In-plane biaxial fatigue life prediction model for high-cycle fatigue under synchronous sinusoidal loading

The unique advantage of in-plane biaxial loading is no rotation of the maximum principal stress during cyclic loading, which has a distinct effect on fatigue life. This study aims to propose a life prediction model for in-plane biaxial fatigue encompassing both in-phase and out-of-phase conditions. For synchronous sinusoidal loadings, an equivalent stress expression is derived using the integral method, accounting for the influences of shear and normal stresses across all planes. The equivalent stress is then compared to a reversed uniaxial constant amplitude loading to predict fatigue life. To validate and compare the model, in-phase and out-of-phase in-plane biaxial fatigue experiments were conducted using 24 nickel-based superalloy cruciform specimens at temperatures of 420℃, 550℃, and 600℃. The results show that the proposed model is superior to conventional stress-invariant based models, with most results staying within the ± 2 error bands. Using the proposed model, the effects of mean tensile stress, biaxiality and phase shift are discussed. Additionally, a novel non-proportional factor is introduced to enhance multiaxial fatigue life prediction by distinctly separating the effects of principal stress and its directional variations.