End Fitting Effect on Stress Evaluation of Tensile Armors in Unbonded Flexible Pipes Under Axial Tension

This paper deals with the effect of termination restraint due to end fitting on the stress evaluation of tensile armors in unbonded flexible pipes under axial tension. The problem is characterized by one single armoring tendon helically wound on a cylindrical supporting surface subjected to traction. The deviation from the initial helical angle is taken to describe the armor wire path as the pipe is stretched. The integral of this angle change gives lateral displacement of the wire, which is determined by minimization of the energy functional consists of the strain energy due to axial strain, local bending and torsion, and the energy dissipated by friction, leading to a variational problem with a variable endpoint. The governing differential equation of the wire lateral displacement, together with the supplementary condition, is derived using the variational method and solved analytically. The developed model is validated with a finite element simulation. Comparisons between the model predictions and the finite element results in terms of the change in helical angle and transverse bending stress show good correlations. The validated model is then applied to study the effects of imposed tension and friction coefficient on the maximum bending stress. The results show that the response to tension is linear and friction could significantly increase the stress at the end fitting compared with the frictionless case.