Determination of Stress Intensity Factors for a Cracked Shell under Bending with Improved Shell Theories

Abstract

A formulation based on the linearized shallow shell theory has been developed by Delale and Erdogan to determine the stress intensity factors of a shell with a through-the-thickness crack. The drawback in the formulation is that the crack-face closure at the compressive edges when a cracked shell is subjected to a bending load is not taken into account, which results in the penetration of material at the crack faces. The present research is aimed to improve the formulation by including the effect of the crack-face closure on the stress intensity factors. Simulation of the closure is achieved by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results have shown that the crack-face closure significantly influences the magnitude of the stress intensity factors and tends to reduce the maximum stress intensity factor. The magnitude of the reduction varies with the curvatures of the shell and the ratio of the two curvatures as well.