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