PSI - Issue 75

Sgamma M. et al. / Procedia Structural Integrity 75 (2025) 709–718

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Author name / Structural Integrity Procedia 00 (2025) 000–000

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via the maximum damage approach. These findings confirm that the first step of the proposed methodology–using a fast, frequency-domain-based procedure to locate the critical plane–e ff ectively identifies the orientation associated with the most severe fatigue damage.

Fig. 2: Comparison of critical-plane orientations determined by the maximum damage (colorplot on spheres) and maximum variance methods (points) under diverse random loading scenarios.

4.2. Joint PDF Estimation

Figures 3 and 4 compare the two-dimensional distributions of the shear strain amplitude γ a and the maximum normal stress σ n , max in the two load scenarios mentioned above. In Figure 3, the joint probability density function (PDF) of the shear strain amplitude γ a and the maximum normal stress σ n , max is displayed for the narrowband, fully correlated load scenario, comparing the novel frequency-domain approach (Figure 3b) with the multiaxial rainflow results from the time domain (Figure 3a). Because of the strong correlation and relatively narrowband spectrum, each shear strain amplitude nearly pairs with a single maximum normal stress. The two methods produce visually similar distributions, underscoring the consistency of the proposed formulation.

(a)

(b)

Fig. 3: Joint PDF comparison for the narrowband, fully correlated load scenario: results from multiaxial rainflow (a) and from frequency domain formulation (b).