PSI - Issue 19

Masaru Bodai et al. / Procedia Structural Integrity 19 (2019) 64–72 Bodai,M et al. / Procedia Engineering 00 (2019) 000 – 000

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3. Discussion

The stress intensity factor rang ΔK has been calculated by equation of circumferential outer surface semi elliptical surface crack (Shiratori, 1990). The evaluation point A is the deepest point of semi-elliptical surface crack. The following stress intensity factor solution for a linear stress distribution has been applied because the stress distribution in the pipe section can be considered as a linear stress distribution produced by a 4-point bending. ∆ = { × ∆ + bg × ∆ bg }√( ⁄ ) (2) = 1 + 1.464( ⁄ ) 1.65 Valid range as 0.1 ≤ ⁄ ≤ 0.8 , 0.2 ≤ ⁄ ≤ 1 , 1.25 ≤ 0 ⁄ ≤ 10 . Evaluation point A

a

t

2 C

R 0

Fig.8. Circumferential outer surface semi-elliptical surface crack.

In the above piping tests, the load decreased slightly with crack propagation because constant displacement control was applied. In the analyses, the load range of the first cycle is used. The portion to be evaluated has a radius of curvature of 70 mm and a notch of 3 mm in depth. The analyses have been performed based on the nominal bending stress of a pipe of which outer diameter is 216.3 mm and a thickness is 23 mm. The aspect ratio a / C of the flaw shape function Q is set to a constant using the average of the fractured surface for each test. The membrane stress can be set to zero because a 4-point bending was applied to the piping tests. Hence, F bg is necessary for calculating ΔK . F bg is give as Table 4 (Shiratori, 1990) and the closed form of F bg has been developed as a function of a/t as shown in Fig. 9, where the aspect ratio a / C is set to a constant ( a / C =0.6) using the average of the fractured surface for each test.

Table 4. Table of Factor F bg for R i / t =5. a / t a / C =0.4

a / C =0.6

a / C =0.8

1.2

0.1 0.2 0.4 0.6 0.8

1.012 1.090 1.160 1.261 1.346

0.945 1.040 1.072 1.116 1.141

0.887 0.907 0.981 0.977 0.964

1.0

F bg = 0.0893LN(a/t) + 1.1621

0.8

0.6

F bg

0.4

0.2

0.0

0

0.2

0.4

0.6

0.8

1

a/t

Fig. 9. Relationship between F bg and a / t.