A simplified strain energy density approach for multiaxial fatigue predictions

Multiaxial fatigue is a critical challenge in industrial applications, where predicting fatigue life accurately is essential for components with complex geometries and out-of-phase loading conditions. These factors make traditional approaches economically demanding, necessitating simplified yet reliable methods. In this work, a simplified fatigue approach based on strain energy density (SED) is proposed, addressing the need for economically sustainable, accurate, and cautionary fatigue predictions. The proposed model employs a single control radius and an effective SED range, simplifying both the calibration procedure and the required data. This effective SED assigns a sign to the strain energy based on the hydrostatic stress. To validate the approach, multiaxial fatigue tests on aluminum alloy 7075-T6 were performed, investigating various combinations of load ratios, multiaxiality grades, and notch severities. Additionally, previously published fatigue data on ductile cast iron specimens were used for further validation. A comparison is provided between the proposed model and a highly accurate but calibration-intensive predictive model, offering designers a practical evaluation of the method’s capabilities and limitations. The simplified criterion, calibrated using two experimental fatigue curves, yields higher errors than the complete formulation in multiaxial fatigue assessments, with RMS errors on stress amplitudes below 30% for the simplified approach and below 16% for the complete formulation. However, predictions remain generally conservative. This approach is also applicable to complex geometries and loading scenarios where stress components from different modes cannot be distinguished.