PSI - Issue 68

Xiangnan Pan et al. / Procedia Structural Integrity 68 (2025) 1038–1044 X. Pan et al. / Structural Integrity Procedia 00 (2025) 000–000

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1. Introduction Fatigue assessment is always a very difficult task because at least 10 specimens are required to obtain an S-N (stress - number of failure cycle N f ) curve and fatigue testing is time consuming, labor intensive and expensive (Lee et al., 2005). Traditionally, there has been an empirical opinion that high-cycle fatigue (HCF) performance is only dependent on material strength, and this opinion becomes more and more certain as the failure cycle increases (Suresh, 1998; Schijve, 2009). According to statistical results in the literature (Hong et al., 2009), the fatigue resistance σ f-7 at 10 7 cycles under stress ratio R = –1, known as “fatigue limit (Suresh, 1998; Schijve, 2009)”, can be fitted by linear slopes of the ultimate tensile strength (UTS) σ u in low alloy steels, written as σ f-7 = 0.432 σ u + 58.4 and 0.468 σ u . The slope is called “fatigue ratio” at R = –1, and some argue that it makes more sense to use yield strength σ 0.2 instead of the UTS (Schijve, 2009). Note that these statistics (Hong et al., 2009) did not take into account the specific type of fatigue failure. If the failure type is specified as surface crack initiation induced HCF, the statistics (Abe et al., 2004) show that the fatigue ratio is fitted as 0.53 for tempered martensitic steels at R = –1. In the higher regime of HCF, e.g. N f > 10 6 cycles, “fish eye (FiE)” typed fracture usually dominates fatigue failure for high-strength steels (Murakami, 2002). When FiE failure takes over from HCF, the fatigue resistance (Abe et al., 2004) no longer increases with increasing UTS but is related to the size and type (e.g. Al 2 O 3 and CaO) of the inclusions that cause fatal damage and remains essentially constant regardless of the UTS value. With the development of modern industry, the studies (Mayer, 2016; Sakai, 2023; Wu et al., 2024) of very-high cycle fatigue (VHCF) whose failure life exceeds 10 7 cycles have received more and more attention in academia and engineering. In VHCF regime, fatigue resistances σ f-9 , σ f-10 and σ f-11 at 10 9 , 10 10 and 10 11 cycles are not functions of the single UTS variable based on publications (Furuya and Takeuchi, 2014; Furuya, 2021; Furuya et al., 2022; Teng et al., In press). The early researches of VHCF are focused on high-strength steels (Atrens et al., 1983; Naito et al., 1983) and some titanium alloys with bimodal microstructures (Atrens et al., 1983; Neal and Blenkinsop, 1976). Their S-N curves can be characterized by a duplex or staircase shape, where the first slope for HCF corresponds to surface crack initiation and the second slope for VHCF corresponds to internal crack initiation with FiE morphology. It is the presence of the FiE dominated second slope that leads to the loss of a fixed proportionality between the UTS and the fatigue resistances in VHCF regime. Titanium alloys are the third most widely used metallic structural materials, less than steels and aluminium alloys, can be classified as near α, α+β, metastable β and β (Leyens and Peters, 2003; Lütjering and Williams, 2003). For near α and α+β types, there are four typical microstructures of equiaxed, bimodal, lamellar and basketweave (EM, BM, LM and BW), determined by the shapes, distributions and fractions of α grains. Generally, EM and BM are produced by annealing with good performance in HCF and VHCF (Crupi et al., 2017; Cui et al., 2021); LM and BW are produced by forging with high UTS (Nikitin et al., 2016; Wu et al., 2013). On fracture surfaces, fatigue origins can be easily identified by the crack initiation region (CIR) of rough area (RA) for EM and BM types (Heinz et al., 2013; Heinz and Eifler, 2016). In contrast, it is very difficult to locate the CIR for HCF and VHCF of LM and BW types because there is no discernible RA on the fracture surfaces. Additive manufacturing (AM) is a promising technology for its ability to 3D print components and parts with complex configurations (Gibson et al., 2021; Toyserkani et al., 2021). Powder bed fusion - laser beam (PBF-LB) is one of the most important AM techniques for 3D printing of metallic materials (Yadroitsev et al., 2021; Pan et al., 2024a), also known as selective laser melting (SLM) or laser - powder bed fusion (L-PBF). Due to the rapid heating and cooling of PBF-LB process, the additively manufactured (AMed) metallic materials can conveniently achieve high UTS values, e.g. over 1100 MPa for titanium alloys, which belong to the category of so-called “high-strength titanium alloys (Zhao et al., 2022)”. For AMed titanium alloys, even the traditional fatigue limit σ f-7 is no longer proportional to the UTS, let alone the VHCF resistance σ f-8 at 10 8 cycles (Gao et al., 2024). Fatigue indicator parameter (FIP) is considered to be a powerful tool for assessing the incubation of fatigue crack initiation and the level of fatigue damage accumulation (McDowell and Dunne, 2010). However, FIP corresponds to local strains in the cyclically loaded material and requires cumbersome microstructure-sensitive calculations (Dunne and Petrinic, 2005; Raabe, 1998; Roters et al., 2019) to obtain, and is therefore not directly derived from the global quantities of the material. Tensile properties have long been regarded as the fundamental mechanical properties of materials (Ashby, 2016; Meyers and Chawla, 2009), and they can be quickly acquired by quasi-static tests. The aim