Combined resolved shear stresses as an alternative to enclosing geometrical objects as a measure of shear stress amplitude in critical plane approaches

• We propose a new measure of equivalent shear stress amplitude.
• The measure differentiates proportional from non-proportional stress paths.
• The measure is simple and fast to calculate.
• Fatigue limit estimates using the new measure lie within an error band of ±15%.

A measure of shear stress amplitude based on a combination of resolved shear stress amplitudes on two perpendicular directions of a material plane is investigated in this paper. This measure is very fast to calculate. Hence, it turns unnecessary numerical schemes to accelerate the critical plane search, as well as it enables to significantly reduce the processing time of finite element based fatigue calculations, even when small angle increments are used. Findley’s relationship with the proposed shear stress amplitude provided estimates within a ±15% error interval for published fatigue limits obtained under proportional and non-proportional multiaxial loadings. The accuracy and computational cost of the approach are compared with those obtained with other measures of shear stress amplitude available in the literature.