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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1. Introduction

One of the typical aspects of fatigue fracture in the very high cycle regime is the fact that the interior-initiated fracture tends to occur as the most popular fracture mode as reported by Sakai et al. (1999) and Sakai (2009). On the contrary, the surface-initiated fracture takes place in the conventional life regime less than 10 7 cycles at higher stress levels. Based on this aspect, we have the duplex S-N characteristics consisting of the respective S-N curves for the surface-initiated fracture and the interior-initiated fracture as reported by Sakai et al. (1999). The stress distribution in the rotating bending has a steep slope across the section, while the distribution in the axial loading is uniform across the entire section. Thus, the surface-initiated fracture can be caused together with the interior-initiated fracture within a thin surface layer in the rotating bending, whereas the interior-initiated fracture tends to occur anywhere in the entire section in the axial loading due to the uniform stress distribution. Another typical evidence in the very high cycle fatigue is a fact that an inclusion is usually found at the core portion of the fish-eye formed on the fracture surface as reported by many researchers such as Murakami et al. (1999) and Sakai et al. (2002) & (2015). When the cyclic loadings are applied to the specimen, stress concentration necessarily takes place around such inclusions. The stress concentration factor would be governed by the shape, the size, the kind of inclusion together with Young’s modulus and Poisson’s ratio of the inclusion and matrix. Although we have such various parameters controlling the stress concentration, a spherical vacancy would be assumed as one of the simplest model to represent the interior defect in this study. Further, assuming that the inclusion size is given by an appropriate size (10µm for example) as a tentative size practically observed on the fracture surface. However, the location of the inclusions inside the material cannot be given in advance. In addition, if the inclusion is located close to the specimen surface, the stress distribution is affected by the free surface. Therefore, spatial distribution characteristics of the inclusion would have an effect on the stress concentration factor of the inclusion at the crack initiation site. In other words, both of the fatigue strength and fatigue life are governed by the spatial distribution of the inclusions inside the material. How can we interpret the statistical fatigue characteristics of metallic materials? From this point of view, the authors have attempted to construct a probabilistic model on the very high cycle fatigue property for metallic materials in rotating bending. 2. Experimental evidence

2000

2.1. Typical example of S-N property for bearing steel in rotating bending Since 1988, T. Sakai and his colleagues have been continuing their long span research project on very high cycle fatigue of metallic materials as a common research in the Research Group for Statistical Aspects of Materials Strength [RGSAMS] organized by Sakai et al. (1992). Among their serial experimental data, fatigue test results for the bearing steel (JIS:SUJ2) obtained in rotating bending are indicated in Fig.1, where the duplex S-N characteristics consisting of the respective S-N curves for the surface-initiated fracture and the interior- initiated fracture are obviously confirmed. The first S-N curve in

Surface-initiated fracture Interior-initiated fracture with a fish-eye

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Stress amplitude, (MPa) 1600 1400 1200 1000

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10 2

10 3 10 4

10 5

10 6 10 7

10 8

10 9 10 10

Number of stress cycles to failure, N

Fig.1 Rotating bending S-N characteristics of bearing steel in very high cycle regime

short life region gives that for the surface-initiated fracture, whereas the second one in long life region is the S-N curve for the interior-initiated fracture. Paying attention to the experimental results along the second S-N curve in the long life region, we can find a couple of data points in the surface-initiated fracture, though all the other data points are in the interior-initiated fracture.