PSI - Issue 2_A

Akiyoshi Nakagawa et al. / Procedia Structural Integrity 2 (2016) 1199–1206 Author name / Structural Integrity Procedia 00 (2016) 000–000

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According to experimental results in the very high cycle fatigue by Sakai et al. (2001) and Shiozawa et al. (1999), the crack initiation site in rotating bending is restricted within the surface layer as shown in Fig.4. When the applied stress is high (short life), shallow inclusion tends to cause the fatigue fracture. However, in the long life region (low stress), the fatigue fracture can take place from both of shallow and deep inclusions regardless of the inclusion depth. Based on the experimental evidence in Fig.4, the critical depth of the inclusion causing the crack is given as µ ξ ξ 250 ≤ = c m. 3. Probabilistic model on crack initiation modes

Fig.4 Inclusion depth versus fatigue life

3.1. Stress distribution across the section of specimen

As explained in section 2.1, the surface-initiated fracture was observed in a certain number of specimens belonging to the second S-N curve in the very high cycle regime, although the predominant fracture pattern is the interior-initiated fracture. How can we explain this aspect? From this point of view, the authors have attempted to calculate the probability appearing the surface-initiated fracture in the loading type of rotating bending. In this loading type, the stress distribution across the section has a distinctly steep slope as illustrated in Fig.5. Of course, the maximum stress s σ takes place at the specimen surface, whereas the stress at the center of the section becomes zero. Thus, slope of the stress distribution is given by r s / σ , where r indicates the radius of the bar specimen. The local stress at the site having the depth ξ is given by ( ) r s / 1 ξ σ σ ξ = − . When several inclusions are included along the section, the stress distribution has peek stresses at the edges of inclusions as illustrated in Fig.6.

ξ

σ ξ

σ ξ

ξ

Fig.5 Stress distribution across the section in rotating bending

Fig.6 Stress distribution around inclusions in rotating bending

If every inclusion is replaced by spherical cavity having the radius of ρ , the stress concentration factor for deep inclusion is given by 2.0 ≅ α as reported by Nisida (2001). However, the factor for inclusion located within thin surface layer becomes further due to the effect of the free surface on the stress distribution. Therefore, although peak