Creep-fatigue life prediction under fully-reversed multiaxial loading at high temperatures

https://doi.org/10.1016/j.ijfatigue.2006.06.010Get rights and content

Abstract

A multiaxial fatigue damage parameter based on the critical plane approach was proposed to calculate the pure fatigue damage under uniaxial/multiaxial loading at constant high temperatures. For the fully-reversed low-cycle fatigue loading under low frequency at high temperature, one-half of the maximum equivalent stress response value at cyclic stabilization is used as the creep stress to evaluate the multiaxial creep damage. The linear damage accumulation rule is used to predict the multiaxial creep-fatigue life at high temperature. The creep-fatigue experimental data of thin tubular specimens with GH4169 superalloy and 2.25Cr–1Mo steel were used to verify the proposed creep-fatigue life prediction model. The results showed that the proposed creep-fatigue damage calculation model can be used under either uniaxial or multiaxial nonproportional loading at high temperature. The proposed model is used to predict multiaxial creep-fatigue life, and a good agreement is demonstrated with experimental data.

Introduction

Many structural components or elements of modern engines and power plants are subjected to multiaxial cyclic loading at high temperature. Development of the appropriate multiaxial fatigue life prediction approaches is strongly needed for the design purpose of these machine components under operating conditions at high temperatures. In order to predict accurately the service life of these components, it is necessary to take into account the effect of multiaxial cyclic stress/strain loading and creep on the damage. The multiaxial cyclic stress–strain states are either proportional (in-phase) loading or nonproportional (out-phase) loading, so that the relationship between the stress and strain at a high temperature is very complicated due to thermal softening. Therefore, it is difficult to predict the creep-fatigue life, especially under multiaxial nonproportional loading. At present, there have been many investigations on multiaxial fatigue at high temperatures [1], [2], [3]. Some research results indicated that the complex stress–strain characteristics are shown with the change of temperature and controlled strain under uniaxial or multiaxial low-cycle fatigue at high temperatures [4], [5], [6], [7], [8], [9], [10]. A large number of creep-fatigue life prediction models have been developed in the past, such as the linear damage summation rule [11], strain range partitioning method [12], damage-rate method [13], ductility-exhaustion method [14], overstress concept [6] and so on. However, these approaches are usually used for the uniaxial creep-fatigue life prediction. When they are used to predict the multiaxial creep-fatigue life, especially under nonproportional multiaxial loading, more errors can be induced at high temperatures.

The objective of this paper is to develop a unified creep-fatigue damage model on the basis of the multiaxial fatigue experiments at high temperatures as well as the theory of linear damage summation. The creep-fatigue damage model can be used to determine the creep-fatigue life under either uniaxial or multiaxial fully-reversed loading at high temperatures. For the components of aeronautical turbine disk on active service at high temperature, the proposed method can be used a reference approach to predict the life.

Section snippets

Determination of the critical damage plane

For a thin walled tubular specimen used for the tension–torsion multiaxial fatigue test, under the strain-controlled loading condition, the applied strains can be given by the following matrix of the strain tensor:εx1/2γxy01/2γxy-νεx000-νεxwhere εx and γxy are the applied axial and shear strains, respectively.

The strains on the plane that makes an angle θ with the specimen axis, are expressed as:εθ=εx+εy2+εx-εy2cos(2θ)+γxy2sin(2θ)γθ2=εx-εy2sin(2θ)-γxy2cos(2θ)where εy = νεx.

Eqs. (2), (3) can be

Theory of linear damage summation

Creep damage is basically an internal process as a result of initiation and growth of grain boundary cracks or cavities, which depends primarily on the history of stress and temperature applied to the component, while fatigue damage is resulted from the cyclic stress and contains primarily time independent plastic strain [14]. At high temperature, if Miner’s rule and Robinson’s [11] linear damage summation rule are used, the total damage is the linear sum of the fatigue damage independent on

Experimental verification

Two kinds of materials were used to verify the proposed multiaxial creep-fatigue life model. They are the nickel-base superalloy GH4169 and 2.25Cr–1Mo steel, respectively.

Conclusions

  • 1.

    The sinusoidal function analysis approach can be used to determine the orientation of the critical damage plane under multiaxial triangle waveform loading.

  • 2.

    The normal strain excursion between adjacent turning points of the maximum shear strain and the maximum shear strain amplitude on the critical plane are combined as equivalent strain amplitude, which can be used to calculate the pure fatigue damage at high temperature.

  • 3.

    One-half of maximum equivalent stress response value at cyclic

Acknowledgements

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (10172010, 50575004) and Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality.

References (23)

  • L.J. Chen et al.

    Creep-fatigue interaction behavior of a nickel-based superalloy and life time prediction

    J Aeronaut Mater

    (1998)
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