PSI - Issue 71

Karthik K R. et al. / Procedia Structural Integrity 71 (2025) 210–217

216

J-Integral maximum value (mJ/mm 2 )

Peak applied Stress (MPa)

Initial flaw depth, a (mm)

Final flaw depth (mm)

J-Integral at deepest point (mJ/mm 2 )

% Increase in depth

Initial a/t

SL no.

Thickness (mm)

1 2 3 4 5 6 7 8 9

5.84 5.84 5.99 5.82 6.12 5.94 5.87 9.73 9.68

124.1 140.0 140.0 144.8 131.0 131.0 131.0 140.0 140.0 148.9 155.1 133.8 135.8 142.7 148.2

4.11 4.14 5.41 5.33 5.18 5.23 5.13 8.26 8.43 8.38 8.13 8.13 8.38 7.87 8.38

4.11 4.22 5.51 5.49 5.33 5.38 5.31 8.43 8.51 8.81 8.31 8.28 8.69 8.18 9.14

0.00 1.93 1.85 3.00 2.90 2.87 3.51 2.06 0.95 5.13 2.21 1.85 3.70 3.94 9.07

0.70 0.71 0.90 0.92 0.85 0.88 0.87 0.85 0.87 0.87 0.84 0.84 0.86 0.82 0.88

3.58 5.98 8.33 9.85

3.34 5.43 7.15 9.30

10.30 10.99 11.11 11.87 13.00 14.96 17.25 16.88 18.39 20.90 21.18

10.30 10.99 11.11 9.83 11.72 12.36 15.19 15.63 18.11 19.00 21.08

10 9.68 11 9.65 12 9.63 13 9.75 14 9.58 15 9.50

It can be observed from the LUL test data that cracks start to grow at a value between 3.34 to 5.43 mJ/mm 2 . This agrees with the earlier results. Therefore, a value of J 1e =4.3 mJ/mm 2 is taken as critical value, considering 10% margin on 4.8, assuming that the crack will start to grow when the J value exceeds this critical value. Steps for general assessment methodology are given in Figure 9.

Figure 9: Details of J-Integral evaluation methodology

Figure 10: FE model of shell long-seam weld

Critical weld location of the hardware is at long-seam weld of cylindrical shell as it experiences maximum principal stress (hoop stress). Crack that is oriented in meridional direction will tend to grow due to the hoop stress. FE model of the surface crack in long seam weld is shown in Figure 10. Biggest crack size that can be missed during NDE (corresponding to RT) is taken for the analysis. Same material data and modelling from specimen simulation has been used for hardware level simulation. J value is obtained for the biggest crack for the L-seam weld corresponding to proof pressure condition. This is found to be lower than critical J 1e with positive margin of safety against crack growth initiation. 4. Conclusion As a part of the design, fracture assessment of the pressure vessel is carried out for the biggest crack size that can be missed during NDE for the proof pressure condition. Assessment is carried out by using elastic-plastic fracture parameter called J-Integral. Critical J 1e value is found out from simulating SCT tests. This is compared with the maximum value of J obtained from the tank level analysis to check the structural integrity against crack growth initiation. Tank is having positive margin of safety at proof pressure for the biggest crack. Present work has only considered test data pertaining to deep cracks of a/t ratio higher than 0.5 with specimen