In the present paper, a simplified critical plane-based criterion is employed to evaluate the multiaxial high-cycle fatigue strength of smooth metallic specimens. According to such a criterion, the critical plane orientation is correlated to the weighted average directions of the principal stresses, and the multiaxial fatigue strength is assessed through an equivalent stress expressed by a quadratic combination of the shear stress amplitude and the amplitude of an equivalent normal stress acting on the critical plane. The criterion is a simplified version of the original Carpinteri-Spagnoli (C-S) criterion. The proposed modifications are related to: the weighting procedure of the principal stress axes; the definition of the equivalent normal stress by taking into account the mean normal stress effect; the expression of the quadratic combination of stresses. Several experimental results related to the high-cycle fatigue strength for smooth metallic specimens, subjected to in-phase or out-of-phase biaxial loading with different mean stress values and various ratios of the stress amplitudes, are analysed by employing the C-S criterion, its simplified version, and other criteria available in the literature.
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