Invariant formulation of a gradient dependent multiaxial high-cycle fatigue criterion

Abstract

Experimental evidence has shown that the fatigue limit of metallic cylindrical specimens in fully reversed bending is significantly higher than the respective limit in fully reversed tension-compression. The higher values of the bending fatigue limits observed have to be attributed to the benign influence of the gradient of the bending normal stress on the fatigue strength of the metal. Although many approaches for modelling the gradient effect under uniaxial normal cyclic stress have already been tried, attempts to model the very same problem under multiaxial cyclic stress systems are scarce. The present paper starts re-analyzing existing experimental results under cyclic normal stress (i.e. bending, tension-compression) and under cyclic shear stress (i.e. torsion). This closer examination shows that although the fatigue endurance is strongly affected by the gradient of the normal stress in bending tests, it remains insensitive to variations of the gradient of the shear stress in torsion tests. Based on these observations, a gradient dependent multiaxial high-cycle fatigue criterion function of the stress invariants is formulated.