Analytical and Numerical Calculation of Stress-Intensity Factors in a Pressurized Cylindrical Shell With a Clamped Crack

Abstract

The primary goal of this paper is to compute the stretching stress-intensity factor at the tip of a crack in a pressurized cylindrical shell. Shallow shell theory is used and the governing equations are reduced to singular integral equations along the crack, following earlier work by Folias and Copley and Sanders. The solution of the integral equations depends on a dimensionless parameter λ proportional to the crack length divided by the square root of the thickness times the midsurface radius of curvature. Series solutions are obtained for λ < 1 and numerical solutions for 0 ≤ λ ≤ 10. The major contribution of the paper is an asymptotic solution as λ → ∞. To avoid an intractable double Weiner-Hopf problem, the edge of the crack is assumed to be clamped in such a way that it can expand tangentially but cannot rotate or displace perpendicular to the midplane.