Integrating von Mises and hydrostatic stresses in frequency domain multiaxial fatigue criteria for vibration fatigue analysis

The article presents a multiaxial fatigue criterion in the frequency domain. The criterion uses the power spectral density of the hydrostatic stress, the stress consistent with the von Mises criterion and determines the equivalent power spectral density as the sum of these quantities for further use in fatigue analyses. The methodology for deriving the criterion weights in two cases of determining the equivalent tensile stress and equivalent torsion is presented. An algorithm for determining fatigue life according to this criterion, specifically for vibration fatigue, is developed and presented. Verification of the proposed criterion was conducted using experimental fatigue test results from the literature. These tests involved cruciform specimens subjected to varying phase shifts between load components. The experimental verification confirmed the accurate performance of the criterion. The developed algorithm was applied in FEM-supported fatigue calculations for a simple component subjected to random vibration. The simulation considered three load combinations with specified correlations and two material compositions. It was shown that the developed criterion correctly takes into account differences in SN curves for tension and torsion and responds to the correlation of stress tensor components.