Fatigue of Flexible Risers Considering Alternative Constitutive Models
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- Institutt for marin teknikk 
The flexible riser is made up of both polymeric layers and steel layers, including steel tendons. Due to internal pressure and tension of the pipe, the tendons act with a normal force on the layer underneath. In the beginning when the riser is being bend, the frictional force will prevent the layers from slipping. However, for a given bending moment, these layers slip. This interaction between the layers results in a non-linear response.The main purpose of this thesis was to investigate on the dynamic response and fatigue estimate when taking this non-linear behaviour into account. Most of today's current practice assumes a linear behaviour with a low bending stiffness, resulting in an overly conservative estimate. To examine this non-linear response, three different material models were established: One non-linear model, representing the stick-slip effect due to friction between the layers, and two linear models. The linear models differ in which stiffness was used: Either the stiffness corresponding to when the pipe is depressurised, or when it is fully pressurised and assuming that the pipe layers cannot slip.The process was carried out in the following way: First, the global response of a flexible riser was calculated. This was done for each of the three models, and the tension and curvature history was printed out. This was used as input to a detailed local model, which was able to calculate the stresses in the tendons along the cross section. Based on the stress history, the fatigue damage was calculated. The response for regular waves heading in plane and in 45 degrees was checked, along with one irregular sea-state.The non-linear model estimated a yearly damage about 25\% higher than the linear stick-stiffness model. The linear slip-stiffness model, which is the model closest to today's practice, predicted a damage 7 times greater than the non-linear model. This model seems to predict an overly conservative answer both in terms of the dynamic response and the fatigue damage. With regard to the time consumption, the non-linear model took about three times longer to complete. By using a dedicated analysis computer, a full irregular analysis could be done in about four days.The increased motion of the vessel when waves were heading in 45 degrees led to an earlier slip of the layers. This led to a slightly higher difference in damage between the non-linear and the linear slip-stiffness model. Thus, hysteresis seems to be more critical when the waves lead to motion about all axes, given that the waves are equal.These results showed that taking the non-linear stick-slip effect into account could significantly reduce the predicted damage, compared to using the overly conservative linear slip-stiffness model. This can be applied to prove that designs, which before was deemed unviable by using a linear model, is safe with respect to fatigue. This opens up for the use of lower-cost solutions while still proving the design to be safe. With the performance of today's computers, taking this stick-slip effect into account is a realistic option.