INTERACTION BETWEEN A SURFACE CRACK AND A SUBSURFACE INCLUSION

A numerical method for the integration of the singular integral equati on resulting from the interaction of a surface crack with a subsurface inclusion is presented. The crack is modelled as a pile-up of disloca tions, and the dislocation density function is partitioned into three parts: A singular term due to the load discontinuity imposed by the in clusion, a square root singular term from the crack tip, and a bounded and continuous residual term. By integrating the singular terms expli citly the well behaved residual dislocation density function only has to be determined numerically, together with the intensity of the squar e root singular term. The method is applied to the determination of th e stress intensity factor for a surface crack growing towards and thro ugh a circular inclusion whose diameter is equal to the distance from the free surface, and to the determination of the characteristic stres s intensity factors when the crack enters the inclusion and leaves it for arbitrary ratios between the inclusion diameter and the distance f rom the surface.