Issue 31

A.R. Maligno et alii, Frattura ed Integrità Strutturale, 31 (2015) 97-119; DOI: 10.3221/IGF-ESIS.31.08 106 FE Results: Casing The same methodology described in Section 3.2 was used to evaluate the minimum size of an elliptical surface crack on the inner wall of the casing tube. Therefore, by means of the stress intensity factor K I , calculated analytically for different stress ranges and crack sizes, the number of fatigue cycles was evaluated and compared with the levels of the S-N curve of Quality Category 2 in Code BS7910. This iterative process was carried out until a close match was found. Using the K I values for different a/B ratios from the analytical solution, a polynomial curve K 1 =8.724( a/B ) 3 – 14.796( a/B ) 2 + 12.583( a/B ) + 0.4198 (9) was fitted. The minimum value of a evaluated analytically was 3.18 mm, and the number of fatigue cycles evaluated under the reference stress range of 80 MPa was nearly equal to 2.03×10 6 . In order to achieve the fatigue life closer to 2.03×10 6 cycles, further iterations were carried out using Zencrack software to determine the minimum crack size. As described in Section 3.2.3, the finite-element model of the casing pipe was developed to evaluate the residual life based on fracture mechanics and using the Paris growth law with material parameters, A = 5.21×10 -13 and m =3. Crack-propagation analyses with the initial elliptical (semi-circular) crack with a (minor-axis) values of 3.184 mm and 2.873 mm were carried out and the number of fatigue cycles compared with the S-N curve (Tab. 4 and 5). Stress range Cycles ( S-N curves) Cycles (FE solution) 300 3.852E+04 3.4968E+04 80 2.031E+06 1.8440E+06 50 8.320E+06 7.5530E+06 20 1.300E+08 1.1802E+08 Table 4 : Comparison of S-N curve data and numerical results for 3.184 mm initial "calibration" crack Stress range Cycles ( S-N curves) Cycles (FE solution) 300 3.852E+04 3 .8172E+04 80 2.031E+06 2.0130E+06 50 8.320E+06 8.2452E+06 20 1.300E+08 1.2883E+08 Table 5 : Comparison of S-N curve data and numerical results for 2.873 mm initial crack In order to get the residual life closer to the target value of 2.03x10 6 cycles, further FE analyses were carried out and the initial value of a = 2.839 mm was determined (Tab. 6). Stress range Cycles ( S-N curves) Cycles (FE solution) 300 3.852E+04 3.856E+04 80 2.031E+06 2.033E+06 50 8.320E+06 8.328E+06 20 1.300E+08 1.301E+08 Table 6 : Comparison of S-N curve data and numerical results for 2.839 mm initial crack The crack propagation profiles showing the elliptical crack (symmetrical model) growing from its initial size a = 2.839 mm to the outer wall of the pipe are shown in Fig. 12.