Slip and stress of tensile armors in unbonded flexible pipes close to end fitting considering an exponentially decaying curvature distribution

Abstract

An analytical model is given to investigate the end-fitting effect on slip and stress of tensile armors in unbonded flexible pipes under tension, torsion and varying bending in the absence of friction. An exponentially decaying curvature distribution is assumed to represent controlled curvature over the end region. The deviation from the initial helical angle is taken to describe the armor wire path as the pipe is stretched, twisted and bent, which is determined by minimization of the strain energy functional using the Euler equation. The obtained simultaneous differential equations are numerically solved by transforming them into a boundary value problem. An analytical solution is found by neglecting the twisting rotation of the wire cross-section. The developed model is validated with a finite element simulation and geodesic based analytical expressions for constant curvature and with a current numerical model for varying curvature. Reasonable correlations are observed between the model predictions and the results from other methods. The validated model is then applied to typical flexible pipe designs to find the level and location of the greatest increases in stress. The results show that the end restraint could cause a significant stress increase in the armor wire at the end fitting vicinity and the critical location is close to the extreme fiber position on the compressive side of the pipe for typical cases. The effect of end restraint on layer bending stiffness is also evaluated.