Stress Intensity Factors for a Circular Ring with Uniform Array of Radial Cracks of Unequal Depth

Abstract

The plane problem of a uniform array of unequal depth radial cracks originating at the internal boundary of a pressurized circular ring is considered. The 12-node quadrilateral isoparametric elements with collapsed singular elements around crack tips are used to compute stress intensity factors at crack tips. In a previous study of equal depth radial cracks, the weakest configuration (having highest values of stress intensity factors) was a ring with two diametrically opposed cracks. The current study shows that if for any reason one of the two cracks should grow a little faster than the other, the stress intensity factor at the tip of the longer crack increases at a much faster rate to enhance the faster growth of the longer crack. Numerical results are also obtained for cases of three and four radial cracks. They show the same trend: that once one or two cracks grow a little more than the rest, the stress intensity factors at these deeper cracks will be increased progressively higher to keep the faster pace of growth. This explains why failure caused by a single major crack has been observed most frequently. The finite element results show that the relationship between the stress intensity ratio and the crack depth ratio is approximately linear. This approximation enables us to estimate stress intensity factors at unequal depth cracks by a simple numerical method. The estimations thus obtained are close to stress intensity factors computed from the finite element method.