Effective Fatigue Stress and Criterion for High-Cycle Multi-axial Fatigue

Multi-axial fatigue criterion corresponding to the limiting condition of complicated multi-axial stress state is very important in application. Stresses and deformations are usually elastic if cyclic loadings are near to the limiting condition. A definition of effective fatigue stress has been proposed. Adopting the effective fatigue stress, a multi-axial fatigue criterion has been proposed by considering the equivalence of multi-axial stresses to a uni-axial problem. To clarify the fatigue criterion for a uni-axial problem with arbitrary mean stress, a quantitative relationship between fatigue limit and mean stress has also been proposed and examined. To verify the multi-axial fatigue criterion, examinations have been carried out for the cases of pure shear, shear and axial, and two-axial fatigue by experimental results. It is found that the criterion agrees well with experimental results, even for the cases with various multi-axial mean stresses and phase differences. It is also found that the shear fatigue limit is not an independent material property in common metals.