became longer, it remained ductile for less curved or planar cracks but became relatively brittle in the case of a highly curved crack. The strain energy was also significantly affected by crack length, and increased rapidly with length when the latter was small; regardless of the crack radius of curvature. With increasing length, it became less affected by the length. The dependence upon the radius of curvature was unclear, with a larger radius corresponding to a slightly higher strain energy.

Elastic Interaction between Screw Dislocations and a Circular Surface Crack. K.M.Lin, H.C.Lin, K.C.Chen, H.L.Chang: Materials Science and Engineering A, 1997, 224, 216-20