In general, case-hardened components are assumed to have a brittle edge area and a ductile core. An alternating strength ratio of \(\tau _{W}/\sigma _{W}=1\) characterises an ideally brittle material, while ductile behaviour is characterised by \(\tau _{W}/\sigma _{W}=1/\sqrt{3}\) . Regarding the design of shafts, knowledge of the alternating strength ratio is a prerequisite for the correct selection and application of an equivalent stress hypothesis. This is used to calculate a scalar characteristic stress value for multi-axial or non-proportional stress conditions. In practice, however, the required cyclic material parameters are often not available, which is why the material behaviour to be assumed especially for case-hardened shafts remains unknown. The publication first provides an overview of equivalent stress hypotheses used in practice. In order to investigate the potential of the various hypotheses in the context of case-hardened surface layers, fatigue strength tests from the literature are investigated. The test data is used to recalculate the theoretical fatigue strengths which are then contrasted to the corresponding experimental results. A comparison of the equivalent stress hypotheses under variation of the alternating strength ratio shows that a conservative estimation of the safety factor is possible using the distortion energy criterion (also known as von Mises criterion) with less scatter than applying the normal stress criterion. Thus, the assumption of ductile behaviour and consequently the use of an alternating strength ratio of \(\tau _{W}/\sigma _{W}\approx 1/\sqrt{3}\) also appears possible for case-hardened surface layers.
