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Strain rate sensitivity will change the cyclic mechanical response of materials under multiaxial thermomechanical fatigue loading; thus, it will lead to errors in fatigue life prediction if strain rate sensitivity is not considered in constitutive simulation. In order to more accurately express the time/rate dependence of viscoplastic behavior, a strain rate sensitivity factor is proposed to modify the viscoplastic function of Chaboche model first. On this basis, a viscoplastic constitutive model considering strain rate sensitivity under multiaxial thermomechanical fatigue loading is proposed, which can describe the varying influence of strain rate sensitivity on cyclic mechanical behavior. Meanwhile, the exponential isotropic hardening rule with the linear term is adopted to characterize the initial rapid softening and subsequent stable softening of the material under fatigue loading at elevated temperature. Moreover, the material‐dependent nonproportional hardening coefficient and the loading path‐dependent rotation factor are used in the kinematic hardening rule to consider the effect of nonproportional additional hardening on the cyclic mechanical behavior of materials. Finally, the proposed method is verified by the stress–strain data of titanium alloy TC4 and Ni‐based superalloy GH4169 under uniaxial and multiaxial thermomechanical fatigue loadings, and a good agreement is obtained. HighlightsThe time/rate dependence of viscoplastic behavior is expressed more accurately.Initial rapid cyclic softening and subsequent stable cyclic softening are described.The effect of nonproportional hardening on cyclic mechanical behavior is considered.The proposed model is verified by two materials with different damage types. [ABSTRACT FROM AUTHOR]

A new calculation approach is suggested to the fatigue life evaluation of notched specimens under multiaxial variable amplitude loading. Within this suggested approach, if the computed uniaxial fatigue damage by the pure torsional loading path is larger than that by the axial tension–compression loading path, a shear strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage; otherwise, an axial strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage. Furthermore, the presented method employs shear strain‐based and axial strain‐based multiaxial fatigue damage parameters in substitution of equivalent strain amplitude to consider the influence of nonproportional additional hardening. The experimental data of GH4169 superalloy and 7050‐T7451 aluminium alloy notched components are used to illustrate the presented multiaxial fatigue lifetime estimation approach for notched components, and the results reveal that estimations are accurate. [ABSTRACT FROM AUTHOR]

A new creep–fatigue damage cumulative model is proposed under multiaxial thermomechanical random loading, in which the damage at high temperature can be divided into the pure fatigue damage and the equivalent fatigue damage from creep. During the damage accumulation process, the elementary percentage of the equivalent fatigue damage increment is proportional to that of the creep damage increment, and the creep damage is converted to the equivalent fatigue damage. Moreover, combined with a multiaxial cyclic counting method, a life prediction method is developed based on the proposed creep–fatigue damage cumulative model. In the developed life prediction method, the effects of nonproportional hardening on the fatigue and creep damages are considered, and the influence of mean stress on damage is also taken into account. The thermomechanical 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 model. The results showed that the proposed method can obtain satisfactory life prediction results. [ABSTRACT FROM AUTHOR]

A fatigue–oxidation–creep damage model that can take into account the effect of multiaxial cyclic feature on the damage mechanism is proposed under axial-torsional thermo-mechanical fatigue loading. In the proposed model, the effects of non-proportional additional hardening on fatigue, oxidation, and creep damages are considered, and the variation of oxidation damage under different high temperature loading conditions is also described. Moreover, the intergranular creep damage needs to be equivalent to the transgranular damage before accumulating with the fatigue and oxidation damages. The fatigue, oxidation, and creep damages can be expressed as the fractions of fatigue life, critical crack length, and creep rupture time, respectively, which allows the linear accumulation of different types of damages on the basis of life fraction rule. In addition, the proposed model is validated by various fatigue experimental results, including uniaxial thermo-mechanical fatigue, axial-torsional thermo-mechanical fatigue, and isothermal axial-torsional fatigue under proportional and non-proportional loadings. The results showed that the errors are within a factor of 2. [ABSTRACT FROM AUTHOR]

The multiaxial thermomechanical fatigue properties for nickel-based superalloy GH4169 in aeroengine turbine discs are investigated in this paper. Four types of axial–torsional thermomechanical fatigue experiments were performed to identify the cyclic deformation behavior and the damage mechanism. The experimental results showed that the creep damage can be generated under thermally in-phase loading while it can be ignored under thermally out-of-phase loading, and the responded stress increasing phenomenon, that is, non-proportional hardening, can be shown under the mechanically out-of-phase strain loading. Based on the analysis of cyclic deformation behavior and damage mechanism, a life prediction method was proposed for multiaxial thermomechanical fatigue, in which the pure fatigue damage, the creep damage, and the interaction between them were simultaneously considered. The pure fatigue damage can be calculated by the isothermal fatigue parameters corresponding to the temperature without creep; the creep damage can be calculated by the principle of subdivision, and the creep–fatigue interaction can be determined by creep damage, fatigue damage, and an interaction coefficient which is used to reflect the creep–fatigue interaction strength. The predicted results showed that the proposed method is reasonable. [ABSTRACT FROM AUTHOR]

