PSI - Issue 52

Akihide Saimoto et al. / Procedia Structural Integrity 52 (2024) 323–339

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A. Saimoto et al. / Structural Integrity Procedia 00 (2023) 000–000

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1.00

0.15

0.95

0.10

0.90

0.85

0.05

0.80

0.75

0.00

0.01

0.01

0.006

0.006

0.0

0.0

0.002

0.004

0.002

0.004

0.008

0.008

Fig. 6. A demonstration for linear convergence of SIF solution of problem in Fig.5(a), with inverse of the square of number of crack division 1 / n 2 , for material type I-1, α = 45 ◦ and h / b = 0 . 2 , 1 . 0 , 2 . 0 cases (left: mode I, right: mode II normalized SIF at crack tip A in Fig.5(a)).

1.1

0.15

1.0

0.10

0.9

0.8

0.05

0.7

0.6

0.00

0

30

60

90

120

150

180

0

30

60

90

120

150

180

Fig. 7. Influence of angle α onSIF ( h / b = 1 . 0) for the problem of shield cracks (Fig.5(a)).

1.10

0.25

0.20

1.00

0.15

0.90

0.10

0.80

0.05

0.70

0.00

0.1

1

10

0.1

1

10

Fig. 8. Influence of ratio h / b onSIF ( α = 60 ◦ ) for the problem of shield cracks (Fig.5(a)).

division. For example, in α = 45 ◦ and h / b = 1 . 0 situation, n = 5 and 10 division results F A I = 0 . 84476 and 0 . 84510, respectively. By assuming a linear solution convergence of SIF with 1 / n 2 , the extrapolated value for n → ∞ will be (0 . 84510 × 10 2 − 0 . 84476 × 5 2 ) / (10 2 − 5 2 ) = 0 . 84521, while the numerical solution for n = 960 division gives F A I = 0 . 84518, which was found to be within 0.004% relative absolute error.