PSI - Issue 14

Y. Akaki et al. / Procedia Structural Integrity 14 (2019) 11–17 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

16 6

are listed in Table 1. The value of  K  th is given by the following equation based on Eq. (1): ∆ th = 0.69 ∙ (2 th )√ √ (2) where  th is the threshold stress amplitude and √ area s is the square root of the crack area of a semi-circular surface crack. In this study, the crack was assumed to be of a semi-circular shape, i.e. √ = √ ⁄2 ∙ or = √2 ∙ ⁄ . Okazaki et.al (2011, 2014) reported that in the region of small cracks, the value of  K  th exhibited a crack size dependency of ∆ K τ th ∝ (√ area s ) 1 3 ⁄ at room temperature in air for a bearing steel of JIS-SUJ2. Furthermore, they proposed the following predictive equation of  K  th : ∆ K τ th = 1.26( F +1.33) (√ area s ) 1 3 ⁄ (3) where F is the area fraction of the crack surfaces interacting to each other and in this study, F = 1 since the whole crack area is in contact. In addition, the coefficient of 1.26 is the value obtained for a material with the Vickers hardness of HV = 753. Therefore, considering HV = 800 of the material used in this study, this coefficient is corrected to be 1.26 × (800/753) = 1.34. Consequently, the following equation is used in this study: ∆ K τ th = 1.34(1+1.33) (√ area s ) 1 3 ⁄ = 3.12 (√ area s ) 1 3 ⁄ (4) Fig. 6 shows a comparison of the prediction line of Eq. (4) with the experimental data of  K  th . Two experimental values of  K  th measured for Crack A and Crack B under the non-charging condition agree well the prediction line.

 K  th (MPa ∙ m 25.5

Table 1.  K  th calculated using experimental values of a and  th .

Environmental Condition Non-charging

Crack

a (  m)

 th (MPa)

1/2 )

470 370 440 360

393 538 442 652

1

23.5 25.3 25.2

H-charging

Non-charging

2

H-charging

Fig.6 Relationship between the threshold SIF ranges,  K  th and the length, a , of shear-mode fatigue cracks.