13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- by the cracking of inclusion itself is not circular but somewhat angular in accordance with the inclusion shape. Hence, we approximate the cracks forming at nonmetallic inclusions as planar cracks by projecting the 3-D shape of the inclusion onto the plane perpendicular to the tensile axis of the specimen [7, 8, 10]. For a planar internal crack with arbitrary shape under tension shown in Fig. 11(a), KImax along the crack front is approximately given by [7, 8, 10]. KImax = 0.5σ0 area π (2) Thus, KTH for H-precharged smooth specimens associated with KImax is expressed by KTH = 0.5σf area π (3) KTH obtained through this equation yields a magnitude which differs from that of Eq. (1) for the perfectly penny-shaped crack by only about 4%. All the fracture data are listed in Table 1. The primary objective in this study is to determine the initiation threshold KTH for the onset of crack propagation from small cracks in components exposed to high pressure hydrogen gas. It is well known in metal fatigue that ΔKth for small cracks is not a material constant; ΔKth for small cracks is smaller than that for long crack [7, 8, 10, 16]. In this study, we will explore whether such a size dependence exists or not in the case of small cracks in H-precharged specimens under static loading. Figure 12 shows KTH plotted respectively against the inclusion size area and the residual hydrogen content measured right after the final fracture of each specimen CH, R [12]. Regardless of some visible scatter in the experimental data in Fig. 12, one can note the following trends: • KTH, decreases with an decrease in the inclusion size area . • KTH, decreases with an increase in the residual hydrogen content CH, R. By means of these two dominant factors, the experimental data shown in Fig. 12 can be linearly interpolated by KTH = 3.89 + 0.0555 area − 0.494CH, R (4) Where, area is in μm and CH, R is in mass ppm. Figure 13 replots the data in Fig. 12 modified based on Eq. (4) [12]. Equation (4) is expressed as a linear function of area and CH, R, because the variation range of these variables are small such as 10-30μm of inclusion size. However, the equation applicable to wider variation range of these variables must be reconstructed as described later. The reason for the dependence of KTH on the inclusion size is explained as follows. Recall that the distribution of tensile stress along the axis of symmetry (x direction) ahead of the crack of length 2a in an infinite plate under remote tensile stress σ0 in the y direction is described by 2 2 0 yy x a x (5)
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