Issue 31

A.R. Maligno et alii, Frattura ed Integrità Strutturale, 31 (2015) 97-119; DOI: 10.3221/IGF-ESIS.31.08 102 Figure 5 : Trend of K I vs . a/B for deepest point of conductor’s crack. Using the curve fitting techniques, a curve was fitted through the tabulated values for a/B , on the X-axis, and SIFs, related to the maximum fibre stress of 1 MPa, on Y-axis, as shown in Fig. 5. The polynomial equation representing this curve is: K I =10.68( a/B ) 3 - 18.122( a/B ) 2 + 15.411( a/B ) + 0.5142 (4) This equation was used to perform analytic crack-propagation calculations to estimate the initial crack size. Finite-element strategy After the preliminary analysis, a finite-element (FE) model was developed to evaluate the residual life of the pipe system under study with an initial semi-circular crack. The details of the numerical model used for the crack growth FE analyses are shown in Fig.6. (a) (b) Figure 6 : FE model used in the crack propagation analysis: (a) mesh without crack; (b) mesh with crack and position of nodes of interest. The Thickness node will degenerate into the External Surface node while reaching the external surface. The elements used were full-integration 20 -node hexahedral elements. In the model with the crack, Zencrack introduced the crack details by replacement of a line of eight elements with crack blocks, resulting in the FE model of the cracked pipe. The mesh of the crack so created was a focussed mesh, consisting of quarter-point crack-tip elements along the crack front with r -1/2 singularity. The number of elements in the FE models with the crack and without it (conductor and casing separately considered) was never less than 135000. The node lying on the outer radius is referred to as external surface node , the node on the inner radius as internal surface node and the node on the wall thickness as thickness node (Fig. 6b). Estimation of Initial Crack Size for S-N Relation A comparison of the stress intensity factors, evaluated at the deepest crack-front point, for different initial crack configurations, is presented in Tab.3. As demonstrated in Tab. 3, the analytical and numerical values show excellent agreement and confirm that this type of meshing is suitable for crack-growth predictions. The maximum discrepancy in these results is equal to nearly 1.7% (for a/B = 0.8).