Issue 31

A.R. Maligno et alii, Frattura ed Integrità Strutturale, 31 (2015) 97-119; DOI: 10.3221/IGF-ESIS.31.08 113 Analytical Study: Stage 2 In order to further investigate inversion of the trend of the stress–intensity-factor, an analytical approach was carried out. The overall procedure for the analytical study was based on the following steps: 1) Evaluation of an area of the cracked conductor at different crack extensions; 2) Evaluation of the cracked conductor’s moment of inertia; 3) Determination of the position of the neutral axis (NA) for the cracked conductor; 4) Estimation of the moment of inertia of the combined system (cracked conductor/casing pipes); 5) Determination of the position of the NA of the combined system; 6) Assessment of the updated distance from the crack; 7) Stress assessment in the conductor at the crack level; 8) Evaluation of stress intensity factors for different crack extensions. The Roark's Formulas [26] were used to calculate the second moment of inertia of the cracked conductor. The area and distances from the centroid to extremities can be calculated using the following formulae for a sector of the hollow circle (Fig. 23): ) 2( t R t A    (10)                      R t R t R y c 2 1 1 3 sin2 1 1   (11)                                3 cos 3 sin2 1 ) 2(3 sin2 1 R t R t R y c (12)  sin 1 R x c  (13) All the terms present in the previous expressions are explained in Fig. 23. Figure 23 : Sector of hollow circle [26]. The moment of inertia about the central axis X for different values of angle  is given by the following expression:                                    2 2 2 2 2 2 3 3 2 2 3 6 1 ) 2( 3 sin sin2 cos sin 4 2 3 1 R t R t R t R t R t R t R t tR I x        The analytically determined stress intensity factors (related to the bending stress of 1 MPa applied on the external surface of the conductor) were plotted versus the crack position  . The respective curve in Fig. 24 shows a very close agreement between the values of the inversion angles, calculated with FE analyses (nearly 85 o ) and analytical analysis (nearly 82 o ). Stage 3 The crack-propagation analysis at Stage-3 was carried out when the crack in the conductor pipe was prevented to grow further because its crack front reached the compression zone. The FE mesh of the model at the end of Stage 2 (after crack in the conductor pipe reached TW5) was modified as illustrated in Fig. 25, and the crack-propagation analysis started until the crack propagating in the casing pipe through its thickness became a through-the-thickness crack. In this case, the residual ligament in the conductor was deemed to remain of constant size throughout the simulation.