Issue 31

A.R. Maligno et alii, Frattura ed Integrità Strutturale, 31 (2015) 97-119; DOI: 10.3221/IGF-ESIS.31.08 100 provides conditions that are more realistic for the case with parallel surfaces in the region, in which the bending moment is applied. For this reason this constraint was preferred to the distributing coupling, which allows more freedom to the displacements in the loaded section. (a) (b) Figure 3 : Effect of distributing (a) and kinematic (b) couplings. P RELIMINARY STUDY LEFM-based methodology, which adopted a Paris-crack propagation law, was developed to calculate the crack growth rate and perform initial crack-size calibration exercise for the conductor and the casing considered separately. In order to achieve a close match between the residual life, based on the Paris law, and the fatigue life, based on the weld S-N curves (E class type [18]) in the conductor pipe, the following iterative procedure was implemented:  Determination of initial crack size for the calibration exercise.  Determination of crack-growth data for the appropriate material in a seawater environment (-1100 mV cathodic protection).  Analytical crack-growth analysis for different stress ranges.  Crack-growth analysis from the initial crack to the failure condition using Zencrack.  Comparison of preliminary numerical and analytical data.  Re-adjustment of the initial crack size depending upon the results of the analysis. The outcome of this activity was the determination of the Paris-law data and the initial crack size to be applied in subsequent crack modelling of the conductor/casing system. It is paramount to emphasise that FE simulations were based on linear elastic fracture mechanics with the values of stress intensity factor (SIF) K calculated employing the J contour integral [21-22]. SIFs were calculated at multiple points along the crack [16, 17]. The failure condition was assumed to occur when the crack either grows through the wall thickness (and reaches the opposite surface) or reaches an unstable crack size (critical K ) under the applied cyclic loading. Analytical Evaluation of Stress Intensity Factor K I An analytical expression was derived to estimate the stress intensity factor as a function of crack depth. This was subsequently used to estimate the initial crack size for the finite-element calibration analysis. A number of available publications [18, 23] were considered to evaluate analytically the stress intensity factors at the deepest point of an elliptical crack located circumferentially on the inner wall of a cylinder as shown in Fig. 4. The procedure described in BS 7910 [18] using Eq. 1 for the evaluation of SIFs was found to give non-reliable results due to an error in the value of the term ( Y  ) as prescribed in the equation M24 of the Annex M of BS 7910: ( ) I K Y a    (1) A