Issue 31

A.R. Maligno et alii, Frattura ed Integrità Strutturale, 31 (2015) 97-119; DOI: 10.3221/IGF-ESIS.31.08 101 Figure 4 : Surface flaw of internal cylinder. This error was possibly due to a mistake in equation M24 for the contribution of stress due to the global bending moment. It was therefore decided to use the procedures described in the publication, “Stress Intensity Factor and Limit Load Handbook” edited by British Energy Generation Ltd [23]. The equation used to calculate the SIFs at the deepest point of the elliptical crack is: 3 0 2 2 , , , , i i I i i bg bg i r r a c a c K a f f B a B B a B                          (2) The sizes considered for the cylinder (conductor pipe) are:  outer radius r o = 18";  wall thickness ( B ) = 1.5";  internal radius r i = 16.5”;  the dimensions of the planar circumferential elliptical crack on the inner wall of the cylinder are a and 2 c , where a is the depth and 2 c the length measured at the inner radius (Fig. 4). The values of the coefficient f bg used in the analytical evaluation of the SIFs and the calculated values of SIFs are given in Tab. 2. The term  bg in Eq. 2 is defined as the maximum outer-fibre bending stress. The SIF values have been determined for the following ratios a / B : 0.01 (~0.0); 0.2; 0.4; 0.6 and 0.8. The tabulated coefficients for Eq. 2 are provided in [23]. The (mode-I) stress intensity factor at the deepest point of the crack has been calculated for the following ratio between the crack depth a and half-arc length c : a/c = 1 This ratio is assumed to remain constant throughout the analytical calculation. This assumption was considered acceptable in the preliminary calibration study. Since in this study only bending stresses are taken into account, Eq. 2 can be simplified as follows: 2, , i I bg bg r a c K a f B a B                (3) SIFs in Tab. 2 are given for unit outer fibre stress. The trend of the stress intensity factor I K is shown in Fig. 5. a / B a [mm] a/c f bg I K Bending stress 1 MPa 0.01 0.381 1.0 0.599 0.655 0.2 7.62 1.0 0.613 2.999 0.4 15.24 1.0 0.636 4.401 0.6 22.86 1.0 0.659 5.585 0.8 30.48 1.0 0.685 6.703 Table 2 : Coefficients f bg and SIFs for a range of crack sizes.