A semi-infinite kinked crack in an infinite solid which consists of elastically homogeneous material with negligible body force is analyzed. Two loading cases are considered.
First one is a kinked crack problem where a pair of anti-plane concentrated shear loads are applied to the main crack. Introducing a displacement perpendicular to the plane and formulating the problem by Mellin transform, a Wiener-Hopf equation is derived. Solving the equation by Wiener-Hopf technique, a closed form solution for the displacement around the crack tip is obtained. Stress intensity factor calculated from the solution can be applied to any kinked length and kink angle. Particular emphasis is put on the stress intensity factor as the kinked length approaches zero, where two limit processes(both the distance from the crack tip and the kinked length approaching zero) are involved. It is found that the stress intensity factor depends on the order of performing the two limit processes. The results are compared with those by previous researchers. Also the energy release rate for this problem is computed.
Second one is a problem where a pair of in-plane concentrated loads are applied. Introducing Airy stress function and formulating the problem by Mellin transform, a pair of Wiener-Hopf equations are derived. Solving the equation by Wiener-Hopf technique, Airy stress function around the crack tip is obtained. From the solution stress intensity factor is determined. In particular stress intensity factor as the kinked length approaches zero is calculated rigorously. Also the energy release rate for this problem is computed.
