PSI - Issue 76

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

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factor range, D K, for a given equivalent crack length associated with the defect, and the propagation threshold, D K th , for the same crack length: D K/ D K th . To define the propagation threshold, it is further proposed to consider the concept of a resistance curve, allowing the threshold to be continuously estimated from the microstructural threshold, associated with the characteristic microstructural size d ( D K dR ), up to the long-crack threshold, D K thR . Further, the propagation threshold curve is estimated using Chapetti’s model (Eq. 2). Figure 2 schematically illustrates this concept for a given defect size ( a i ) and an applied nominal stress range ( Ds i ) greater than the fatigue limit of the configuration ( Ds e ). Each defect corresponds to an equivalent initial crack length a i , and under the applied load Ds i , a corresponding D K value is determined. This D K is then compared to the threshold D K th at the same crack length. The fatigue life, N , is estimated by integrating Eq. (3) over the crack growth interval, from the initial defect size a i to the final crack size a f . By repeating this process for different combinations of defect size ( a i ) and applied stress range ( Ds i ), various D K values are obtained, which, together with the corresponding estimated fatigue lives, lead to the derivation of the following expression: = ? : ∆ ∆ @ @ "# ; , ( (7) for D K > D K th , and C M and m M are material constantsvoid hyphenation at the end of a line. 7. Applications The experimental data published by Merot et al. (2022), Qu et al. (2022), Yamashita et al. (2018) and Meneguetti et al. (2018) are analyzed in this section. The fatigue life data, reported in the form of Ds - N curves, are evaluated using three approaches: the method proposed by Shiosawa and Lu (2008), the method by Murakami et al . (2020), and the new one introduced in the previous section. In all cases, the defect sizes (initial crack length, a i ), applied stress ranges ( Ds ), applied D K values, and the necessary data to estimate the propagation threshold according to Eq. (2) are provided or taken from literature. Figures 5, 6, 7 and 8 present the corresponding results from the four studies, each analyzed using the following methods: (a) Ds - N , (b) Ds / Ds th - N , (c) D K- N / a , and (d) D K/ D K th - N plots. Merot et al. (2022) investigated the fatigue behavior of 316L stainless steel produced by laser powder bed fusion, containing defects such as lack of fusion flaws, corrosion pits, and hemispherical defects introduced via electric discharge machining. The reported defect sizes ranged from 0.01 mm to 0.4 mm, thus covering the full range of short cracks for this alloy, and extending beyond (Merot et al. 2022, Chapetti et al. 2023). Figure 5 displays the four corresponding plots for the different approaches. The proposed method demonstrates a strong correlation, considering the intrinsic scatter characteristic of fatigue data, and clearly improves upon the Murakami approach, which itself shows a noticeable improvement over the Shiosawa method. Figure 6 presents the results from the analysis of data reported by Qu et al. (2022), who investigated the influence of defects on the fatigue properties of Ti-6Al-4V produced by laser powder bed fusion. In their study, the fatigue strength of the printed material was evaluated after different heat treatments, resulting in various microstructures. In the present work, only the results corresponding to the stress-relieved condition are reanalyzed. Defect sizes were reported to range from 0.03 mm to 0.12 mm, clearly within the short crack regime for this material (Qu et al. 2022, Peters et al. 2002). In this analysis, the application of expression (7) (Figure 10(d)) yields very satisfactory results, revealing a clear trend where nearly all data points lie above the fatigue limit line ( D K/ D K th = 1). Figure 7 presents the results of data analysis from Yamashita et al. (2018), who investigated the fatigue behavior of a Ni-based superalloy 718 produced via selective laser melting. In their study, observed defect sizes ranged from 0.05 to 0.25 mm, well above the short crack regime for this alloy (Yamashita 2018). The data shown in Figure 7(b) were not estimated in the present study but are directly reproduced from the original work by Murakami et al. (2020). In Figure 8 the results of the analysis of the data reported by Meneguetti et al. (2018) are shown, in which the influence of defects on the axial fatigue strength of maraging steel specimens produced by additive manufacturing was analyzed. In this case, two sets of data were reported, corresponding to two printing orientations: 0° (round symbols) and 90° (square symbols).