A critical assessment of methods for the determination of the shear stress amplitude in multiaxial fatigue criteria belonging to critical plane class

•A comparison of the definitions of shear stress amplitude in fatigue is carried out.•An alternative definition of mean value of shear stress is proposed.•A new method for the determination of shear stress amplitude is presented.•Attention is focused on the concept of equivalent shear stress function.

Multiaxial high cycle fatigue criteria based on the critical plane approach necessitate unambiguous definitions of the amplitude and mean value of the shear stress (τa and τm) acting on the material planes. Four of the existing definitions relate the values of τa and τm to a geometrical element of the curve described by the tip of the shear stress vector (curve Ψ), respectively, the radius of the Minimum Circumscribed Circle, the Longest Chord, the Longest Projection, the diagonal of the Maximum Rectangular Hull (MRH).In this paper a critical assessment of the above definitions is proposed, focusing on that based on the concept of MRH, which is the most recently developed. The main issues of the comparison are the uniqueness of the solution in the determination of τa and τm, the ability to differentiate proportional and non-proportional stresses, the differences of the values of τa obtained by each of the 4 methods for differently shaped curves Ψ.