Stress Field near Crack Tips in Pressurized Thick-Walled Cylinders with Single and Multiple Cracks in Linear Elastic Fracture Mechanics: Analytical and Numerical Analysis of Stress Field and Crack Behavior

<div>Arrays of radial cracks often appear at the bore of pressurized cylinders, posing potential safety risks and leading to possible structural failures. This article presents an analytical approach to evaluate the stress field arising from single or multiple uniform radial cracks in thick-walled pressurized cylinders within the context of linear elastic fracture mechanics (LEFM) under mode-I loading. This formulation is based on the fundamental equations of elasticity and approximations of stress intensity factors (SIF) reported in the literature. Hence, the SIF were revisited and their range of validity was highlighted. The study considers two types of internal pressure loading: one applied only to the cylinder’s inner surface with no pressure on the crack faces and another applied to both the inner surface and the crack faces. The influence of the number and length of cracks relative to cylinder thickness on the stress field is analyzed. A finite element model of the pressurized vessel is constructed to verify the proposed analytical solution, showing good agreement with numerical results for a limited number of cracks.</div>