Recent developments in frequency domain multi-axial fatigue analysis

The purpose of this paper is to discuss the recent developments in multi-axial spectral methods, used for estimating fatigue damage of multi-axial random loadings from Power Spectral Density (PSD) data. The difference between time domain and frequency domain approaches in multi-axial fatigue is first addressed, the main advantages of frequency domain approach being pointed out. The paper then critically reviews some categories of multi-axial spectral methods: approaches based on uniaxial equivalent stress (strength criteria, “equivalent von Mises stress”, multi-axial rainflow counting), critical plane criteria (Matake, Carpinteri-Spagnoli, criterion based on resolved shear stress on critical plane), stress-invariants based criteria (Crossland, Sines, “Projection-by-Projection”). The “maximum variance” method and the Minimum Circumscribed Circle/Ellipse formulations defined in the frequency domain are also discussed. The paper critically analyses also non-proportional multi-axial loadings and the role of material fatigue parameters (e.g. S/N curves for bending/torsion) in relation to specific methods. The paper concludes with general comments on advantages and possible limitations in the use of multi-axial spectral methods, with special focus on the assumption of stationarity and Gaussianity in modelling multi-axial random loadings.