PSI - Issue 52

Akihide Saimoto et al. / Procedia Structural Integrity 52 (2024) 323–339 A. Saimoto et al. / Structural Integrity Procedia 00 (2023) 000–000

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3.2. Analysis of step cracks

The 2nd numerical example concerns a step cracks (Fig.5(b)). In this problem, the SIFs take di ff erent values at the outer crack tip A and at the inner crack tip B. When the ratio h / b tends to zero, the 2 cracks form one straight crack, and the SIF at crack tip A becomes theoretically K A I = σ √ 2 π b , that is, F A I = √ 2, regardless of material properties or angle α . In this problem, the mode I SIF is larger than in the stand-alone case as a result of interference between two cracks. Fig.9 shows the relationship between the SIF and h / b at the outer crack tip A. The SIFs for mode I and mode II are illustrated on the left and right sides of this figure, respectively. From this figure, it can be seen that the mode I SIF is larger for materials III, I-1, and II in that order over a wide range of h / b . At least in the range of h / b < 2 . 0, this trend is confirmed. As for the mode II SIF, it is observed to vary in sign as h / b varies. The largest variation is observed for material III and the smallest for material II. When h / b becomes somewhat large, the mode II SIF at crack tip A becomes negative value, indicating that the crack tends to propagate in a direction perpendicular to the external tension. As h / b increases, F A I and F A II finally converges to 1.0 and 0.0 respectively. It means that the interference e ff ect has disappeared. The same calculation results are shown in Fig.10 for the case where α = 60 ◦ . Compared to Fig.9, the range of variation of the SIF is larger for both mode I and mode II. However, the general trend is similar to the case where α = 0 ◦ .

3.000

0.300

2.500

0.200

A'

B'

2.000

0.100

A B

1.500

0.000

1.000

-0.100

0.500

-0.200

0.000

-0.300

0.1

1

10

0.1

1

10

Fig. 11. Normalized SIFs F B

I and F B II at inner crack tip B for α = 0 ◦ condition for the problem of step cracks (Fig.5(b)).

3.000

0.300

2.500

0.200

A'

B'

2.000

0.100

A B

1.500

0.000

1.000

-0.100

0.500

-0.200

0.000

-0.300

0.1

1

10

0.1

1

10

Fig. 12. Normalized SIFs F B

I and F B II at inner crack tip B for α = 60 ◦ condition for the problem of step cracks (Fig.5(b)).