PSI - Issue 76

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

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responsible for data scatter. Today, it is recognized that the Ds - N curve is influenced by several material-related parameters, including microstructure size, defect size and nature, and the threshold for fatigue crack propagation across different crack sizes. Extensive literature documenting these factors has been published. The statistical distribution of these parameters is considered responsible for the overall scatter observed in the Ds - N curves. As noted by Miller (1993) the presence of a knee point in the Ds - N curve of a defect-free material is mechanically attributed to the intrinsic fatigue limit being reached when a nucleated micro-crack becomes non-propagating (microstructural threshold for micro-crack propagation). A similar condition is considered when material defects act as cracks, defining a fatigue limit associated with a crack propagation threshold. Therefore, the fatigue limit is not regarded as the critical stress for crack initiation, but rather as the threshold stress below which an initiated crack cannot grow. In this work, configurations of metallic alloys with defects larger than the average microstructural size are analyzed, in which it is possible to propose the hypotheses that the defects can be considered as cracks, with the nucleation stage being assumed negligible, and that an equivalent crack can be assigned to these defects (Murakami and Endo 1994, Murakami 2019). Then, the fracture mechanics methodology can be applied, particularly the concept of the resistance curve ( D K th vs. a ), which is compared with the applied loading ( D K vs. a ), both as functions of crack length. Traditional curves used to analyze fatigue life as a function of nominal stress level, Ds vs. N , as well as recently proposed plots, D K vs. N / a (Shiozawa and Lu 2008) and Ds / Ds th vs. N (Murakami et al. 2020), are analyzed. In order to contribute to reliable fatigue design in the presence of defects, an alternative plot, D K/ D K th vs. N , is proposed, based on the fracture mechanics approach and the concept of the threshold curve (cyclic R -curve). The analysis is carried out using various literature data (Merot et al. 2022, Meneguetti et al. 2018, Qu et al. 2022, Murakami et al. 2020) on metallic alloys with manufacturing-induced defects, where the crack nucleation stage is suppressed, and fatigue life is conservatively determined by crack propagation from these defects to final failure. 2. The fracture mechanics approach Fatigue assessment based on the cyclic R -curve describes the increase in the fatigue crack growth threshold, D K th , with crack extension, D a (Tanaka and Akiniwa 1988). This approach allows the behavior of small cracks to be estimated, mainly influenced (though not exclusively) by the early development of closure mechanisms. Figure 1 schematically illustrates the cyclic R -curve, incorporating the microstructural threshold conceptually introduced by Miller (1993) and explicitly included by Chapetti (2003) in his predictive model. In this framework, the cyclic R -curve indicates that the intrinsic (free-defect) fatigue limit ( Ds eR ) is actually a microstructural propagation threshold, D K dR , defined by Chapetti (2003) as follows: ∆ !" = ∆ #" √ (1) where d is the average microstructural dimension and the parameter Y is taken equal to 0.65 for a semicircular crack.

Fig. 1. The threshold curve in terms of the local applied stress range, Ds th vs a .