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

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Abstract
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 Fracture Analysis Code (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 exhibits the largest magnitude. Thus, the Mode-I stress intensity factor (KI) was adopted for the numerical integration of the fatigue life equation. Furthermore, the influence of normal and transverse loads (σy and σx, respectively) on the crack path plane and SIF was examined for λ. The analysis revealed that lower λ values led to faster crack propagation, while higher λ values resulted in extended fatigue life due to an increased number of cycles to failure. The comparison demonstrated good agreement with reference data, confirming the reliability of the proposed modeling approach over a wide range of biaxial loading conditions.

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