Shakedown, ratchet, and limit analyses of 90° back-to-back pipe bends under cyclic in-plane opening bending and steady internal pressure

Nak-Kyun Cho, Haofeng Chen

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A 90° back-to-back pipe bend structure subjected to cyclic in-plane bending moment and steady internal pressures is analysed by means of the Linear Matching Method (LMM) in order to create the limit, shakedown, and ratchet boundaries. The analyses performed in this work demonstrate that the cyclic moment has a more significant impact upon the structural integrity of the pipe bend than the constant pressure. Full cyclic incremental analyses are used to verify the structural responses either side of each boundary and confirm correct responses. In addition, the shakedown boundary produced by the LMM is compared to another shakedown boundary of an identical pipe bend computed by the simplified technique and it is shown that the LMM calculates results more accurately. Parametric studies involving a change of geometry of the pipe bends and loading type are carried out. From the studies of the geometry, two semi-empirical equations are derived from correlations of the reverse plasticity limit and the limit pressure with the bend characteristic. Finally, the results presented in this paper provide a comprehensive understanding of post-yield behaviours of the 90° back-to-back pipe structure under the combined loading as well as offering essential points to be concerned for the life assessment of the piping system.
Original languageEnglish
Number of pages26
JournalEuropean Journal of Mechanics - A/Solids
Publication statusAccepted/In press - 7 Oct 2017


  • pipe bends
  • shakedown
  • rachetting
  • reverse plasticity
  • linear matching method (LMM)
  • 90° back-to-back pipe bend

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