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

333 11

√ π b , F A

√ π b ).

Table 2. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 0 ◦ ( F A I = K A I /σ

A II /σ

II = K

division

Type I-1

Type I-2

Type I-3

Type II

Type III

number n F A I

A II

A I

A II

A I

A II

A I

A II

A I

A II

F

F

F

F

F

F

F

F

F

30 60

0.69929 0.18732 0.71740 0.27446 0.73630 0.32637 — — 0.71935 0.27700 0.70018 0.18647 0.71775 0.27381 0.73652 0.32579 — — 0.71971 0.27634 0.70035 0.18623 0.71782 0.27363 0.73657 0.32563 0.70468 0.08920 0.71977 0.27616 0.70039 0.18617 0.71783 0.27359 0.73658 0.32559 0.70528 0.08902 0.71979 0.27612 0.70040 0.18615 0.71783 0.27358 0.73658 0.32558 0.70539 0.08897 0.71979 0.27611 0.70040 0.18615 0.71783 0.27357 0.73658 0.32558 0.70541 0.08896 0.71979 0.27610

120 240 480 960

√ π b , F A

√ π b ).

Table 3. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 30 ◦ ( F A I = K A I /σ

A II /σ

II = K

division

Type I-1

Type I-2

Type I-3

Type II

Type III

number n F A I

A II

A I

A II

A I

A II

A I

A II

A I

A II

F

F

F

F

F

F

F

F

F

30 60

0.70013 0.18644 0.75690 0.19030 0.79574 0.15974 — — 0.75668 0.18983 0.70100 0.18557 0.75661 0.18936 0.79534 0.15891 0.61641 0.20264 0.75643 0.18891 0.70117 0.18532 0.75651 0.18912 0.79523 0.15871 0.61669 0.20260 0.75635 0.18867 0.70121 0.18526 0.75649 0.18906 0.79520 0.15866 0.61676 0.20260 0.75633 0.18862 0.70122 0.18524 0.75648 0.18905 0.79520 0.15864 0.61678 0.20259 0.75632 0.18860 0.70122 0.18524 0.75648 0.18904 0.79520 0.15864 0.61678 0.20259 0.75632 0.18860

120 240 480 960

√ π b , F A

√ π b ).

Table 4. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 45 ◦ ( F A I = K A I /σ

A II /σ

II = K

division

Type I-1

Type I-2

Type I-3

Type II

Type III

number n F A I

A II

A I

A II

A I

A II

A I

A II

A I

A II

F

F

F

F

F

F

F

F

F

30 60

0.70014 0.18548 0.76898 0.15814 — — — — 0.77124 0.15809 0.70102 0.18460 0.76797 0.15695 0.81396 0.12636 0.70118 0.23551 0.77024 0.15693 0.70119 0.18436 0.76770 0.15667 0.81366 0.12613 0.70117 0.23547 0.76998 0.15666 0.70122 0.18429 0.76764 0.15660 0.81359 0.12607 0.70117 0.23546 0.76991 0.15659 0.70123 0.18427 0.76762 0.15658 0.81357 0.12606 0.70117 0.23546 0.76990 0.15658 0.70123 0.18427 0.76761 0.15658 0.81357 0.12605 0.70117 0.23546 0.76989 0.15657

120 240 480 960

√ π b , F A

√ π b ).

Table 5. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 60 ◦ ( F A I = K A I /σ

A II /σ

II = K

division

Type I-1

Type I-2

Type I-3

Type II

Type III

number n F A I

A II

A I

A II

A I

A II

A I

A II

A I

A II

F

F

F

F

F

F

F

F

F

30 60

0.69983 0.18449 0.77189 0.13494 — — 0.77484 0.22887 0.77941 0.13333 0.70073 0.18362 0.76954 0.13326 — — 0.77385 0.22825 0.77668 0.13165 0.70090 0.18337 0.76897 0.13290 0.82621 0.10156 0.77363 0.22812 0.77606 0.13129 0.70094 0.18331 0.76883 0.13281 0.82602 0.10149 0.77358 0.22809 0.77591 0.13120 0.70095 0.18329 0.76879 0.13279 0.82598 0.10147 0.77356 0.22808 0.77588 0.13118 0.70095 0.18329 0.76879 0.13278 0.82597 0.10147 0.77356 0.22808 0.77587 0.13118

120 240 480 960

(due to the number of division n is too small) and its position is indicated by a horizontal bar in tables. The numerical results show that even in the case of h / b = 0 . 1, where the two cracks are very close, a solution that converges at least to the fourth decimal place is obtained when n = 120. In most cases, the number of divisions of n = 480 and n = 960 yielded solutions that converged perfectly to the fifth decimal place, indicating that the present numerical solution can be regarded as practically exact.