Application of distributed dislocation method to curved crack moving near a press-fitted inclusion in a two-dimensional infinite plate

This paper describes the application of the distributed dislocation method to the problem of a curved crack moving near a press-fitted inclusion in a two-dimensional infinite plate which is subjected to a tensile loading. The formulation is based upon the superposition of the following three fundamental problems: a continuous distribution of edge dislocations along the crack line in an infinite plate with an inclusion, residual stress generated by the press-fitted inclusion without the crack, and stress field in the infinite elastic plate containing the circular inclusion, but without the crack, which is subjected to a uniform tensile loading. The superposition leads to simultaneous singular integral equations, which are introduced by relating the traction-free condition along the curved crack line to the dislocation density functions as unknown functions in the integral equations. The stress intensity factors can be derived directly from those dislocation density functions. In this study, the crack-propagation program, which is considered that the crack tip is automatically moved in a direction satisfying the restriction that the stress intensity factor K-II is zero, was developed. The developed program is applied to the elastic problem including the press-fitted inclusion and crack, and the influence of the initial crack locations and residual stress generated by inserting the inclusion into the hole on the geometry of the crack path is discussed.