PSI - Issue 79

Lazar Jeremić et al. / Procedia Structural Integrity 79 (2026) 117 – 123

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5. Risk based analysis According to the size and position of defect 1.1 (edge surface crack in a circumferential welded joint, the stress intensity factor is defined as:    / , / / 2 1.25 87 32 1090MPa mm I K Y a W a c pR t a        (1) where Y(a/W,a/c) is the geometry factor, p – operating pressure (8.1 MPa), R – vessel radius, (1075 mm), W – thickness (50 mm). Now one can calculate the ratio K I /K Ic =0.69, knowing that the minimum fracture toughness of a weld metal is K Ic =1580 Mpa  mm, [3]. The ratio of net stress and its critical value is given: 87 2.78 / 0.38 640 R n F S       (2) taking  F =640 Mpa, as the half summ of Yield Stress (560 MPa) and Tensile Strength (720 MPa). Now, the ccoordinates in FAD are (0,38;0,83), so that the corresponding point is the safe region, as shown in Fig. 9. Based on the arguments given in [2] one can estimate the likelihood of potential failure to be 0.85 (85%). Considering the larger of two defects detected by combined use PAUT and TOFD, namely the internal crack with 2c=53.1 mm and 2a=16.7 mm, the stress intensity factor can be calculated as follows:    / , / / 2 1.01 87 8.35 450MPa mm I K Y a W a c pR t a        (3)

leading to the ratio K R =K I /K Ic =0.28, where Y(a/W,a/c)=1.01 in this case. Ratio between critical cross-section stress and critical stress in this case is: 87 1.5 / 0.20 640 R n F S      

(4)

The coordinates of the point in the Fracture Assessment Diagram (FAD) are now (0.23;0.28), so the level of fracture likelihood is 0.29 (29%).

Figure 9. FAD for vessel 971, defect 1.1: conventional UT (0,38;0,83) advanced UT (0.23;0.28)

Using these two values (0.85 and 0.29) as measure of failure likelihood and estimating the consequences to be of the highest category (5), as explained in [3], one can also estimate the risk of failure to be very high for conventional UT indication, but only low for PAUT and TOFD indication, according to the risk matrix, Figure 10.