Elastic interaction between screw dislocations and a circular surface crack

The behaviour of a screw dislocation around a circular surface crack was analyzed using the conformal mapping method. The effects of the crack length l and its radius of curvature R on the shielding effect and the strain energy were discussed in detail. It was found that for a dislocation being fixed at a constant distance from the crack tip and located on a plane tangent to crack surface at the tip, there exists a critical crack length l* corresponding to a maximum shielding effect induced by the dislocation on the circular surface crack. The l* increases with R and approaches infinity as the crack becomes planar (i.e. R → ∞). The shielding effect vanishes as the crack disappears. It increases rapidly with l if 0 < l ≪ l*, regardless of R. After reaching the maximum, it decreases slightly for larger R but significantly for smaller R as the crack becomes longer. The shielding is more pronounced for larger R than that for smaller R, with the difference increasing with crack length. As a result, a surface microcrack propagates initially in a rather brittle manner then becomes more ductile. When the crack gets longer, it still keeps ductile for a less curved or a planar crack but becomes relatively brittle for a severely curved crack. In addition, the strain energy is also significantly influenced by crack length and increases rapidly with l when l is rather small, regardless of R. With increasing l, it become less affected by l, and the variation with R is still not obvious, with larger R corresponding to a slightly higher strain energy.