Multi-kinked or slightly curved cracks in two-dimensional anisotropic elastic solids

In this paper, multi-kinked or slightly curved cracks in two-dimensional anisotropic elastic solids are solved with the Stroh formalism and perturbation method. Since a multi-kinked crack is a reduced polygonal hole with coinciding edges, the solution of a multi-kinked crack can be reduced from that of an arbitrary polygonal hole, which is a perturbation solution based on elliptical hole problems. By using the Schwarz–Christoffel mapping, the exterior of a multi-kinked crack can be mapped onto the exterior of a unit circle, which is necessary for the subsequent derivation. A slightly curved crack can be regarded as a straight crack with deviation of the crack path, allowing the application of the perturbation method based on the solution of a straight crack. The stress intensity factors of a multi-kinked crack are calculated using the path-independent H-integral, which is suitable for mixed-mode fracture, while that of a slightly curved crack is determined by directly evaluating the limit in the definition of stress intensity factors. Examples are provided to demonstrate the present methods, and the results are verified with existing solutions or finite element results.