Reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion

In the present paper, a new computationally-efficient frequency domain formulation of the critical plane-based Carpinteri–Spagnoli (C–S) criterion is proposed to evaluate the fatigue lives of smooth metallic structures subjected to multiaxial random loading. The critical plane orientation is here proposed to depend on the Power Spectral Density (PSD) matrix of the stress tensor. Then, the PSD function of an equivalent normal stress is defined by considering a linear combination of the PSD functions of the normal stress and the projected shear stress along the direction of maximum variance, with such stresses acting on the critical plane. Such an equivalent PSD function allows us to apply the Tovo–Benasciutti method to estimate the fatigue life of the structural components. The present frequency domain formulation of the C–S criterion is applied to some relevant fatigue tests related to smooth specimens under non-proportional bending and torsion random loading.