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

334 12

√ π b , F A

√ π b ).

Table 6. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 90 ◦ ( 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

0.69866 0.18342 — — — — — — — — 0.69960 0.18255 0.69145 0.10222 0.78358 0.05150 0.71190 0.14288 0.69141 0.09467 0.69979 0.18231 0.69257 0.10179 0.69158 0.04872 0.71273 0.14247 0.69290 0.09421 0.69983 0.18224 0.69278 0.10167 0.69404 0.04848 0.71288 0.14236 0.69318 0.09407 0.69984 0.18223 0.69283 0.10163 0.69448 0.04840 0.71291 0.14233 0.69324 0.09403 0.69984 0.18222 0.69284 0.10162 0.69457 0.04838 0.71291 0.14232 0.69325 0.09402

120 240 480 960

Table 7. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 120 ◦ ( F A I = K A I /σ √ π b , F A II = K A II /σ √ π b ). 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

0.69783 0.18426 0.68882 0.09059 — — 0.60340 0.24773 0.69537 0.08038 0.69879 0.18341 0.69106 0.09021 — — 0.60450 0.24730 0.69745 0.08003 0.69899 0.18316 0.69163 0.09011 0.85437 -0.07021 0.60483 0.24717 0.69799 0.07995 0.69903 0.18310 0.69178 0.09008 0.85450 -0.07020 0.60492 0.24714 0.69813 0.07994 0.69904 0.18308 0.69182 0.09007 0.85452 -0.07018 0.60495 0.24713 0.69817 0.07993 0.69904 0.18308 0.69182 0.09007 0.85452 -0.07018 0.60495 0.24712 0.69818 0.07993

120 240

480

960

Table 8. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 150 ◦ ( F A I = K A I /σ √ π b , F A II = K A II /σ √ π b ). 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

0.69816 0.18622 0.70296 0.16809 0.78474 -0.01420 — — 0.71126 0.15868 0.69909 0.18537 0.70371 0.16771 0.78520 -0.01439 0.77161 0.22396 0.71193 0.15833 0.69928 0.18513 0.70388 0.16761 0.78524 -0.01432 0.77129 0.22378 0.71208 0.15823 0.69932 0.18507 0.70392 0.16758 0.78524 -0.01430 0.77122 0.22374 0.71211 0.15821 0.69933 0.18505 0.70393 0.16757 0.78524 -0.01429 0.77120 0.22373 0.71212 0.15820 0.69933 0.18505 0.70394 0.16757 0.78524 -0.01429 0.77120 0.22373 0.71212 0.15820

120 240 480 960

Table 9. Convergence of the SIF at crack tip A in Fig.5(a) for h / b = 0 . 1 ,α = 180 ◦ ( F A I = K A I /σ √ π b , F A II = K A II /σ √ π b ). division Type I-1 Type I-2 Type I-3 Type II

Type III

A I

A II

A I

A II

A I

A II

number n F 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 0.73653 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

Obviously, the results for α = 0 ◦ (Table 2) and 180 ◦ (Table 9) should be completely identical, but to confirm this, the calculation was performed to verify that the developed program was correct. The result of convergence verification for α = 45 ◦ situation was plotted in Fig.6. As can be seen from this figure, the SIF solution has the property of converging linearly with the inverse of the square of the division number 1 / n 2 . This property has been confirmed in many analyses in the BFM, when the resultant force method was used, and is quite useful when one wishes to obtain an accurate and practically exact solution from the results of a small number of the crack line