Issue 31

A.R. Maligno et alii, Frattura ed Integrità Strutturale, 31 (2015) 97-119; DOI: 10.3221/IGF-ESIS.31.08 99 X80 steel (Casing) X65 steel (Conductor) Young’s modulus [GPa] 210 Poisson ratio (µ) 0.3 Yield stress [MPa] 550 448 Fracture Toughness (K IC) 7115 MPa  mm (225 MPa  m) Table1 : Material properties. (a) (b) Figure 2 : Numerical model of wellhead system: (a) full-system (A refined mesh was used in the cracked region; the crack is placed at L/2); (b) cross section of conductor/casing system in this study. Loading and Boundary Conditions The applied load is a bending moment at the reference point (RP), shown in Fig. 2, which corresponds to a cyclic stress with a magnitude of 1 MPa (R=-1) on the outer surface of the conductor pipe. This is then scaled to get the required stress value, when needed. The initial study was based on the stress value of 80 MPa at the outer face of the conductor pipe. In the finite-element model, two loading surfaces are “constrained” together to the RP via kinematic coupling. The boundary conditions are described with the help of Fig. 2:  The bending moment was applied to RP (reference point) and via a kinematic coupling constraint to nodes on the remote end face at Z = L.  The conductor and casing were constrained to undergo zero displacements at Z = 0. Boundary Conditions: Kinematic vs Distributing Coupling A separate study was performed to check the adequacy of this coupling compared to the distributed boundary conditions. Kinematic coupling was enforced in a strict master-slave approach [20]. Degrees of freedom (DOFs) at the coupling nodes were eliminated, and the coupling nodes were constrained to move with the rigid-body motion of the reference node. Generally, kinematic coupling constraint does not allow relative motion among the constrained DOFs, while allowing relative motion of the unconstrained ones.Distributing coupling was enforced in an average sense [20]. DOFs at the coupling nodes were not eliminated. Rather, the constraint was enforced by distributing loads such that the resultants of the forces at the coupling nodes were equivalent to the forces and moments at the reference node, and force and moment equilibrium of the distributed loads about the reference point was maintained. A distributing coupling allows relative motion of the constrained and unconstrained DOFs. The effect of these two different coupling constraints should be evaluated during the crack propagation in the conductor and casing as depicted in Fig. 3. The kinematic coupling