PSI - Issue 22

Meng-Fei Hao et al. / Procedia Structural Integrity 22 (2019) 78–83 Meng-Fei Hao et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Mises equivalent strain or stress criterion [6]. However, under out-of-phase or non-proportional loading conditions, the principal axes of stress and strain rotate during cyclic loadings, which often introduced additional cyclic hardening of the material and results into more fatigue damage [7, 8]. Until now, various multiaxial fatigue models have been developed for multiaxial fatigue life prediction, among them, the Fatemi-Socie criterion has been commonly used in practice [6]. Since the fatigue damage of the material is caused by the critical value of shear stress along the slip direction on the slip plane, and then the accumulation of local slip belt, the critical plane is generally located in the maximum shear stress (strain) range plane. However, the normal stress on the critical plane usually accelerate the crack growth process [7, 8], thus it is of great significance to locate the critical plane for fatigue life prediction of engineering components. In particular, various multiaxial fatigue models have been put forward by combining the critical plane-based method with stress/strain-based parameters [9] as well as strain energy-based damage parameters, which combine the effects of loading histories and both states of stress and strain [10-14]. In this regard, this work highlights a strain energy-based critical plane damage parameter for fatigue life assessment of turbine disc alloys under multiaxial loadings. Specifically, it introduces a weight factor to correct the von Mises equivalent stress. Combining the equivalent strain and corrected stress, an equivalent strain energy-based damage parameter is newly developed. Then, experimental data of GH4169, TC4 and Al 7050-T7451 alloys under multiaxial loadings are used for model validation and comparison. Finally, we concludes the current work. Nomenclature ′ Shear fatigue ductility coefficient ′ Fatigue strength coefficient ′

Cyclic strain hardening exponent ′ Shear fatigue ductility coefficient ′ Cyclic strength coefficient Shear strain Shear stress Number of cycles to failure ′ Shear fatigue strength coefficient 0 ′ Shear cyclic strength coefficient Elastic Poisson’s ratio Shear modulus Equivalent strain with shear form Equivalent stress with shear form Tested life Predicted life 0

Shear fatigue strength exponent 0 Shear fatigue ductility exponent 0 ′ Shear cyclic strain hardening exponent , Maximum normal stress 2 Proposed strain energy-based critical plane model Through the von Mises criterion, the shear form of equivalent stress considering the maximum stress stress with the principal stress can be given on the maximum shear strain plane: ∆ 2 = √( ∆ 2 ) 2 + 1 3 ( ∆ 2 ) 2 (1) For the thin walled tubular specimen with strain-controlled mode subjected to tensile loading, the shear stress amplitude, ∆ ⁄2 and the principal stress amplitude, ∆ ⁄2 are equal to the the applied shear stress amplitude, ∆ ⁄2 , and 0. Then, Eq. (1) can be rewritten as follows: