PSI - Issue 75

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

717

9

for industrial and research scenarios where complex loading histories or large datasets may render direct time domain computations impractical.

In conclusion, these preliminary results suggest that the frequency-domain formulation of the Fatemi–Socie crite rion can provide a viable and e ffi cient framework for multiaxial fatigue assessments under complex loading situations. By combining an e ffi cient critical-plane selection procedure with a spectral-based damage evaluation, the approach successfully integrates the strengths of the original Fatemi–Socie criterion with the advantages of frequency-domain analysis. This hybridization indicates strong potential for addressing a range of random loading conditions–from nar rowband, fully correlated signals to broadband, uncorrelated scenarios–while maintaining computational e ffi ciency.

Acknowledgements

This study was financed by the European Union – NextGenerationEU (National Sustainable Mobility Center CN00000023, Italian Ministry of University and Research Decree n. 1033 – 17 / 06 / 2022, Spoke 11 – Innovative Materials & Lightweighting). The opinions expressed are those of the authors only and should not be considered as representative of the European Union or the European Commission’s o ffi cial position. Neither the European Union nor the European Commission can be held responsible for them.

References

[1] Bannantine, J., Socie, D., 1992. A multiaxial fatigue life estimation technique, in: Advances in fatigue lifetime predictive techniques. ASTM International. [2] Bannantine, J.A., Socie, D.F., 1989. A variable amplitude multiaxial fatigue life prediction method. Third International Conference on Biax ial / Multiaxial Fatigue , 12.1 – 12.20. [3] Benasciutti, D., Sherratt, F., Cristofori, A., 2016. Recent developments in frequency domain multi-axial fatigue analysis. International Journal of Fatigue 91, 397–413. doi: 10.1016/j.ijfatigue.2016.04.012 . [4] Benasciutti, D., Tovo, R., 2006. Comparison of spectral methods for fatigue analysis of broad-band Gaussian random processes. Probabilistic Engineering Mechanics 21, 287–299. doi: 10.1016/j.probengmech.2005.10.003 . [5] Carpinteri, A., Spagnoli, A., Vantadori, S., 2003. A multiaxial fatigue criterion for random loading. Fatigue and Fracture of Engineering Materials and Structures 26, 515–522. doi: 10.1046/j.1460-2695.2003.00620.x . [6] Carpinteri, A., Spagnoli, A., Vantadori, S., 2017. A review of multiaxial fatigue criteria for random variable amplitude loads. doi: 10.1111/ffe. 12619 . [7] Chiocca, A., Frendo, F., Marulo, G., 2023a. An e ffi cient algorithm for critical plane factors evaluation. International Journal of Mechanical Sciences 242, 107974. doi: 10.1016/j.ijmecsci.2022.107974 . [8] Chiocca, A., Sgamma, M., Frendo, F., 2023b. Closed-form solution for the Fatemi-Socie extended critical plane parameter in case of linear elasticity and proportional loading. Fatigue & Fracture of Engineering Materials & Structures doi: 10.1111/FFE.14153 . [9] Chiocca, A., Sgamma, M., Frendo, F., 2024. A closed-form solution for evaluating the Findley critical plane factor. European Journal of Mechanics, A / Solids 105, 105274. doi: 10.1016/j.euromechsol.2024.105274 . [10] Chiocca, A., Sgamma, M., Frendo, F., Bucchi, F., 2023c. Rapid and accurate fatigue assessment by an e ffi cient critical plane algorithm: application to a FSAE car rear upright. Procedia Structural Integrity 47, 749–756. doi: 10.1016/J.PROSTR.2023.07.044 . [11] Cianetti, F., Palmieri, M., Braccesi, C., Morettini, G., 2018. Correction formula approach to evaluate fatigue damage induced by non-gaussian stress state. Procedia Structural Integrity 8, 390–398. [12] Cristofori, A., Benasciutti, D., Tovo, R., 2011. A stress invariant based spectral method to estimate fatigue life under multiaxial random loading. International Journal of Fatigue 33, 887–899. doi: 10.1016/j.ijfatigue.2011.01.013 . [13] Davenport, A.G., 1964. Note on the distribution of the largest value of a random function with application to gust loading. Proceedings of the Institution of Civil Engineers 28, 187–196. [14] Dirlik, T., 1985. Application of computers in fatigue analysis. Ph.D. thesis. University of Warwick. [15] European Committee for Standardization (CEN), 2005. Eurocode 3: Design of steel structures — Part 1-9: Fatigue 50, 77. [16] Fatemi, A., Kurath, P., 1988. Multiaxial fatigue life predictions under the influence of mean-stresses . [17] Fatemi, A., Socie, D.F., 1988. A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue and Fracture of Engineering Materials and Structures 11, 149–165. doi: 10.1111/j.1460-2695.1988.tb01169.x . [18] Fricke, W., Gao, L., Paetzold, H., 2017. Fatigue assessment of local stresses at fillet welds around plate corners. International Journal of Fatigue 101, 169–176. doi: 10.1016/j.ijfatigue.2017.01.011 . [19] Gao, D., Yao, W., Wen, W., Huang, J., 2021a. A multiaxial fatigue life prediction method for metallic material under combined random vibration loading and mean stress loading in the frequency domain. International Journal of Fatigue 148, 106235. doi: 10.1016/j.ijfatigue.2021. 106235 .