Abstract: A new multi-axial fatigue model based on the ellipse equation is developed. The model is based on the concept of critical plane, uses the parameters of maximum shear strain amplitude and normal strain excursion in the critical plane, and considers the effect of additional cyclic hardening by introducing maximum equivalent stress. Theoretical analysis shows that the model can degenerate to the traditional strain based life prediction model under uniaxial tension or torsion loading, which proves the good compatibility of the new model. By adopting the multi-axial fatigue test data of 304 stainless steel and S45C steel, the life prediction scatter band and standard error of the model are compared with those of the traditional multi-axial fatigue life prediction models, which indicates that the scatter band and standard error of the life predicted by the new model are least. The analysis shows that the new model can be applied to both proportional and non-proportional loading in many materials with low life scatter band and standard error. The computation is simple and feasible.

Key words: Elliptic equation form, Multi-axial fatigue, Non-proportional multi-axial loading