numero25

G. Qian et alii, Frattura ed Integrità Strutturale, 25 (2013) 7-14; DOI: 10.3221/IGF-ESIS.25.02 12 Figure 6: Predicted n i of subsurface crack initiation for specimens tested in air, for different loading levels and material properties. The variation of i n with φ and ψ are demonstrated in Fig. 6 by assuming φ to be 1.1, 1.2, 1.4, 2 and 4, and ψ varying from 0 to 2. It is shown that fatigue life i n increases with the decrease of φ , i.e. the decrease of fatigue loading Δ σ or the increase of the resistance of dislocation movement k . For a given loading state ( φ being constant), i n generally decreases with the increase of ψ , i.e. the increase of inclusion size r or the decrease of grain size l . The trends are in agreement with the experimental observations. Yang et al. [20] observed that the fatigue life increases with the decrease of inclusion size for an alloy steel. It is widely observed that the fatigue life increases with the decrease of the applied loading [1-16]. Zhao et al. [10] found that the fatigue life increases with the resistance of the dislocation movement, i.e. the yield stress of material. For fatigue crack initiation at surface, by considering the surface crack factor and half cycling process [7, 19], surface crack initiation cycle N s is   s s 2 4 1.25 2 AW N l k     (9) where W s is surface energy related to surface crack initiation. The normalized surface crack initiation cycle s n is   s s 2 w 4 1.25 1 N N n k      (10) where k w is the ratio of surface energy for crack formation at subsurface to that at surface ( W i / W s ). Note that both i n and s n are functions of φ and ψ . In short, Eqs. (8) and (10) are used to calculate the fatigue life for crack initiation at surface or at subsurface in different environmental medias. For the case tested in air, k w is taken as 3 in the calculation [8, 21]. For the case tested in 3.5 % NaCl solution, k w is taken as 25 times of that in air, i.e. 75, from the relationship of K Ic in air and the aqueous solution [8, 22]. The fatigue life for surface crack initiation s n and subsurface crack initiation i n in air as a function of φ and ψ is compared in Fig. 7 (a). It is seen that the subsurface crack initiation life is higher than the surface crack initiation life for a high φ (high loading or low material yield stress). Thus, surface crack initiation occurs much easier in this stage. With decreasing φ , the surface crack initiation life is higher than the subsurface crack initiation life at the same φ , which as a consequence leads to the subsurface crack initiation in this stage. At points A, B and C, the subsurface crack initiation life equals to the surface crack initiation. The three points correspond to the transition plateau in an S-N curve from the subsurface to the surface crack initiation. Fig. 7 (b) compares the surface crack initiation life with subsurface crack initiation life in 3.5% NaCl solution. A similar trend as that in air is found. However, the transition from surface to subsurface crack initiation in 3.5% NaCl solution is much lower than that in air. This is in agreement with the experimental observations that in aqueous environmental media, the crack initiation starts from the surface even in VHCF regime. It is also seen from Figs. 7 (a) and (b) that when subjected to the same loading, the fatigue life in air is much longer than that in aqueous medias. This explains the characteristics of the S-N curve in Fig. 2.