Multiaxial fatigue life prediction by equivalent energy-based critical plane damage parameter under variable amplitude loading

A new path-independent multiaxial fatigue damage parameter sigma n*$$ {\sigma}_n<^>{\ast } $$, which is defined as the largest normal stress range between adjacent turning points of the maximum shear stress on the critical plane, is proposed to describe multiaxial fatigue damage. By combining the maximum normal stress sigma n,max$$ {\sigma}_{n,\max } $$ or the largest normal stress range sigma n*$$ {\sigma}_n<^>{\ast } $$ with the maximum shear stress range on the critical plane, two axial equivalent stress modification factors, keq sigma$$ {k}_{\mathrm{eq}}<^>{\sigma } $$ and keq sigma*$$ {k}_{\mathrm{eq}}<^>{\sigma \ast } $$, are proposed, which can account for the influence of non-proportional additional hardening. The sensitivity of the proposed axial equivalent stress modification factors to multiaxial variable amplitude loading sequences is analyzed. Furthermore, two new multiaxial fatigue damage models based on the axial equivalent stress modification factors are proposed to estimate fatigue life. The applicability of the presented methodology was verified by the experimental data of En15R steel and 7050-T7451 aluminum alloy, and the results showed that the predicted fatigue lifetimes agree well with the experimental data under variable amplitude multiaxial loading.