A direct method on the evaluation of ratchet limit

H.F. Chen, Alan R.S. Ponter

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This paper describes a new Linear Matching Method (LMM) technique for the direct evaluation of ratchet limit of structure subjected to a general cyclic load condition, which can be decomposed into cyclic and constant components. The cyclic load history considered in the paper contains multi-load extremes to include most complicated practical applications. The numerical procedure is described which uses LMM state-of-the-art numerical technique to obtain a stable cyclic state of component, followed by a LMM shakedown analysis, to calculate the maximum constant load, i.e. the ratchet limit, which indicates the load carrying capacity of the structure subjected to cyclic load condition to withstand an additional constant load. This approach is particularly useful in conjunction with the evaluation of the stable cyclic response, which produces the cyclic stresses, residual stresses and plastic strain ranges for the low cycle fatigue assessment. A benchmark example of holed plate under the combined action of cyclic thermal load and constant mechanical load is presented to verify the applicability of the new ratchet limit method, through the comparison with published results by a simplified method assuming a cyclic load with two extremes. To demonstrate the efficiency and effectiveness of the method for complicated cyclic load condition with multi-load extremes, a composite thick cylinder with radial opening subjected to cyclic thermal loads and constant internal pressure is analyzed using the proposed ratchet limit method. The further verification by the Abaqus step-by-step inelastic analysis demonstrates that the proposed new method provides a general-purpose technique for the evaluation of ratchet limit, and has both the advantages of programming methods and the capacity to be implemented easily within a commercial finite element code Abaqus.
Original languageEnglish
Article number041202
Number of pages8
JournalJournal of Pressure Vessel Technology
Issue number4
Publication statusPublished - Aug 2010


  • shakedown
  • ratchet limit
  • stable cyclic state
  • linear matching method


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