Non-symmetric cyclic bending of helical wires in flexible pipes

Troels V. Lukassen*, Steen Krenk, Kristian Glejbøl, Christian Berggreen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


Unbonded flexible pipes have superior fatigue performance as the internal armor layers are allowed to move relative to each other, leading to reduced structural loading. The main interactions between the internal layers are the contact forces and the frictional forces. Frictional interaction leads to a complex non-linear response of unbonded flexible pipes making prediction of cyclic bending fatigue a demanding task. Nevertheless, detailed understanding of local armor wire stresses and the related fatigue phenomena is of paramount importance as unbonded flexible risers are often operated close to their mechanical limits. This paper presents a method for calculating the tensile armor wire loading and the hysteresis effect on flexible pipes when subjected to tension, and non-symmetric cyclic bending. The effect of non-symmetric cyclic bending with different tensile armor lay angles, and frictional conditions are studied. The analysis uses an efficient repeated unit cell finite element model, allowing the analysis to be performed on a desktop computer. The study shows that the tensile armor wires gradually translate towards the compression side of the pipe bending plane, when the unbonded flexible pipe is subjected to combined tension and non-symmetric cyclic bending. In the analysis, cyclic bending is applied until steady-state in the bending response is achieved over a full bending cycle. The global bending response of the flexible pipe and the tensile armor wire loading conditions for fully stabilized non-symmetric cyclic bending become symmetric around the frictionless state for the mean cyclic bending curvature. An approximate analytic model for the tensile armor in the stabilized cycle, based on symmetric bending about the geodesic curve corresponding to the mean pipe curvature, is proposed.

Original languageEnglish
Article number101876
JournalApplied Ocean Research
Number of pages14
Publication statusPublished - 2019


  • Cyclic bending
  • Finite elements
  • Flexible pipes
  • Frictional contact
  • Helical layer
  • Repeated unit cell
  • Tensile armor bending stress


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