Some analytical remarks on the influence of phase angle on stress fields ahead of sharp V-notches under tension and torsion loads

The effect of out-of-phase loadings in multiaxial fatigue is still an open problem which is of interest for engineers and researchers engaged with design against fatigue. In the present contribution, the effect of the phase angle on sharp V-notches subjected to multiaxial fatigue loading is theoretically studied with an analytical frame based on the maximum shear stress averaged over an entire fatigue cycle. The formulation is applicable as it stands to varying V-notch opening angles, biaxiality ratios and phase angles. The proposed frame has in common with critical plane approaches, which in principle cannot be straightforwardly applied to sharp V-notches, the consideration of the shear stress as critical parameter but uses the notch stress intensity factors to describe the asymptotic stress distributions in the highly stressed region surrounding the V-notch tip. Based on linear elastic stress fields, the frame does not take into account the non-linear effects related to cyclic plasticity. Some considerations on the effect of the phase angle can be drawn on the basis of the obtained results. The main conclusion is that the phase angle plays a non-negligible effect on the fatigue strength of pointed notches. This effect is strongly influenced by the biaxiality ratio.