Stress-Intensity Factors for Very Short Cracks in Arbitrary Pressurized Shells

[+] Author and Article Information
J. G. Simmonds, M. R. Bradley

Department of Applied Mathematics and Computer Science, University of Virginia, Charlottesville, Va.

J. Appl. Mech 43(4), 657-662 (Dec 01, 1976) (6 pages) doi:10.1115/1.3423950 History: Received February 01, 1976; Revised July 01, 1976; Online July 12, 2010


A pressurized, shallow, elastically isotropic shell containing a crack is considered. The crack is assumed to lie along a line of curvature of the midsurface. The equations governing the essentially equivalent residual problem, in which the only external load is a uniform normal stress along the faces of the crack, are reduced via Fourier transforms to two coupled singular integral equations. The solutions of these equations depend on three parameters: λ , a dimensionless crack length, κ, the dimensionless Gaussian curvature of the midsurface at the center of the crack, and ν, Poisson’s ratio. Perturbation solutions for small values of λ are obtained by expanding the kernels of the integral equations in series. Explicit formulas for stretching and bending stress-intensity factors are obtained. These represent the first-order corrections due to curvature effects of the well-known flat plate results. The connection with the work of Copley and Sanders for cylindrical shells and Folias for spherical and cylindrical shells is indicated.

Copyright © 1976 by ASME
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