The paper presents a comparison of six recently introduced multiaxial fatigue strength estimation criteria to four methods, the large-scope validation of which has already been published. The results obtained for each newer method are analyzed and discussed. From the newer methods, only the criterion by Böhme reaches an estimation quality similar to the best performing criteria. The validation was performed on the FatLim data sets, but the primary focus of the paper is set to analyzing the validation on a smaller AMSD25 data set derived from it. The comparison shows that the application of AMSD25 for validation practice allows users to reduce the number of evaluated test cases, while generally preserving the worst cases showing the weaknesses of various estimation methods.

The paper discusses one of the key features in the multiaxial fatigue strength evaluation—the procedure in which the stress path is analyzed to provide relevant measures of parameters required by multiaxial criteria. The selection of this procedure affects the complete equivalent stress derived for any multiaxial load combinations. Three major concepts—the minimum circumscribed circle, minimum circumscribed ellipse, and moment of inertia methods—are described. Analytical solutions of their evaluation for multiaxial stress state with components described by harmonic functions are provided. The concepts are validated on available experimental data when included into six different multiaxial fatigue strength criteria. The results show that the moment of inertia results in too conservative results. Differences between both methods of circumscribed entities are much smaller. There are indications however that the minimum circumscribed ellipse solution works better for critical plane criteria and for the criteria based on stress tensor transformation into the Ilyushin deviatoric space. On the other hand, the minimum circumscribed ellipse solution tends to shift integral criteria to the conservative side.