PSI - Issue 71

Shohei Matsuda et al. / Procedia Structural Integrity 71 (2025) 4–9

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Fig. 1. Geometry of artificial 4-hole defect (in µm)

3. Results and discussion Figure 2 displays the S-N data obtained from rotating bending fatigue tests. Although all defects have an identical shape and size ( √ = 287 µ m), there is a large scatter in the fatigue strength (fatigue life and fatigue limit) data. The experimental value of the fatigue limit defined in Chapter 2 was σ w, exp = 100 MPa. However, it should be noted that this measured σ w, exp is not a material constant but an apparent value since the fatigue strength tends to decrease with the number of experimental data when it exhibits a scatter. It is known that when no mean stress is applied ( R = – 1), the fatigue limit of many metallic materials containing small surface defects can be predicted by the following equation, which was proposed based on the √ parameter model (Murakami, 2019): σ w, pred = 1 .(4√3 ( + ) 1 2 0 ) 1/6 (1) where σ w, pred is the predicted fatigue limit [MPa], HV is the Vickers hardness [kgf/mm 2 ], and √ is the square root of the area of the defect projected onto the maximum principal stress plane [µm]. For many steels and nonferrous metals, the prediction error of this equation is within about ±10%. Since the size of the defect in Fig. 1 is √ = 287 µm and the Vickers hardness of this material is HV = 109, the fatigue limit calculated by equation (1) is σ w, pred = 128 MPa. The thick dashed line in Fig. 2 indicates this stress level. Compared to the experimental value ( σ w, exp = 100 MPa), the predicted value results in an overestimation of 28%. Other studies (Ueno et al., 2012; Tajiri et al., 2014) also report that the experimental values are about 30 % lower than the prediction by Eq. (1) for similar materials specimens with small defects. Thus, the material investigated in this study is not anomalous, but the observed phenomenon is common to this type of material (JIS AC4C-T6). Ueno et al. proposed an evaluation method by modifying the coefficient of Eq. (1) by curve-fitting the experimental values of fatigue limit (Ueno et al., 2012). However, they do not discuss the physical meaning of this modification. The √ parameter model is a mechanical model established by assuming that the fatigue limit is determined by the threshold condition for the propagation of a mode I crack emanating from a defect. One of the reasons why the experimental fatigue limit is lower than the value predicted by equation (1) may be that the deformation mode of fatigue cracks in this material is not pure mode I-dominant. Fig. 3. shows the non-propagating cracks observed at the end edge of defects in four specimens that did not break at σ a = 100-112.5 MPa, as shown in Fig. 1. In the other broken specimens, the cracks started propagating from the artificial defects and continued propagating until fracture. These results mean that the threshold condition for crack propagation determines the fatigue limit. As seen in Fig. 3, the cracks emanated from the artificial defects, observed on the surface, often propagated linearly. However, they were not always perpendicular to the tensile direction but in many cases propagated obliquely or kinked,