PSI - Issue 82

Xiangnan Pan et al. / Procedia Structural Integrity 82 (2026) 125–130 X. Pan / Structural Integrity Procedia 00 (2026) 000–000

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2. Basic principles

Fig. 1. A probabilistic S-N curve across different fatigue regimes.

In accordance with the afore-mentioned regime classification of LCF, HCF, VHCF, and runout, Fig. 1 presents a schematic diagram of the probabilistic S-N curves for a specific material with failure probabilities of 5%, 50%, and 95%. These curves describe the distribution of fatigue strength σ w in terms of stress amplitude σ a for different failure cycles, in which σ w-95% , σ w-50% , and σ w-5% represent σ w with failure probabilities of 95%, 50%, and 5%, respectively. For a given fatigue life N f , the fatigue strength σ w can be treated as a random variable, which can be characterized by three parameters of fatigue strength: σ w-95% , σ w-50% , and σ w-5% . In fact, there are many more such parameters. However, constrained by the number of tested specimens, obtaining valid, reliable, and accurate probabilistic S-N curves remains extremely challenging. To overcome this problem, the given fatigue life N f can be extended into a regime, e.g. HCF or VHCF regime, and the corresponding fatigue strength parameters can be defined as will be described in detail in the following examples. Note that all fatigue strengths discussed in this paper are described in terms of stress amplitude. For fatigue strengths described in terms of maximum stress, the method is identical — only the stress amplitude on the y -axis of Fig. 1 needs to be replaced with maximum stress, and the S-N diagram needs to be redrawn accordingly. 3. Application case Fig. 2 shows the S-N data of a forged titanium alloy (Ti62A), whose chemical composition (in weight percentage) is 6.08 Al, 3.21 Mo, 2.08 Sn, 2.04 Zr, 0.12 O, 0.01 C, and the balance Ti. In subfigure of Fig. 2a, for the case of stress ratio R = −1, i.e., the tensile mean stress σ m = 0, fully reversed loading was applied along the specimen axis to 18 specimens. As a result, 4 specimens failed in the HCF regime, 10 specimens failed in the VHCF regime, and 4 specimens survived beyond 2 × 10 8 cycles, which were incorporated into the runout regime. In subfigure of Fig. 2b, for the case of σ m = 28 MPa, i.e., R = −0.8, 6 specimens were tested, in which, 1 specimen failed in the HCF regime, 3 specimens failed in the VHCF regime, and 2 specimens fell in the runout regime. In subfigure of Fig. 2c, for the case of σ m = 141 MPa, i.e., R = −0.2 ~ −0.1, 7 specimens were tested, in which, 1 specimen failed in the HCF regime, 5 specimens failed in the VHCF regime, and 1 specimen fell in the runout regime. In subfigure of Fig. 2d, for the case of σ m = 283 MPa, i.e., R = 0.1 ~ 0.5, 15 specimens were tested, in which, no specimen failed in the HCF regime, 13 specimens failed in the VHCF regime, and 2 specimens fell in the runout regime. In subfigure of Fig. 2e, for the case of σ m = 849 MPa, i.e., R = 0.7 ~ 0.8, 11 specimens were tested, in which, 4 specimens failed in the HCF regime, 7 specimens failed in the VHCF regime, and no specimens could stand 10 9 loading cycles.