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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A number of models have been proposed in the literature for evaluation of the threshold tensile stress for DHC initiation from blunt volumetric flaws. Shi and Puls (1994) proposed that DHC initiation occurs once the net tensile stress, resulting from the combined effect of hydride precipitation and the external stress, in the hydrided region ahead of a flaw exceeds a critical value, say ‘ p c ’. This material parameter ‘ p c ’ , may be viewed as a micro-threshold tensile stress of a brittle hydride that, in turn, depends on the service temperature. A similar model was proposed by Smith (1995) though the details of evaluation of transformation induced stresses are somewhat different. While Shi and Puls (1994) used the Eshelby theory (1957), Smith (1995) employed an edge dislocation model to simulate the stress field in the hydride region. Both these models require knowledge of the size and shape of the hydride region and the critical stress for hydride fracture. This approach has served as the basis for evaluation of blunt flaws in CANDU pressure tubes in an earlier version (before 2001) of fitness for service code (1996). Smith (1996) in a later work, however, argued that a hydride region consists of a distribution of brittle hydride platelets within a ductile zirconium matrix. When an element in the hydride region attains some critical stress say, p* , the progressive failure of the hydride will decrease the stress and a complete loss of cohesion occurs when the relative displacement ( v ) across the thin hydride strip attains a critical v c . Smith proposed a simple strip-yield type model (1996) to represent the failure behaviour of the hydride region based on the classic Dugdale (1960) and Bilby et al. (1963) model. The earlier Fitness-for-Service Guidelines (1996) for volumetric flaws do not consider the effect of flaw geometry in the evaluation of DHC initiation from blunt flaws. The latter experimental studies, however, clearly demonstrate the effect of flaw geometry, especially the flaw root radius on the peak stress required for DHC initiation. To alleviate this limitation of the existing methods, Scarth and Smith (2001 & 2002) proposed a practical method which overcomes most of the above-mentioned limitations and it has been adopted by the Canadian FFS standard (2016) , hereafter simply referred to as the “CSA Standard”. The proposed method is based on a Process zone scheme by Scarth and Smith (2001 & 2002) that involves estimation of a limiting size of the hydride region and a peak threshold stress for DHC initiation for a given flaw geometry and applied loading. The process zone methodology developed by Scarth and Smith (2001 & 2002) is, however, tedious as it involves a set of non-linear equations that need to be solved simultaneously. In the present work, the process zone model is implemented in an in-house computational code (ZIPTAS) and a set of parametric studies are performed to assess the influence of flaw geometry, flaw size and service loads on the maximum nominal stress that will not lead to initiation of DHC from a volumetric flaw in a pressure tube. The effect of residual stress near the rolled joints in a pressure tube on DHC initiation is also accounted for. To simplify the calculations, the residual stress in the rolled joint region is superimposed on the hoop stress in a pressure tube resulting from internal pressure. The developed ZIPTAS code is validated with several published results and is expected to be useful to both plant operators and regulators for quick and robust assessment of flaw size that can be safely permitted for continued operation of PHWRs. 2. Process Zone Model and Implementation The process-zone representation of the stress relaxation at the crack tip caused by hydride formation is based on the strip-yield model proposed by Dugdale (1960) and Bilby et al . (1963). Using this model, it is possible to incorporate the non-uniform thickness of hydride along the length typically observed in the experiments. Since hydrogen diffusion is assisted by stress gradients, hydrides get precipitated at the tip of the blunt notch, as shown in Fig.1. In the model of Scarth and Smith (2001 & 2002) the hydride region ahead of the blunt notch is treated as an infinitesimally thin process-zone. Within this zone, the tensile stress that hydride can carry before fracture is idealized to have a uniform value, say ‘ p H ’, while the relative displacement acr oss the zone at the trailing edge of the flaw surface is equal to ‘ v T ’. Using finite elem ent analysis, Metzger and Sauve (1996) have shown that the assumption of a uniform tensile stress, ‘ p H ’ within the process zone is approximately true for blunt flaws. The process zone displacement, ‘ v T ’ is a measure of hydride expansion , as shown in Fig.1.