Abstract
A numerical method for the integration of the singular integral equation resulting from the interaction of a surface crack with a subsurface inclusion is presented. The crack is modelled as a pile-up of dislocations, and the dislocation density function is partitioned into three parts: A singular term due to the load discontinuity imposed by the inclusion, a square root singular term from the crack tip, and a bounded and continuous residual term. By integrating the singular terms explicitly the well behaved residual dislocation density function only has to be determined numerically, together with the intensity of the square root singular term. The method is applied to the determination of the stress intensity factor for a surface crack growing towards and through a circular inclusion whose diameter is equal to the distance from the free surface, and to the determination of the characteristic stress intensity factors when the crack enters the inclusion and leaves it for arbitrary ratios between the inclusion diameter and the distance from the surface.
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