• Multiaxial fatigue behavior at high temperature is experimentally characterized. • Fatigue-oxidation-creep damage behaviors are comprehensively captured. • The effect of non-proportional hardening on fatigue behavior is considered. • The notch stress–strain history is determined by the elastic-viscous-plastic analysis. • A new method is proposed to evaluate the fatigue life and applied to a notched bar. In this paper, a new life assessment framework is proposed based on the elastic-viscoplastic modeling and the damage behavior for the structural component under multiaxial non-proportional loading at high temperature. The viscoplastic constitutive model with the ability to capture the non-proportional hardening effect is used to obtain the stress–strain fields, in which a new method based on the rotation of strain axis is proposed to evaluate the notch rotation factor. The damage model, which can comprehensively capture the multiaxial fatigue-oxidation-creep behaviors, is used to assess the failure life. In addition, the proposed framework is evaluated by the life results under proportional and non-proportional fatigue loadings at 650 °C, and the errors are found to be within a factor of 2. [ABSTRACT FROM AUTHOR]

• The competition between protective and harmful effects of oxidation is revealed. • A high-temperature environmental damage model is proposed. • A mechanism based multiaxial thermo-mechanical fatigue life model is proposed. • The normal mean stress and cycle period are used to express competition mechanism. • The temperature dependence of material damage is quantitatively described. In this paper, the competition mechanism between protectiveness and harmfulness of oxidation, as well as the effects of cycle period, mean stress and temperature on the damage behavior of TA15 titanium alloy are revealed under multiaxial thermo-mechanical fatigue loading. Based on the damage mechanism, a high-temperature environmental damage model is proposed under multiaxial thermo-mechanical fatigue loading first, then a life prediction method is developed by combining a multiaxial fatigue damage model. The experimental verification results under uniaxial and multiaxial thermo-mechanical fatigue loadings showed that almost all of the prediction errors are within a factor of 2. [ABSTRACT FROM AUTHOR]

[Display omitted] • Path-dependent line integral multiaxial cycle counting method was proposed. • The proposed method can be reduced to a uniaxial rain-flow counting form. • A recursive algorithm is provided to implement the proposed method. • The proposed method achieved excellent results in fatigue life prediction. A multiaxial cycle counting method was proposed by path-dependent line integral (PDLI). In the proposed PDLI multiaxial cycle counting method, the length increment of loading path is assigned a positive or negative sign in the strain space, and the interval from zero to the maximum value of PDLI is defined as a half-cycle. A very concise recursive algorithm is provided to implement the proposed multiaxial cycle counting method. The experimental verification showed that the proposed multiaxal cycle counting method was used to count multiaxial cycle, which can obtain satisfactory life prediction results under multiaxial variable amplitude loading. In addition, the PDLI multiaxial cycle counting method can be reduced to a uniaxial rainflow counting form. [ABSTRACT FROM AUTHOR]

• A novel method of unconstraint ultrasonic vibration used to heal fatigue damage is proposed. • The fatigue crack initiation life of the polycrystalline copper is increased by 3.0 times. • Microstructure after the unconstraint ultrasonic vibration treatment was almost restored to the original state. • Fatigue resistance of the material was recovered due to the unconstraint ultrasonic vibration treatment. The fatigue performance and microstructure of polycrystalline copper treated by one (UUV1), two (UUV2), three (UUV3) passes of unconstraint ultrasonic vibration (UUV) treatment were investigated in this paper. The surface roughness, fatigue life, microstructure, and plastic strain energy before and after UUV treatment were compared. The results revealed that the surface integrity of the sample for UUV treatment higher than that of the original sample, and the microscope observation found that the grain orientation, the dislocation density, the low angle grain boundaries, the plastic strain energy of the damaged sample restored to the original state to a great extent after UUV treatment. The fatigue crack initiation life increased by 3 times after UUV3 treatment. [ABSTRACT FROM AUTHOR]

• A multiaxial total life prediction method based on short crack growth is proposed. • The additional damage from non-proportional loading path is characterized. • Effect of shear stress on crack growth under tensile/compressive stress is considered. • The proposed method is verified by two materials under multiaxial loading. A total life prediction method based on short crack propagation considering additional damage from non-proportional loading is proposed under multiaxial fatigue loading. Firstly, a new calculation method of equivalent stress range is proposed to consider the effect of shear stress on crack propagation under tensile or compressive stress, then it is further modified to consider the additional damage. Combined with Paris formula and crack closure correction, a total life prediction method is proposed. The life results were used to verify the proposed method for two materials, which showed that most errors are within a factor of 3. [ABSTRACT FROM AUTHOR]

