Fatigue Life Analysis of Cruciform Specimens Under Biaxial Loading Using the Paris Equation

The presence of mixed-mode stresses, combining both opening and shearing components, complicates fatigue life estimation when applying the Paris law. To address this, the crack path, along with mode I (opening) and mode II (shear) components, was numerically analyzed using Franc2D based on the linear elastic fracture mechanics (LEFM) approach. Accordingly, fatigue life and stress intensity factors (SIFs) under various biaxial loading ratios (λ) were calculated using the Paris law and compared with available data in the literature. The results show that crack growth is primarily driven by the mode I component, which exhibited the largest magnitude. Thus, KI was adopted for the numerical integration of the fatigue life equation. Furthermore, the influence of normal and transverse loads (σx and σy, respectively) on the crack path and SIF was examined for λ. The analysis revealed that lower λ values lead to faster crack propagation, while higher λ values result in extended fatigue life due to an increased number of cycles to failure. The comparison demonstrates good agreement with reference data, confirming the reliability of the proposed modeling approach over a wide range of biaxial loading conditions.