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 11 In eq. ℎ is the threshold peak flaw-tip stress for onset of DHC initiation under flaw-tip hydride ratcheting conditions and is given by eq. 10. CSA Standard (2016).   1 2 3 1.14 2 1 1 1 pl c th c C C S p C a                          (10) 641







2

IH       c K p

K







IH

S

;



c

8

p



c

, , , i pl C    are used for fitting and can be referred to in the CSA Standard (2016)

The parameters

2.2 Critical Crack size (CCL) The crack which has initiated will grow by DHC mechanism (eq. 3). The depth of the growing crack would become equal to the wall thickness of the pressure tube at some instance leading to leakage of the coolant. If the crack size is greater than the CCL, pressure tube rupture may occur. The critical size is determined by the eq. 11.

(11)

2

K



CCL



c

    



M  

2 8 

ln sec 

h





f

2



f  The parameters is the bulging factor and can be referred to in the CSA Standard (2016)

2.3 Monte Carlo Simulation In structural reliability methods, a component fails when the applied loads ‘ ’ exceed its resistance ‘ ’ i.e. − ≤0 . Generally, this condition is expressed in terms of a failure equation or a limit state equation ( ) . The are the parameters of this function which constitutes the loads and resistance of the limit state. These can be constants, deterministic variables or uncertain variables. The failure is defined by the condition ( )≤ 0 . Thus, this limit state is written such that it is evaluated less than or equal to zero for when the failure definition is met. The uncertain variables are represented using probability density function and are termed as random variables. The probability of failure , thus can be represented by eq. 12. In each Monte Carlo simulation, individual values of the random variables are simulated and the limit state is evaluated. A large number of simulations ‘ ’ are performed and the count of the number of times ‘ ’ the limit state evaluates to less than or equal to zero ( { ( )≤ 0} ) is obtained. This count is divided by the total number of simulations to arrive at the probability of failure . As with any numerical estimation technique, the convergence of the method needs to be ensured. The error estimate in the simulation methods is given by the coefficient of variation ( ) of the result. It is given by eq. 13.   1 f P  (13) f n P N  (12)

cov



P

f