PSI - Issue 68

Vitalii Antonchenko et al. / Procedia Structural Integrity 68 (2025) 1305–1311 Vitalii Antonchenko et al./ Structural Integrity Procedia 00 (2025) 000–000

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Table 1 Shape factors for axial crack ! " # $ % &! &" " # ' =1 A 0.962 0.606 0.475 0.404 0.357 0.168 0.023 B 0.642 0.182 0.068 0.031 0.017 0.258 0.04 " # ' =0.7 A 0.986 0.615 0.48 0.407 0.36 0.178 0.023 B 0.702 0.195 0.072 0.032 0.017 0.296 0.031 Table 2 Shape factors for circumferential crack ! " # $ % &! &" " # ' =1 A 0.967 0.605 0.474 0.402 0.355 0.169 0.021 B 0.655 0.179 0.067 0.03 0.016 0.231 0.027 " # ' =0.7 A 0.992 0.615 0.479 0.405 0.357 0.179 0.022 B 0.708 0.19 0.07 0.032 0.017 0.264 0.031 3.1. Results of test cases To validate the obtained coefficients several practically important cases were studied: • Internal pressure, which leads to membrane loading • Temperature gradient, which leads to bending or linear loading throught the thickness • All these cases were tested using: direct FEM analysis (using ANSYS software), current approach, VERLIFE [2] approach and the one recommended by SOU [3], the results are presented for the deepest point in Table 3 for axial crack and Table 4 circumferential crack. Weld residual stresses – usually described by the cosine law, according to recommendations by IAEA [4],[5].

Current approach ∆,% 327.4 -0.13%

Verlife[2] ∆,% 327.0 -0.25%

∆,% 6.29% 39.8% -74.4% -0.023

Table 3 Comparison of test cases for axial crack FEM

SOU[3]

" # =1

Pressure

327.8

348.4

Quadratic temperature distribution Residual stresses All the power factors

341.5 151.2 380.9 320.9

341.3 154.9 384.3 320.3

-0.06% 2.46%

340.9 154.9 381.9 319.6

-0.16% 2.48%

477.6

38.7

0.009

0.002

372.1

Pressure

-0.17%

-0.39%

−

−

" # =0.7

Quadratic temperature distribution

345.6

336.4

-2.66%

336.2

-2.74%

−

−

Residual stresses

155.6 389.8

157.3 393.3

1.09% 0.009

157.4 390.8

1.15% 0.002

− −

− −

All the power factors

Current approach ∆,% 151.7 -0.04%

Verlife[2] ∆,% 150.7 -0.68%

∆,%

Table 4 Comparison of test cases for circumferential crack FEM

SOU[3]

" # =1

Pressure

151.7

159.9

5.38%

Quadratic temperature distribution Residual stresses All the power factors

244.8 149.9 822.3 150.6 248.2 154.5 822.1

245.9 153.2 825.3 150.3 249.7 160.0 822.9

0.48% 2.18% 0.004 -0.18% 0.58% 3.56% 0.001

244.4 152.2 824.5 149.2 247.9 159.1 821.8

-0.15% 1.51%

375.5 37.5 865.3

53.4% -75.0%

0.003

0.052

Pressure

−

−

" # =0.7

-0.93%

Quadratic temperature distribution

−

−

-0.13% 2.99%

Residual stresses

− −

− −

All the power factors

0.000