Some analytical expressions to measure the accuracy of the "equivalent von Mises stress" in vibration multiaxial fatigue

The “equivalent von Mises stress” (EVMS) was first proposed in 1994 by Preumont and co-workers as a frequency domain reformulation of von Mises stress, for the fatigue analysis of vibrating structures under multiaxial random stresses. The EVMS criterion is a simple, but very powerful tool to estimate fatigue damage with time domain analysis of simulated stress histories, or frequency domain evaluation by spectral methods. Despite its simplicity, the EVMS criterion is based on some inherent assumptions, which may lead to inaccurate damage estimations in some particular conditions (e.g. materials with very different axial/bending and torsion S–N curves). This paper aims to derive some analytical expressions to measure the accuracy of EVMS criterion for various combinations of material fatigue properties and loading conditions (e.g. combined axial/bending and torsion loadings). These expressions constitute an original contribution, as similar analytical approaches have not been proposed in literature. The accuracy of EVMS approach is then tested with typical material fatigue properties from literature. The range of applicability of EVMS criterion is then be identified for specified intervals and combinations of S–N parameters.