PSI - Issue 71

Haru Fujishima et al. / Procedia Structural Integrity 71 (2025) 18–25

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In the case of tension-compression fatigue tests, there is no effect of inertia force; thus, the experimental results for the drilled hole, as well as other types of defects, agree well with the predicted S-N curve, as shown in Fig. 1. Fig. 9 shows the relationship between the number of cycles to failure N f and the stress gradient χ , which is plotted using the experimental results for rotational bending at f = 1 Hz and tension-compression at f = 45 Hz. It is interesting to note that the value of N f for =0 that is extrapolated from the two values of N f for = 0.2 −1 and = 0.4 −1 obtained by the rotational bending test is close to the values of N f obtained by prediction and the tension-compression test. This result suggests that the test frequency in the order of f = 1 Hz has little effect on the RB fatigue test results. As discussed above, the undesirable effect of test frequency is activated by at least two factors: the asymmetry of the specimen’s compliance and the action of inertia force. Conversely, if one or both factors are removed, the test frequency effect will no longer be present. For example, if the size of the initial defect or crack is much smaller compared to the specimen diameter, the compliance asymmetry becomes less important because the propagation life of a small crack within a thin surface layer of the specimen accounts for most of the fatigue life. In particular, the effect of test frequency on the fatigue limit is expected to be minimal since essential fatigue phenomena influencing determination of the fatigue limit are restricted to the thin surface layer of a specimen. When dealing with a large initial defect compared to the specimen diameter, extra attention must be paid to lowering the test speed to mitigate the effect of inertia force or employing specimens without compliance asymmetry, such as circumferential notches. Likewise, the RB testing machine that applies cyclic bending stress to the specimen by a displacement- control means can be problematic. Unless the specimen’s compliance asymmetry is eliminated, the amplitude and the mean value of the stress applied to the specimen will vary during one rotation, regardless of the test frequency.

Fig. 9 Relationship between number of cycles to failure N f and stress gradient at f = 1 Hz.

4. Conclusions Historically, the effects of stress gradient and test frequency on the rotating bending fatigue strength have not been discussed well. The reason is that the physical background determining the form of the S-N curve has not been studied, and the discussion based on the intrinsic form of the S-N curve was impossible. The S-N prediction model (Murakami et al., 2023) recently revealed that the S-N curve has a universal form. The present study began with an experiment that only the experimental results obtained from the RB fatigue tests of the specimens with a hole deviated from the predicted S-N curve (Fig. 2). The effects of two factors of stress gradient and test frequency on the S-N curve (fatigue life and fatigue limit) were studied by conducting rotating bending (RB) and tension-compression fatigue tests using annealed carbon steel specimens with artificial small defects. The effects of these two factors were investigated by comparing the