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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For the runout, VHCF, and HCF regimes, one of the simplest methods to extract characteristic parameters is to take the minimum and maximum stress amplitudes applied to their corresponding specimens, and define them as: σ a-0 , σ a 1 ; σ a-2 , σ a-3 ; and σ a-4 , σ a-5 ; respectively. Herein, for constant-amplitude loading and the same group of specimens, there is a tendency that when the tensile mean stress σ m is constant, the greater the applied stress amplitude, the shorter the specimens’ fatigue life. Therefore, σ a-1 , σ a-2 , σ a-3 , σ a-4 , σ a-5 can be regarded as the intrinsic fatigue strength parameters of the specimens. The reason for referring to specimens rather than materials here is that fatigue strength is closely related to the size and geometry of the specimens (Furuya, 2008, 2011; Montagnoli et al., 2023; Pan et al., 2025; Tao et al., 2024), and it does not merely reflect the intrinsic properties of the material. Obviously, σ a-0 is not an intrinsic fatigue strength parameter, as it depends on the selection of the applied stress amplitude. As long as the value of the latter is sufficiently small, the fatigue life of the specimens can obviously be sufficiently long — that is, falling into the runout regime. When a sufficient number of specimens are tested, σ a-1 will converge to the “true” fatigue limit (or the fatigue strength at 10 9 cycles in this case) asymptotically; σ a-2 and σ a-3 will converge to the minimum and maximum stress amplitudes at which VHCF failure occurs, respectively; and σ a-4 and σ a-5 will converge to the minimum and maximum stress amplitudes at which HCF failure occurs, respectively. In subfigure of Fig. 2a, the inequality σ a-2 < σ a-4 < σ a-1 < σ a-3 < σ a-5 divides the applied stress amplitude into six domains: (1) σ a < σ a-2 , all specimens applied under this load are expected to runout; (2) σ a-2 ≤ σ a < σ a-4 , specimens either undergo VHCF failure or runout, with HCF not expected to occur; (3) σ a-4 ≤ σ a ≤ σ a-1 , VHCF, HCF, and runout can all occur in loaded specimens; (4) σ a-1 < σ a ≤ σ a-3 , specimens either fail in HCF or VHCF regime, and are not expected to runout; (5) σ a-3 < σ a ≤ σ a-5 , all specimens applied under this load are expected to fail in HCF regime; (6) σ a > σ a-5 , specimens applied under this load are expected to fail in HCF or LCF regime. In subfigure of Fig. 2b, the inequality σ a-1 = σ a-2 < σ a-3 < σ a-4 divides the applied stress amplitude into five domains: (1) σ a < σ a-1 , all specimens applied under this load are expected to runout; (2) σ a-1 ≤ σ a ≤ σ a-2 , specimens either undergo VHCF failure or runout, with HCF not expected to occur; (3) σ a-2 < σ a ≤ σ a-3 , all specimens applied under this load are expected to fail in VHCF regime; (4) σ a-3 < σ a ≤ σ a-4 , specimens either undergo VHCF or HCF failure; (5) σ a > σ a-4 , specimens applied under this load are expected to fail in HCF or LCF regime. In subfigure of Fig. 2c, the inequality σ a-2 < σ a-1 < σ a-4 < σ a-3 divides the applied stress amplitude into five domains: (1) σ a < σ a-2 , specimens are expected to runout; (2) σ a-2 ≤ σ a ≤ σ a-1 , specimens either undergo VHCF failure or runout; (3) σ a-1 < σ a < σ a-4 , all specimens applied under this load are expected to fail in VHCF regime; (4) σ a-4 ≤ σ a ≤ σ a-3 , specimens either undergo VHCF or HCF failure; (5) σ a > σ a-3 , specimens applied under this load are expected to fail from LCF, HCF to VHCF regimes. In subfigure of Fig. 2d, the inequality σ a-2 < σ a-1 < σ a-3 divides the applied stress amplitude into four domains: (1) σ a < σ a-2 , specimens are expected to runout; (2) σ a-2 ≤ σ a ≤ σ a-1 , specimens either undergo VHCF failure or runout; (3) σ a-1 < σ a ≤ σ a-3 , all specimens applied under this load are expected to fail in VHCF regime; (4) σ a > σ a-3 , specimens applied under this load are expected to fail from LCF, HCF to VHCF regimes. In subfigure of Fig. 2e, the inequality σ a-2 < σ a-3 < σ a-4 < σ a-5 divides the applied stress amplitude into four domains: (1) σ a < σ a-2 , specimens are expected to either runout or fail in VHCF regime; (2) σ a-2 ≤ σ a ≤ σ a-3 , all specimens applied under this load are expected to fail in VHCF regime; (3) σ a-3 < σ a < σ a-4 , specimens either undergo VHCF or HCF failure; (4) σ a-3 ≤ σ a ≤ σ a-4 , all specimens applied under this load are expected to fail in HCF regime; (5) σ a > σ a-4 , specimens applied under this load are expected to fail in HCF or LCF regime. 4. Conclusions In summary, five intrinsic fatigue strength parameters, namely σ a-1 , σ a-2 , σ a-3 , σ a-4 , σ a-5 , are defined and introduced to quantitatively analyze the occurrence probability of HCF, VHCF, and runout (surviving beyond 10 9 cycles) under varying applied stress amplitude in a forged titanium alloy (Ti62A) subjected to different tensile mean stresses. Regardless of the tensile mean stress, the five groups of specimens all have a runout domain — i.e., when the applied stress amplitude falls within this range, the specimens never undergo fatigue failure. As the tensile mean stress increases, a VHCF domain gradually emerges — where, if the applied stress amplitude falls within this range, the specimens will all undergo VHCF failure. At a stress ratio of R = −1, no such domain exists; instead, there are three transitional domains: runout & VHCF, runout & VHCF & HCF, and VHCF & HCF. When the applied stress amplitude