• A modified incremental multiaxial Neuber notch correction method considering temperature change was proposed. • The proposed approximate calculation method can accurately and quickly obtain the notch-root local stress-strain history. • A fast life prediction method is developed under variable amplitude multiaxial thermo-mechanical loading. The modified incremental multiaxial Neuber rule by considering the temperature change was firstly proposed, which combined with the Chaboche viscoplastic constitutive model to approximately compute the notch local stress and strain under multiaxial thermo-mechanical loading. Based on the proposed method, a life prediction method that can take into account fatigue, oxidation, and creep damage was developed, which can quickly predict notch fatigue failure lifetime under variable amplitude multiaxial thermo-mechanical loading. The proposed method was verified by the coupled thermal-structural nonlinear FEA and the experimental life results for the tenon joint structure specimens under eight thermo-mechanical loading paths. The comparison of computed and analyzed stress-strain history showed that a good agreement can be obtained. Comparing with experimental life data, all predicted lives fall in a 2-factor scatter band. [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]

• Positive correlation between individual modulus and fatigue strength was identified. • Fatigue life model considering individual modulus was proposed. • Fatigue life prediction method under variable amplitude loading was proposed. Needled C/SiC composites are widely used in the aerospace field, making the evaluation of fatigue damage critically important. A fatigue damage model associated with the individual modulus is proposed. Compared to the fatigue damage model by S-N curve, the proposed fatigue damage model can better characterize the fatigue damage behavior of UN-C/SiC composites. By combining the rainflow counting method, the Goodman equation, and the Palmgren-Miner damage accumulation rule, a fatigue life prediction method considering the individual modulus is developed for UN-C/SiC composites under variable amplitude loading. Compared with the experimental life, the predicted fatigue life shows a good result. [ABSTRACT FROM AUTHOR]

• Crack initiation on the oversized facet formed by α p phase cluster cleavage is found. • The size of oversized facet can be predicted by the value of stress intensity factor range. • A simplified model is proposed to describe the microstructure short crack propagation. • A full-life prediction model based on crack propagation is proposed in VHCF regime. • A deterministic life prediction model considering the effect of temperature is proposed. The very high cycle fatigue crack initiation mechanism of Ti60 titanium alloy at different temperatures was studied. The results showed that the initiation of cracks occurred on oversized facets in the subsurface. Based on this crack initiation mechanism, a full-life prediction model based on crack propagation at room temperature was first proposed, and then a very high cycle fatigue life prediction model considering temperature was proposed based on the degradation law of tensile strength at different temperatures. The experimental and predicted life results of Ti60 specimen at room temperature with 300 °C and 500 °C showed that the proposed method can effectively predict the very high cycle fatigue life, and the error is within a factor of 3. [ABSTRACT FROM AUTHOR]

• 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]

• A fatigue limit equation considering the high temperature effect is proposed. • The influence of high temperature on fatigue life prediction is considered. • A stress normalized method is used to reduce the effect of composites dispersion. • The life prediction is proposed for composites dominated by compression damage. Fatigue life prediction method based on stress normalization was proposed to reduce the influence of material property dispersion on life for CFRC (carbon fibre reinforced composites). In order to consider the effect of temperature on fatigue damage, a temperature influence factor was introduced into the fatigue limit equation and the life prediction method under variable amplitude loading at high temperature. Combined with the rainflow cycle counting and Miner linear damage accumulation rule, the proposed fatigue life prediction method was verified by the experimental results of composite multidirectional laminates under constant amplitude and variable amplitude loadings at various temperatures, and the prediction errors are within a factor of 5. [ABSTRACT FROM AUTHOR]

• A life prediction model is proposed under tension–compression loading at high temperature. • The effect of strength contribution of different orientation fibre layers is considered. • The proposed model can consider the degradation of matrix properties by high temperature. In this paper, the mechanical properties of carbon fibre reinforced multidirectional laminates at different temperatures were tested. Based on the consideration of the microstructure and fibre layer thickness of the multidirectional laminates, a stress normalized method is proposed. Based on the normalized static ultimate strength and fatigue stress, a life prediction model suitable for the fatigue process dominated by compression damage is proposed at high temperature. The fatigue test results at different temperatures showed that the proposed fatigue life prediction model considering the strength contribution of different orientation fibre layers and the degradation of matrix properties at high temperature can successfully predict the fatigue life of multidirectional laminates at different temperatures, and the life prediction error is within the range of three factors. [ABSTRACT FROM AUTHOR]