Investigations of Shear Interaction and Stress in Flexible Pipes and Umbilicals
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- Institutt for marin teknikk 
The present thesis deals with numerical modeling and experimental testing related to dynamic stress behavior of flexible pipes and umbilicals, with particular focus on shear interaction and friction effects. For the extreme load condition, 3D effects related to curvature variations along the length of the helices become important and cannot be dealt with by standard 2D models that basically assume constant curvature, i.e., the stresses at a given cross-section are given by the curvature and tension at that same section alone. In addition to this comes the complexities related the cross-section lay-lout in terms of armors, fillers, etc, which involves multiple contact behavior that will affect the load sharing between helices. This requires models that are capable of accurately predicting both longitudinal and radial relative displacement behavior. As full 3D FE modeling by solid elements would lead to both extreme computation time and numerical issues, the strategy adopted in the present work has been based on sandwich beam theory with dedicated curved beam elements and associated penalty based contact elements that are capable of describing both longitudinal and radial relative displacement behavior in an average sense. The present work focuses on the development of friction models that can describe the longitudinal behavior in the context of sandwich beam theory which can be integrated into penalty based contact elements describing both radial and hoop contacts. The proposed friction models are basically characterized by three parameters, i.e., the shear interaction stick stiffness, the friction coefficient and the contact pressure where the latter is calculated based on the penetration and contact stiffness of the radial and hoop contact elements. The friction models developed were based on applying a constant stiffness parameter and numerical studies were used to establish the required minimum value to firstly represent the plane surfaces remain plane condition without compromising numerical convergence. As smaller stick stiffness was observed in the moment-curvature diagram of a 4 inch flexible pipe full scale test, the stiffness parameter was applied to also include the effect from shear deformation of the plastic layers. The associated stiffness parameter value was confirmed by both numerical studies with reference to the full-scale test data and small scale friction tests where the tensile wire and anti-wear tape were taken from the same 4 inch pipe specimen. Flexible risers are normally exposed to both dynamic tension and bending loads, resulting in dynamic contact pressure between layers. The dynamic contact pressure not only influences the alternating stick-slip-restick conditions, but also determines the slip friction force value. Therefore, the proposed models were designed to calculate the friction stress with updated contact pressure. Significant hysteresis was noted in the moment-curvature diagram obtained from the 4 inch flexible pipe full scale test data even at very low internal pressure. Assuming that the basic source of such behavior is the shrinking of the outer sheath introduced by the manufacturing process, the initial strain concept was applied by prescribing a fixed initial strain value in the outer sheath. This gave consistent results for all test pressure levels and corresponding numerical results, thus pointing the way forward with respect to dealing with this effect in stress analysis. The industry practice with regard to friction modeling is to use a Coulomb friction coefficient taken as an average value between the static and dynamic friction coefficients obtained from testing. As there were some doubts related to the conservatism of this procedure, friction models were established to include both static and dynamic friction coefficients. Numerical studies were then carried out with input from small scale testing to investigate the consequences in terms of stress behavior. Shallow grooves in the anti-wear tape following the helical path of the armor wires were observed in the cross-section of the 4 inch flexible pipe. As this may influence the slip criteria and result in redistributing the friction forces in the longitudinal and transverse directions, an anisotropic friction model was proposed. A sensitive study was then performed to investigate the effects from anisotropic friction on the axial stress behavior. Significant nonlinear 3D effects were observed in the measured axial stresses of a steel tube umbilical exposed to constant tension and variable curvature. The modeling procedure described above was therefore applied for correlation studies where it was noted that the axial stress was very sensitive to the selection of contact spring stiffness and the resulting load sharing between the helical elements. As the cross-section included fillers to avoid direct contact in the circumferential direction of the steel tubes, a hoop contact element was proposed to improve the load sharing behavior. In addition, the constraint in the transverse direction was considered in the numerical model as deep grooves were observed on the surface of inner sheath for the large tube.