PSI - Issue 75

Sgamma M. et al. / Procedia Structural Integrity 75 (2025) 709–718 Author name / Structural Integrity Procedia 00 (2025) 000–000

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A similar comparison is shown in Figure 4 for the broadband, uncorrelated load case, where a broader distribution of σ n , max values emerges at each strain amplitude. In this broader spectrum with partial or negligible correlation, a wider range of σ n , max values is associated with each γ a , forming a more dispersed set of pairs. Nonetheless, the agreement between the time-domain (Figure 4a) and frequency-domain (Figure 4b) distributions remains satisfactory, indicating that the proposed approach captures the essential physics of the broadband case as well.

(a)

(b)

Fig. 4: Joint PDF comparison for the wideband, uncorrelated load scenario: results from multiaxial rainflow (a) and from frequency domain formulation (b).

Overall, these comparisons confirm that the frequency-domain approach–employing the Dirlik-based PDF for strain amplitudes and an appropriate statistical representation of maximum normal stress–provides results consis tent with more traditional time-domain multiaxial rainflow computations. Ongoing investigations will complement these findings by introducing more quantitative KPIs and by providing a systematic evaluation of the computational advantages, to be detailed in forthcoming works.

4.3. Concluding Remarks

The proposed frequency-domain adaptation of the Fatemi–Socie criterion exhibits promising capabilities in han dling multiaxial random fatigue, as evidenced by the initial comparisons with time-domain results. The key contribu tions and findings can be summarized as follows: • a crucial step in extending the Fatemi–Socie parameter P FS to the frequency domain involves expressing it in terms of the covariance matrices of stress and strain. By doing so, one can apply the maximum variance approach to determine the critical plane without resorting to extensive damage calculations across multiple orientations. This process uses variance-derived expressions for the equivalent shear strain amplitude and maximum normal stress in accordance with Davenport’s theory, substantially reducing computational overhead; • the adaptation of the Fatemi–Socie criterion to random loading requires identifying pairs of shear strain am plitudes and maximum normal stresses at a fixed plane orientation. In the time domain, this is achieved via the multiaxial rainflow algorithm. The proposed frequency-domain approach, however, replaces explicit cycle counting with a two-dimensional probability distribution obtained by combining Dirlik’s amplitude PDF with a statistical model (e.g., normal distribution) for peak stress values. This joint PDF relies solely on spectral parameters derived at the critical plane, thus eliminating the need for time-domain data; • numerical comparisons demonstrate that the frequency-domain criterion captures the occurrence and magni tudes of the ( γ a ,σ n , max ) pairs similarly to standard rainflow-based methods. In particular, the probability dis tribution developed reproduces the essential features of time-domain analyses, making it a reliable alternative