Application of singular integral equation to crack moving near an inclusion in two-dimensional infinite plate

Abstract

This paper describes application of singular integral equation method to crack moving near an inclusion in two-dimensional infinite plate which is subjected to a tensile loading at infinity. The theoretical formulation is based upon the superposition of the problem of a continuous distribution of edge dislocations spread along the crack locus in an infinite plate with single inclusion and the problem for the same geometry without crack which is subjected to a tensile loading. The superposition leads to simultaneous singular integral equation, and they relate the surface zero-tractions to the dislocation densities along the curved crack locus. The stress intensity factors are derived directly from the crack-tip stress field. Then, the crack tip is automatically moved to a direction as satisfying the restriction that the stress intensity factor KII is zero, which was developed in this study. The direction search is conducted by rotating the tip of virtually incremented crack around the origin crack tip. The search and extension processes are repeated in sequence. In this numerical calculation, the influence of the initial crack locations on crack moving path is discussed.