PSI - Issue 60

D. Sen et al. / Procedia Structural Integrity 60 (2024) 44–59 Deeprodyuti Sen/ Structural Integrity Procedia 00 (2024) 000 – 000

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solubility limit , the excess hydrogen precipitates as δ -hydride phase with a platelet morphology. The precipitated phase is brittle compared to the zirconium matrix and may crack, thus, leading to the initiation of DHC. Although, the manufacturing procedures ensure that the pressure tubes put into service do not contain any macroscopic flaw, volumetric or planar flaws, however, may develop during the service life. Typically, volumetric flaws develop from the scratch marks left by the fretting of bearing pads of the fuel bundles or by scratches formed by fretting of debris present in the heat transport system. The primary aim of Fitness for Service (FFS) evaluation, is to estimate the limiting flaw size for which DHC initiation can be ruled out. * Deeprodyuti Sen. Tel.:+022-255926745. E-mail address: ddsen@barc.gov.in Nomenclature

Radial Flaw Depth. Flaw half-length in the pressure tube circumferential direction. Flaw half-length in the pressure tube axial direction.

a b c f j

geometry correction factor for the stress intensity factor for a crack at a planar surface of a semi-infinite solid, corresponding to the j th stress term in the power-law stress distribution. non-dimensional geometry coefficient for the stress intensity factor that accounts for the effects of the blunt notch geometry and finite wall thickness, corresponding to the j th stress term in the power-law stress distribution. non-dimensional geometry coefficient for the crack mouth opening displacement that accounts for the effects of the blunt notch geometry and finite wall thickness, corresponding to the j th stress term in the power-law stress distribution. Stress concentration factor. Elastic stress concentration factor for 3-D flaw. Elastic stress concentration factor for 2-D flaw (infinitely long). Threshold stress for delayed hydride cracking initiation at a planar surface. Internal Pressure Process-zone restraining stress that is idealized as uniform in the process zone. Radial direction in pressure tube. Length of the process zone, or length of a crack. Critical process-zone displacement at onset of delayed hydride cracking initiation. Process-zone displacement that is a function of the flaw geometry, the process-zone restraining stress p H , and the applied loads. Wall thickness of the pressure tube. Direction ahead of flaw tip. Length over which the cubic fit is performed. Stress coefficient in the cubic polynomial stress distribution equation. Young’s modu lus of elasticity. Stress intensity factor for the fictitious crack of length ‘s’ . Stress intensity factor for 2-D (infinitely long) Stress intensity factor for 3-D Stress Intensity factor for DHC initiation from a crack.

g j

h j

k t k t3D k t2D

p c p r p H

r s

v c v T

w x

x 0 A j E K Ij

K I2D K I3D K IH R o R i σ A (x) σ TH σ n

Outer Radius of Pressure Tube Inner Radius of Pressure Tube Stress field variation in front of flaw tip. Threshold Peak Stress Applied nominal stress Poisson’s Ratio Flaw tip root radius. Circumferential direction in pressure tube.

υ ρ θ