This paper deals with the fatigue behaviour of complex, three-dimensional, stress concentrations under multiaxial loadings. Starting from the stress field obtained by means of a linear elastic analysis and taking advantage of the so-called implicit gradient approach, a safety factor is calculated for high-cycle fatigue. In this first attempt, attention has been focused on the stress-invariant based approaches in the highcycle fatigue regime. The multiaxial damage evaluation is obtained by analysing the full loading path of the Crossland five-dimensional invariant deviatoric stress in Euclidean space by means of the variance reference frame. Explicit analytical solutions of the proposed criterion are given in the case of biaxial sinusoidal loads. The method was validated by comparison with experimental data involving multiaxial in-phase and out-of-phase loading of specimens which contained three-dimensional stress concentrations. These types of stress concentrations are known to present problems for other predictive methods.
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