A continuum approach to multiaxial high-cycle fatigue modeling for ductile metallic materials

Abstract

In this work we propose a generalization of the endurance function employed in the continuum approach to high-cycle fatigue modeling by Ottosen et al. (2008). The von Mises-type backstress-modified effective stress term of the original formulation is replaced by the non-quadratic Hershey-Hosford function, which introduces flexibility with respect to the predicted fatigue limit in pure shear. While the original model assumes a fixed ratio between the fatigue limits in fully reversed torsion and fully reversed bending of 0.5774 for all materials, the modification enables the ratio to take on values on the interval from 0.5 to 0.5852 by calibration to experimental data that is readily available in the literature. Like the original formulation simplifies to the invariant-based Mises-Sines fatigue limit criterion for proportional stress histories, the current proposal can be written as a Hershey-Hosford-Sines criterion. A systematic validation to experimental multiaxial infinite fatigue life data from eight different mild and semi-hard metals with fully reversed torsion and bending fatigue limit ratios lower than 0.6 demonstrates that the proposed modification increases the accuracy and reduces the number of non-conservative predictions.