A Thick-Walled Cylinder With an Axisymmetric Internal or Edge Crack

Abstract

The paper considers the elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack. Using the standard transform technique the problem is formulated in terms of an integral equation which has a simple Cauchy kernel for the internal crack and a generalized Cauchy kernel for the edge crack as the dominant part. As examples the uniform axial load and the steady-state thermal stress problems have been solved and the related stress-intensity factors have been calculated. Among other findings the results show that in the cylinder under uniform axial stress containing an internal crack the stress-intensity factor at the inner tip is always greater than that at the outer tip for equal net ligament thicknesses and in the cylinder with an edge crack which is under a state of thermal stress the stress-intensity factor is a decreasing function of the crack depth, tending to zero as the crack depth approaches the wall thickness.

The elasticity problem for a thick-walled cylinder containing a circumferential crack

“…-1-problem is considered ·for arbitrary .non~x.isynmetric loading conditions. The related prob1en for an elastic solid cylinder containing a pennyshaped crack isconsideredin [6][7][8], and that for a hollow cylinder under· axisymmetric loading conditions in [9].…”

Axisymmetric crack problem of thick-walled cylinder with loadings on crack surfaces

“…In this case there is a considerable interaction between the crack and the stress-free inner surface of the cylinder. The Kernel used in the present study is no longer bounded in the corresponding closed interval, and, of course, the single-valuedness condition is no longer valid [1]. However for the cases r 1 = A/B = 0.125 and r 1 = A/B = 0.2, a similar behavior is not observed because the crack is far enough from the inner surface of the cylinder.…”

“…One of the most widely used method of solution of crack problems leading to calculation of the stress intensity factors in infinite domains is the integral transform. A thick-walled cylinder with an axisymmetric internal or edge crack has been studied by Erdol and Erdogan [1]. The problem is formulated in terms of a singular integral equation which has a simple Cauchy Kernel for the internal crack and a generalized Cauchy Kernel for the edge crack.…”

Stable crack growth in a surface compression-strengthened hollow cylinder

“…2). The inner and outer radii of the cylinder are given by a and b, respectively, with the inner crack radius given by c and outer crack radius given by d. This problem has been solved for both symmetrical [9] and nonsymmetrical [10] axial stress distribution a z. For the axisymmetrical stress distribution, the mixed boundary value problem depicted by Fig.…”