Issue 35

X. Liu et alii, Frattura ed Integrità Strutturale, 35 (2016) 88-97; DOI: 10.3221/IGF-ESIS.35.11 96 Fig. 10 shows the comparison of the predicted fatigue strength by the present model, Goodman formula and Gerber formula with experimental data. The parameter α in the present model in Fig. 10 is taken as -0.713. It is seen that the present model is better in agreement with the experimental data in VHCF regime. The predicted fatigue strength by Goodman formula is larger than the experimental data, while the predicted value by Gerber formula has very big error with the experimental data. C ONCLUSIONS he effects of stress ratio and inclusion size on the fatigue property of a high-strength steel in VHCF regime were investigated. The following conclusions are drawn. (1) Fatigue strength decreases with the increase of stress ratio. The tendency of the S-N curves from low-cycle fatigue to VHCF fatigue is similar for different stress ratios. Fatigue crack initiates from the surface of specimen in low- cycle fatigue regime and initiates mostly from the inclusion in the interior of specimen for high-cycle and VHCF regimes, which is irrespective of stress ratio. (2) The morphology of FGA is clear for the stress ratios of -1 and -0.5, and becomes obscure for the stress ratios of 0.1 and 0.3. The observation of microstructure below the FGA at R =-1 by TEM verifies the existence of fine granular area. Further, the absence of fine grains at R =0.3 indicated that FGA was generated by the numerous cyclic pressing between crack surfaces. (3) The effect of stress ratio and inclusion size on fatigue strength is in good agreement with the formula of σ a ∝ a 0 m [(1- R )/2] α , where m is -1/6 and α is -0.713. The comparison with Goodman formula and Gerber formula indicates that the present model is better to correlate stress ratio and fatigue strength for VHCF regime. A CKNOWLEDGEMENTS he research of this paper was supported by the National Basic Research Program of China (No: 2012CB937500) and by the National Natural Science Foundation of China (Nos: 11172304 and 11202210). R EFERENCES [1] Zhao, A., Xie, J., Sun, C., Lei, Z., Hong, Y., Effects of strength level and loading frequency on very-high-cycle fatigue behavior for a bearing steel, Int. J. Fatigue, 38 (2012) 46-56. DOI: 10.1016/j.ijfatigue.2011.11.014 [2] Oguma, H., Nakamura, T., The effect of microstructure on very high cycle fatigue properties in Ti–6Al–4V, Scripta Mater., 63 (2010) 32-34. DOI: 10.1016/j.scriptamat.2010.02.043 [3] Naito, T., Ueda, H., Kikuchi, M., Fatigue behavior of craburized steel with internal oxides and nonmartensitic microstructure neear the surface, Metall. Mater. Trans. A, 15 (1984) 1431-1436. DOI: 10.1007/bf02648572 [4] Kikuchi, M., Ueda, H., Naito, T., Fatigue behavior of carburized steel with internal oxides near the surface, Metall. Mater. Trans. A, 18 (1987) 156-158. DOI: 10.1007/bf02646234 [5] Sakai, T., Sato, Y., Oguma, N., Characteristic S–N properties of high-carbon–chromium-bearing steel under axial loading in long-life fatigue, Fatigue Fract. Eng. Mater. Struct., 25 (2002) 765–773. DOI: 10.1046/j.1460- 2695.2002.00574.x [6] Zhao, A., Xie, J., Sun, C., Lei, Z., Hong, Y., Prediction of threshold value for FGA formation, Mater. Sci. Eng. A, 528 (2011) 6872–6877. DOI: 10.1016/j.msea.2011.05.070 [7] Nguyen, H.Q., Gallimard, L., Bathias, C., Numerical simulation of the coupling between thermal dissipation and fish- eye crack growth in very high cycle fatigue regime, Fatigue Fract. Eng. Mater. Struct., 36 (2013) 450–461. DOI: 10.1111/ffe.12016 [8] Sakai, T,. Lian, B., Takeda, M., Shiozawa, K., Oguma, N., Ochi, Y., Nakajima, M., Nakamura, T., Statistical duplex S–N characteristics of high carbon chromium bearing steel in rotating bending in very high cycle regime, Int. J. Fatigue, 32 (2010) 497-504. DOI: 10.1016/j.ijfatigue.2009.08.001 [9] Murakami, Y., Nomoto, T., Ueda, T., Murakami, Y., On the mechanism of fatigue failure in the superlong life regime (N > 10 7 cycles) Part I: influence of hydrogen trapped by inclusions, Fatigue Fract. Eng. Mater. Struct., 23 (2000) 893- T T