Variance integral method for predicting in-plane biaxial fatigue life under asynchronous sinusoidal loading

The asynchronous fatigue loading typically leads to a more complex damage mechanism and early fatigue failure. In this study, a novel Variance Integral Method (VIM) is proposed based on the framework of the integral method to determine an equivalent stress for fatigue life prediction under asynchronous loading. Firstly, the equivalent stress is obtained by performing a spherical integration of the resolved stress across all material planes, rather than focusing on a critical plane, to avoid the complexity of direction selection. Subsequently, asynchronous in-plane biaxial fatigue experiments were conducted on 8 nickel-based superalloy cruciform specimens at 420 °C, considering variations in frequency ratios and initial phase differences. Predicted fatigue lives under different loading paths were evaluated using the modified Papadopoulos model. The results show that the predicted fatigue lives are in good agreement with the experimental data, with a scatter factor within 2 about the mean life. Additionally, the effects of asynchrony including the frequency ratio and the phase difference effects are discussed. The findings suggest that the in-plane biaxial fatigue loading path does not induce non-proportional additional hardening of materials. © 2025