X. Liu et alii, Frattura ed Integrità Strutturale, 35 (2016) 88-97; DOI: 10.3221/IGF-ESIS.35.11 89 [8], “hydrogen assisted crack growth” [9], and “decohesion of spherical carbide” [10]. However, the formation mechanism of FGA is still not clearly understood, and needs more investigation. Fatigue tests are time-consuming and expensive especially for the fatigue of large number of cycles. The application of ultrasonic fatigue machine (frequency about 20 kHz) greatly cuts the testing time for VHCF of metallic materials and has accumulated a large amount of VHCF data [11, 12]. For example, Kovacs et al [13] investigated the effects of mean stress on fatigue life of a low-carbon steel by using ultrasonic fatigue machine. In their results, the continuous S-N curves presented the same tendency for all the stress ratios, but FGA was only observed at R = ‒ 1. Sander et al [14] also used ultrasonic frequency testing to investigate the effects of mean stress and variable stress on the fatigue property of a medium-carbon steel, and reported that FGA was not observed for all stress ratios. Shiozawa et al [15] (used frequency 80 Hz) and Sakai et al [16] (used frequency 50 Hz) investigated the effects of stress ratio on the VHCF property of a high- strength steel, SUJ2, by using conventional frequency fatigue machine, respectively. In their results, the FGA turned obscure with the increase of stress ratio. The effects of stress ratio on the fatigue strength of metallic materials have been an important topic. For low-cycle and high-cycle fatigue, Goodman formula and Gerber formula are usually used to correlate stress ratio and fatigue strength. However, for VHCF regime, the application of these two formulae needs more validation. Murakami et al [17, 18] proposed a model for predicting the fatigue strength of high-strength steels, which combined the fatigue strength σ (MPa), stress ratio R , Vicker hardness Hv (kgf/mm 2 ) and the square root of inclusion or defect projection area as follows: 1/6 (Hv 120) 1 2 C R area (1) where α=0.226+Hv×10 4 , C =1.43 for surface inclusions or defects and C =1.56 for interior inclusions or defects. Recently, Sun et al [19, 20] developed a model for estimating the effects of stress ratio and inclusion size on fatigue strength for high-strength steels with fish-eye mode failure based on experimental results: , 0 1 2 l m a R R CN a (2) where C , l and α are material parameters obtained by fitting the experimental data, and a 0 denotes the inclusion size. The model of Eq. (2) incorporates the effect of fatigue life on fatigue strength, and the model of Eq. (1) is a special case of Eq. (2). In this paper, the effects of stress ratio on VHCF property of a high-strength steel, GCr15, were investigated. Fatigue test was performed by using ultrasonic (20 kHz) fatigue test machine with a value of mean stress superimposed. The stress ratios were -1, -0.5, 0.1 and 0.3. The microstructure below FGA for the fracture surfaces at R =-1 and R =0.3 was observed by transmission electron microscopy (TEM). The observations show the different crack initiation characteristics and reveal the mechanism of crack initiation for different stress ratios. Moreover, the effect of inclusion size on fatigue life is discussed with the results showing that the effect of stress ratio and inclusion size on fatigue strength is well described by our proposed formula. M ATERIALS AND TESTING METHODS Materials he material used in this investigation is a high-carbon chromium bearing steel (GCr15). The main chemical compositions (mass percentage) are: 1.04 C, 1.51 Cr, 0.29 Mn, 0.24 Si, 0.0058 P, 0.0030 S and balance Fe. Specimens were machined into hourglass shape from annealed steel bar. Then, the specimens were heated at 845°C for 1 hour in vacuum, oil-quenched and tempered for 2 hours in vacuum at 180 ℃ , and air-cooling. Fig. 1 presents the microstructure of the heat-treated material, which is typical martensite structure with spherical carbide particles distributed randomly in the matrix. T

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