An analytical approach to measure the accuracy of various definitions of the "equivalent von Mises stress" in vibration multiaxial fatigue

This paper aims to review and compare various definitions of the "equivalent von Mises stress" (EMVS), which is used as a criterion to analyse multiaxial stationary Gaussian random stresses in the frequency-domain. Since the original definition of EVMS proposed in 1994 by Preumont and Piéfort, several modified formulations have been suggested by other authors. In particular, this paper focuses on the definitions proposed by Braccesi et al. (2008) and Niesłony (2008). Such modified formulations aimed to correct some incoherencies in the Preumont’s definition of EVMS, which can lead to inaccurate estimations for particular combinations of material fatigue properties. In this work, analytical expressions are derived to check the accuracy of the original and modified EVMS criterion for different random loading types (e.g. pure bending, pure torsion, combined bending plus torsion). Such analytical expressions will allow engineers to understand when the original EVMS criterion and its modifications can safely be applied in fatigue design