PSI - Issue 77

J.A. Alves et al. / Procedia Structural Integrity 77 (2026) 440–446

445

S t =

Σ n 2 n − 1 i = 1 z

(7)

Where n represents the number of fully reversed tests that resulted in failure; in this study, n equals 13. Figure 4 shows the relationship of the stress standard deviation for each model.

Fig. 4. Stress standard deviation for each equivalence model.

The Goodman model exhibited the lowest stress standard deviation of 0.039. In contrast, the ASME Elliptic model reached a value of 0.278. As shown in Figure 4, it is evident that linear models were less inconsistent in fitting experimental data in VHCF compared to quadratic models.

4. Conclusion

Based on the present work, the following conclusions could be drawn:

• The DIN 34CrNiMo6 steel exhibited an endurance limit of around 48% of σ uts , close to the 50% reported in the literature. • Linear equivalence models, such as Goodman and Soderberg, showed a better fit to the experimental VHCF data, yielding stress standard deviations ( S t ) of 0.039 and 0.099, respectively. • Quadratic models, such as ASME Elliptic and Gerber, exhibited the highest S t values, 0.249 and 0.278, respec tively. It has been reported in the literature that fatigue life extension tends to produce greater scatter. Moreover, the ASME Elliptic and Gerber models are described as being less conservative compared to the Goodman model. In summary, the large variability in fatigue lives for a given stress level in the VHCF regime makes non-conservative models unreliable for fatigue life prediction. Bathias, C., 2006. Piezoelectric fatigue testing machines and devices. International Journal of Fatigue 28, 1438–1445. Budynas, R.G., Nisbett, K.J., Nisbett, J.K., Shigley, J.E., 2015. Shigley’s Mechanical Engineering Design. Mcgraw-Hill Series in Mechanical Engineering. 10. ed. in si units ed., McGraw-Hill Education, New York, NY. Dieter, G., Bacon, D., Bacon, D., 1988. Mechanical Metallurgy. Materials Science and Engineering Series, McGraw-Hill. E28 Committee, a. Test Method for Youngs Modulus, Tangent Modulus, and Chord Modulus. doi: 10.1520/E0111-04R10 . E28 Committee, b. Test Methods for Tension Testing of Metallic Materials. doi: 10.1520/E0008_E0008M-24 . Furuya, Y., Hirukawa, H., Takeuchi, E., 2019. Gigacycle fatigue in high strength steels. Science and Technology of Advanced Materials 20, 643–656. doi: 10.1080/14686996.2019.1610904 . Liu, Y., Li, Y., Li, S., Yang, Z., Chen, S., Hui, W., Weng, Y., 2010. Prediction of the S–N curves of high-strength steels in the very high cycle fatigue regime. International Journal of Fatigue 32, 1351–1357. doi: 10.1016/j.ijfatigue.2010.02.006 . Meggiolaro, M., Castro, J., Topper, T., 2009. Fadiga - Te´cnicas e Pra´ticas de Dimensionamento Estrutural Sob Cargas Reais de Servic¸o: Volume I - Iniciac¸a˜o de Trincas. CreateSpace Independent Publishing Platform. References