The tensile armor behavior of unbonded flexible pipes close to end fitting under uniform bending

A theoretical model is presented to investigate the impact of end fitting on slip and stress of tensile armors in unbonded flexible pipes under axial tension and uniform bending in the presence of friction. The problem is characterized by a single armor wire helically wound around a cylindrical supporting surface which is subjected to tension and bending. The deviation from the initial helical angle is used to describe the path of the armor as the pipe is stretched and bent. The integral of this angle change gives the lateral displacement of the wire, which is determined by minimizing the energy functional that consists of the strain energy due to axial strain, local bending and torsion, and the energy dissipated by friction. This leads to a variational problem with fixed endpoints. The obtained differential equation is transformed into a boundary value problem, which is solved numerically. The developed model is verified using a finite element (FE) simulation. Comparisons between the model predictions and the FE results regarding the transverse slip and local bending stress demonstrate good correlations. The results also show that the theoretical solutions of axial slip and stress are in good agreements with the numerical outputs when the wire starts from the intrados or extrados points. The verified model is then applied to study the effects of imposed tension, global curvature, friction coefficient and initial polar angle on the transverse bending stress at the end fitting. The results show that the end restraint could cause a significant stress increase in the armor wire at the end fitting vicinity. The response is linear with respect to tension but nonlinear to curvature. Friction could significantly increase the stress at the end fitting compared to the frictionless case. The critical location is on the tensile side of the pipe. The effect of initial hoop position on the axial stress is also studied. The fixed condition has no influence on the axial stress in the tendon close to the end when it starts from the intrados or extrados points.