PSI - Issue 76

Mirco Daniel Chapetti et al. / Procedia Structural Integrity 76 (2026) 89–98

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Figure 8 shows a strong correlation between all parameters and fatigue life for each printing direction, including the D K vs. N/ a shown in Figure 8(c). In this case, the defect size range was located between 0.15 and 0.55 mm, with relatively large values compared to the range of short cracks for this material, which has been almost fully developed at crack lengths between 0.1 and 0.2 mm (estimated applying Eq. 2). In this situation, the characterization of defects and the determination of the applied ΔK involve significant uncertainties, associated with the development of cracks from relatively large defects, where the size effect begins to provide a significant influence, especially for volumetric defects. In this case, almost all the data can be explained using the long crack threshold, D K thR . 8. Analysis and discussion The comparisons presented in the previous section highlight the effectiveness of using expression (7) to correlate fatigue life, N , with a parameter that accounts for the combined effects of material properties, defect size, and loading conditions. This proposed parameter is intrinsically linked to the fracture mechanics concept of a threshold curve for crack propagation (cyclic R -curve), which can be continuously defined for any defect size or crack length greater than the microstructural size d . However, a more detailed examination of the proposed approach is necessary to identify potential sources of scatter in such plots. One key factor is the influence of varying defect sizes (and consequently different initial crack lengths, a i ), which result in different small-crack propagation behaviors, even when the applied D K/ D K th ratio is held constant. Moreover, when comparing different Δ K /Δ K ₜₕ ratios, the resulting curves will vary depending on whether the initial defect size a i is held constant and the nominal stress range Ds is varied, or vice versa. These variations are further influenced by the range of defect sizes considered, since transitions between governing mechanisms may occur depending on whether the defects fall within or beyond certain thresholds. Additionally, the material's strength plays a significant role in defining the behavior described by expression (7) (and even expression (5)). Strength (or more specifically, hardness), not only defines the extent of the small-crack regime but also influences the applied D K level associated with the fatigue limit. 9. Conclusions From the development of this work, the following conclusions can be drawn: - The approach proposed by Shiosawa and Lu ( D K- N / a i curve), has not been found to yield satisfactory results when quantifying the influence of defects on fatigue strength. - The approach proposed by Murakami et al . ( Ds / Ds th -N curve) has produced acceptable results. However, improvements could be achieved by replacing the Murakami-Endo model with an alternative capable of estimating the propagation threshold curve in a continuous and comprehensive manner. This would allow for more accurate estimations of Ds w vs. a , extending beyond the original limitations of the model. - The proposed fracture mechanics approach ( D K/ D K th - N ), based on the use of a model that enables continuous estimation of the propagation threshold (cyclic R -curve) across the entire range of crack lengths analyzed, has been shown to produce highly reliable results. This has allowed for a more robust and insightful explanation of the influence of defect size across different configurations and alloys. Acknowledgements The author acknowledges the financial support provided by CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas). References Basquin, O.H, 1910. The exponential law of endurance tests. Am Soc Test Mater Proc 10:625–30. Chapetti, M.D., 2003. Fatigue propagation threshold of short cracks under constant amplitude loading. Int J Fatigue 25:1319–26. Chapetti, M.D., 2022. Fracture mechanics for fatigue design of metallic components and small defect assessment. International Journal of Fatigue 154:106550. Chapetti, M.D., Gubeljak, N., Kozak, D., 2023. Intrinsic fatigue limit and the minimum fatigue crack propagation threshold. Materials 16, 5874.