PSI - Issue 2_A

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

1206

8

2

d

2 900 c w σ

ξ

(

) ( ) f ξ =

f

σ

=

. (8)

w

9

3

d

F

σ

w

9

9

The pdf of 9 w σ given by Eq.(8) is depicted in Fig.11. The lower bound of the distribution is 900MPa, whereas its upper bound is 1080MPa as explained above. Although these bounds of the distribution are in good agreement with the distribution characteristics of the experimental results in Fig.1, applicability of the probability density function calculated by Eq.(8) is still unconfirmed. Paying an attention to the distribution pattern of the fatigue strength 9 w σ in Fig.11, there can be several factors other than the inclusion depth to govern the fatigue strength distribution. Experimental data in the very high cycle regime are not enough to make all the factors clear at the present stage of the work. In order to clarify the precise distribution characteristics of 9 w σ , sufficient data should be accumulated and further discussed in the future. Main conclusions obtained in this study are summarized as follows; (1) Assuming that inclusions are sited at random inside the material, the probability density function and the cumulative distribution function of the inclusion depth ξ are given by ( ) ξ ξ 2 1 and ( ) 2 F = − . (2) The inclusion depth at the crack initiation site is restricted within the range of µ 0 250 − m in the case of rotating bending. In addition, if the inclusion depth is less than the radius of the inclusion, the fatigue crack initiation mode becomes “surface-initiated fracture”. Based on this concept, the actual probability of the surface-initiated fracture in the very high cycle regime is successfully explained. (3) The lower and upper bounds of the distribution of the fatigue strength at 9 10 = N cycles can be well interpreted as the nominal stresses at the inclusion depths of 0 = ξ (specimen surface) and c ξ ξ = (critical inclusion depth). The respective stress levels are in good agreement with the distribution aspect of experimental results. But, the further experimental results should be accumulated to discuss the distribution pattern of the fatigue strength. References Sakai, T., Takeda M., Shiozawa K., Ochi Y., Nakajima M., Nakamura T., Oguma N., 1999. Experimental evidence of duplex S-N characteristics in wide life region for high strength steels, Proc. Fatigue’99, 1, 573-578. Sakai T., 2009. Review and prospects for current studies on very high cycle fatigue of metallic materials for machine structural use, J. Solid Mechanics and Materials Engineering 3, 425-439. Murakami Y., Nomoto T., Ueda T., 1999. Factors influencing the mechanism of super-long fatigue failure in steels, Fatigue Fract Eng Mater Struct 22, 581-590. Sakai T., Sato Y., Oguma N., 2002. Characteristic S-N properties of high-carbon-chromium-bearing steel under axial loading in long-life fatigue, Fatigue Fract Eng Mater Struct 25, 765-773. Sakai T, Oguma N, Morikawa A, 2015. Microscopic and nanoscopic observations of metallurgical structures around inclusions at interior crack initiation site for a bearing steel in very high-cycle fatigue, Fatigue Fract Engng Mater Struct 38, 1305-1314. Sakai T., Tokaji K., Hasegawa N., Nakajima M., 1992. Statistical distribution patterns of static and fatigue properties for metallic materials, J. Soc. Mat. Sci., Japan 41, 1014-1024. Shiozawa K, Morii Y, Nishino S, Lu L, 2006. Subsurface crack initiation and propagation mechanism in high strength steel in a very high cycle fatigue regime, Int J Fatigue 28, 1521-1532. Sakai T., Sato Y., Oguma N., 2002. Characteristic S-N properties of high –carbon-chromium-bearing steel under axial loading in long-life fatigue, Fatigue Fract Engng Mater Struct 25, 765-773. Sakai T., Takeda M., Tanaka N., Kanemitsu M., Oguma N., Shiozawa K., 2001. S-N property and fractography of high carbon chromium bearing steel over ultra wide life region under rotating bending, Trans. JSME 67, 1805-1812. Shiozawa K, Lu L., Ishihara S., 1999. Subsurface fatigue crack initiation behaviour and S-N curve characteristics in high carbon chromium bearing steel, J. Soc. Mat. Sci., Japan 48, 1095-1100. Nisida M., 2001, Stress concentration, Morikita Publishing Co., Ltd., Tokyo, 523-525. Murakami Y., Kodama S., Konuma S., 1988. Quantitative evaluation of effect nonmetallic inclusions on fatigue strength of high strength steel, Trans. Jpn Soc. Mech. Eng. 54, 688-695.      =  − r r f 2 2 1 ξ ξ ξ r r 4. Concluding remarks