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• A multiaxial cycle counting algorithm was proposed for thermomechanical random loading. • An interaction modulus B Ti varying with temperature was proposed. • A prediction model was proposed under multiaxial thermomechanical variable amplitude loading. Based on the Wang-Brown method, a time-dependent multiaxial cycle counting algorithm was proposed under multiaxial thermomechanical variable amplitude loading. By using the proposed multiaxial cycle counting algorithm, a new thermo-mechanical fatigue life prediction method was proposed, in which the pure fatigue damage, creep damage, and the interaction damage taking into account the interaction modulus varying with temperature were calculated for each reversal counted by the cycle counting algorithm. Three types of damage from all the counted reversals for the whole strain-time history were accumulated, and the thermo-mechanical multiaxial fatigue life can be predicted. The thermo-mechanical fatigue experimental data for thin-walled tubular specimen of superalloy GH4169 under multiaxial constant amplitude and variable amplitude loadings were used to verify the proposed method. The results demonstrated that the proposed method can provide very satisfactory prediction results. [ABSTRACT FROM AUTHOR]

• An equivalent energy-based critical plane damage parameter is proposed. • No other additional material constants are needed for the proposed method. • Non-proportional cycle hardening and mean stress can be reflected more perfectly. • The method shows great potential under multiaxial random fatigue loading. Combining the concept of energy on the critical plane, a multiaxial fatigue damage parameter without any weight coefficient was proposed and the effects of non-proportional additional hardening and mean stress on fatigue damage can be reflected more perfectly using an equivalent form of shear strain energy. Furthermore, two sets of experimental data are employed to verify the proposed method, and the sensitiveness to fatigue life of the proposed equivalent stress correction factor is discussed as well. The results show that satisfactory and conservative assessments can be obtained by the proposed method, especially under multiaxial irregular loading with great randomness. [ABSTRACT FROM AUTHOR]