The application of the combined method of weight functions for the determination of a through-wall crack opening area in a shell

Abstract

The crack opening area of a through-wall crack in a shell is one of the main design parameters in the leak-before-break concept. The available methods for determining this parameter essentially consider the shell as a plane body and disregard the linearly varying component of the displacement field (as in the plate theory). Based on a combined method of weight functions, a simple procedure is put forward to derive an approximate expression for the fundamental field of displacements under the action of a concentrated force and moment onto the crack faces in the form of a sum of a uniform component and a component that linearly varies through the wall thickness. This provides, in particular, convenient formulas to find the crack opening area in a polynomial field of membrane stresses as well as linear ones. For a cylindrical shell with a longitudinal or transverse crack, the calculated values of the crack opening area are compared with those reported elsewhere. The contribution of the linear component to the total crack opening area is assessed.