PSI - Issue 60

P.A. Jadhav et al. / Procedia Structural Integrity 60 (2024) 631–654 P.A. Jadhav et. al./ Structural Integrity Procedia 00 (2019) 000 – 000

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The probability estimates are obtained assuming that the volumetric flaw is existing in the PT. The time at which this flaw got formed is not considered in the study. The studies are done for the bearing pad fretting flaw whose characterized dimensions are show in in Fig.1 and 2. The flaw depth and flaw length are taken as lognormal distributed random variables in studies reported by Oh et. al. (2012), (2014). The coefficient of variation considered in flaw length is 80% and that in flaw depth is 120%. In their paper Oh et. al. have (2012) also considered the flaw size as a lognormal random variable. The mean of crack length values considered in this study are 1.5 mm, 2.875 mm and 5 mm. The crack depth by thickness ratio considered in this study are 2%, 4%, 10% and 20%. The root radius is kept as a deterministic random variable in the work. Results are reported for the root radius values (in microns) of 10, 30, 50, 100, 200, 300, 400 and 500. The distribution of is taken as Normal as given by Oh et. al.(2014). The distribution of is taken as Lognormal Kwak and Lee (2003). Table 1: Deterministic variables used in the analysis Parameter Value Thickness of Pressure tube: 3.4 mm Internal Diameter: 82.6 mm Pressure: 10 MPa Operating Temperature: 298 OC Young’s Modulus: 91681 MPa Residual Stress (MPa): 0, 50, 100, 120 Hydrogen concentration (ppm): 25, 30, 35, 40, 45, 50 Delayed Hydride Crack growth velocity: A = 3 × 10-3 m/s, Q = 45.5 kJ/mol, refer eq. (1)

Table 2: Probabilistic variables used in the analysis Probabilistic variables PDF type Mean

2 ⁄

cov

Lognormal Lognormal

1.5, 2.875, 5 2, 4, 10, 20

120%

(%)

80%

(microns)

Fixed

10, 30, 50 , 100, 200, 300, 400, 500

Normal Normal

450

2%

4.5

20% 15% 2.5%

Log-Normal 159.0

Normal

687.5

4. Results 4.1 Probability of initiation of DHC and probability of break-before-leak The results are presented in the terms of probability of initiation of DHC ( _ ) and probability of BBL ( _ ) . The _ defines the condition in which, for the set of input variables, the DHC crack gets initiated from a volumetric flaw. Once initiated, this crack grows in the radial-axial plane of the PT. At some point in time the crack is expected to become TWC. The coolant will leak through this crack into the annulus space between Calandria Tube and PT. The length of this crack may exceed the CCL leading to a situation of BBL. The probability of occurrence of this event is evaluated as _ . Limit state function for the initiation of the volumetric flaw is given by eq .15. 1 = max( ℎ − , ℎ − ) (15)