An accurate method for solving crack problems with discontinuous crack-line tractions

A numerical method for the integration of the singular integral equation resulting from a surface crack with discontinuous tractions is presented. The crack is modelled as a pile-up of dislocations, and the dislocation density function is partitioned into three terms: A singular term due to the traction discontinuity, a square-root-singular term from the crack tip, and a bounded and continuous residual term. By integrating the singular terms explicitly only a well-behaved residual dislocation density function has to be determined numerically, together with the intensity of the square-root-singular term. The method is applied to the determination of stress intensity factors for a surface crack growing towards, and through, a circular inclusion, and to a surface crack growing into a zone of phase-transformable material.