A new four-dimensional ratcheting boundary: derivation and numerical validation

Jun Shen, Haofeng Chen, Yinghua Liu

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A new four-dimensional ratcheting boundary is derived analytically for the first time considering the interaction among four types of stresses: constant mechanical membrane stress, mechanical bending stress, cyclic thermal membrane stress, and thermal bending stress. A uniaxial beam model is used to derive the closed-form ratcheting boundary for these combined cyclic and constant loadings. The Tresca yield condition and elastic-perfectly plastic behavior are assumed. A novel two-plane FE model is proposed for numerical validation and the results predicted by analytical solution agree very well with that obtained by two-plane FE model. The solution of the classical Bree problem is the one of special cases when this new four-dimensional ratcheting boundary is reduced into two-dimensional style. The relationship between the three-dimensional ratcheting boundary adopted by the newly implemented ASME VIII -2 Pressure Vessel Code and the proposed four-dimensional ratcheting boundary is also discussed.
Original languageEnglish
Number of pages29
JournalEuropean Journal of Mechanics - A/Solids
Publication statusAccepted/In press - 2 Mar 2018


  • ratchet boundary
  • shakedown
  • two-plane model
  • plastic FEA
  • noncyclic method

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