An Improved Shell Theory Applied for Failure Analysis of Pressure Vessels

Crack-face closure occurs physically at the compressive edges when a shell is subjected to bending loads. However, in traditional shell theories, crack closure effects are not concerned when evaluating the stress intensity factor (SIF). In reality, crack closure effects influence significantly the SIF. This article presents the theoretical and numerical analyses of crack-face closure effects on the stress intensity factor of shells under bending. The theoretical formulation is based on the shallow shell theory of Delale and Erdogan, incorporating the effects of crack-face closure, which are modeled by a line contact at the compressive edges of the crack faces. It is shown that due to curvature effects crack closure in shells may not occur on the entire length of the crack, depending on the nature of the bending loading and the geometry of the shell. To validate the theoretical solution finite element analysis (FEA) is also performed; the two results agree well. As an example, the stress intensity factor for a pressurized cylinder containing an axial crack is determined based on the improved shell theory which takes into account the effects of crack-face closure.