Leung, Andrew Yee TakAndrew Yee TakLeungSu, R. K. L.2022-05-072022-05-071998https://repository.sfu.edu.hk/handle/sfu/3101Cracks that are developed in pipes, pressure vessels and circular bars due to improper welding are often idealized to be circumferential, penny-shaped or flat toroidal. Based on the three-dimensional Navier's equations in cylindrical coordinates, we derive the general displacement functions for both the penny-shaped and circumferential cracks by eigenfunction expansion method. We find that only those terms of the first order displacement and stress are similar to the case of three-dimensional straight plane cracks and that the higher order terms are coupled through the equilibrium equations. The strength of coupling depends on the ratio <i>Sr̄</i> = r/a where r is the radius normal to the crack front and 2a is the diameter of the circular crack tip. It decreases with <i>Sr̄</i>.enjournal article10.1023/A:1007484809384