Elastic core concept for modified Bree problems considering in-phase and out-of-phase loading conditions

The elastic core concept developed from the Bree problem can be used for structural integrity evaluation of high temperature components, such as creep ratcheting and creep fatigue. The simplified inelastic analysis method of the ASME 2013 III-1 NH Code adopts the idea of core stress, which protects against creep rupture and collapse of the structure by limiting the accumulated inelastic strain. Currently, the formulas of core stress and evaluation diagram of effective creep stress parameter for Tests B-1 and B-3 adopted by the APPENDIX NH-T are developed from the classical loading Bree problem, however, the related concepts and evaluation diagrams of modified Bree problems considering generalized loading conditions have not been reported. This paper first reviews the development history of the elastic core concept and its corresponding analysis methods. Based on the modified Bree problems considering in-phase and out-of-phase loading developed by Bradford, the corresponding formulas of the core stress in the non-plastic ratcheting zone are completely proposed, and the corresponding evaluation diagrams of effective creep stress parameters are constructed for the first time. By comparing the core stress formulas and effective creep stress parameter diagrams under three loading cases, the conservatism and applicability of the classical core stress method are discussed. In addition, the differences and relations between two creep ratcheting assessment methods applicable to transient and sustained thermal load conditions respectively are clarified. The new results and conclusions presented in this paper can deepen the understanding of structural response under complex loading conditions, and provide guidance for shakedown analysis and creep ratcheting assessment of high-temperature components.