Crack Opening Area for an Isolated Crack Subjected to a Symmetric Mode I Stress Distribution

In developing a leak-before-break case for a component in a pressurized system, a key element is an estimation of the size of through-thickness crack that will give a measurable leakage under normal operating conditions, and this requires a knowledge of the crack opening area. In this context, the paper presents a simple derivation of an expression for the crack opening area associated with an isolated crack that is subjected to a general Mode I symmetric tensile stress distribution which could arise from a combination of applied and residual stresses. The paper also presents a simple derivation of an expression for the crack opening displacement at the crack centre which, coupled with the assumption that the crack opening profile conforms to an elliptical shape, has been used as the basis for a simplified procedure for estimating the crack opening area. The resulting expressions are validated by comparing them with known results for specific stress distributions. They are also used to give new results for a cosine stress distribution.