Back-to-back pipe bends are widely adopted applications in many industries including nuclear sectors. Evaluation of their load bearing capability under complex cyclic loading is very important. Recently, a couple of research reported shakedown boundary of a 90° back-to-back pipe bends by adopting a conservative approach but no comprehensive post yield structural behaviors have been dealt with. In this research the concerning pipe bends subjected to cyclic opening in-plane (IP)/out-of-plane (OP) bending and steady internal pressures are analyzed to construct shakedown and ratchet limit boundary by means of the Linear Matching Method. Analyzed results present that the concerning pipe bends under out-of-plane bending has higher resistance to cyclic bending than under in-plane bending. In additions, the out-of-plane bending causes very small alternating plasticity areas, unlike the in-plane bending. Full cyclic incremental analyses known as step-by-step analysis are performed to verify the structural responses either side of each boundary and confirm correct responses. Parametric studies are carried out with respect to changes in geometry of the concerning pipe bends subjected to the same loading, and semi-empirical equations are derived from relationships of the reverse plasticity limit and the limit pressure with the bend characteristic. This paper offers broad understandings of structural responses of the 90° back-to-back pipe bends under the complex cyclic loading as well as providing key points to be considered for the life assessment of the piping system.

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