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Zirconium alloys are susceptible to engineering problems associated with the uptake of hydrogen throughout their design lifetime in nuclear reactors. Understanding of hydrogen embrittlement associated with the precipitation of brittle hydride phases and a sub-critical crack growth mechanism known as Delayed Hydride Cracking (DHC) is required to provide the engineering justifications for safe reactor operation. The nature of bulk zirconium hydrides at low concentrations (< 100 wt. ppm) is subject to several contradictory descriptions in the literature associated with the stability and metastability of γ-phase zirconium hydride. Due to the differing volume expansions (12-17%) and crystallography between γ and δ hydride phases, it is suggested that the matrix yield strength may have an effect on the phase stability. The present work indicated that although yield strength can shift the phase stability, other factors such as microstructure and phase distribution can be as or more important. This suggests that small material differences are the reason for the literature discrepancies. DHC is characterised by the repeated precipitation, growth, fracture of brittle hydride phases and subsequent crack arrest in the ductile metal. DHC growth is associated primarily the ability of hydrogen to diffuse under a stress induced chemical potential towards a stress raiser. Knowledge of the factors controlling DHC are paramount in being able to appropriately describe DHC for engineering purposes. Most studies characterise DHC upon cooling to the test temperature. DHC upon heating has not been extensively studied and the mechanism by which it occurs is somewhat controversial in the literature. This work shows that previous thermo-mechanical processing of hydrided zirconium can have a significant effect on the dissolution behaviour of the bulk hydride upon heating. DHC tests with γ-quenched, furnace cooled-δ and reoriented bulk hydrides upon heating and DHC upon cooling suggest that the amount of hydrogen in solution is the primary factor controlling the occurrence of DHC and consistent with the postulation that the stress induced chemical potential is the driving force for DHC. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2012-01-24 06:14:14.152

Pressure tubes pick up hydrogen while they are in service within CANDU reactors. Sufficiently high hydrogen concentration can lead to hydride precipitation during reactor shutdown/repair at flaws, resulting in the potential for eventual rupture of the pressure tubes by a process called Delayed Hydride Cracking (DHC). The threshold stress intensity factor (KIH) below which the cracks will not grow by delayed hydride cracking of Zr-2.5Nb micro pressure tubes (MPTs) has been determined using a load increasing mode (LIM) method at different temperatures. MPTs have been used to allow easy study of the impact of properties like texture and grain size on DHC. Previous studies on MPTs have focused on creep and effects of stress on hydride orientation; here the use of MPTs for DHC studies is confirmed for the first time. Micro pressure tube samples were hydrided to a target hydrogen content of 100 ppm using an electrolytic method. For DHC testing, 3 mm thick half ring samples were cut out from the tubes using Electrical Discharge Machining (EDM) with a notch at the center. A sharp notch with a root radius of 15 µm was introduced by broaching to facilitate crack initiation. The direct current potential drop method was used to monitor crack growth during the DHC tests. For the temperature range tested the threshold stress intensity factors for the micro pressure tube used were found to be 6.5-10.5 MPa.m1/2 with the value increasing with increasing temperature. The average DHC velocities obtained for the three different test temperatures 180, 230 and 250oC were 2.64, 10.87 and 8.45 x 10-8 m/s, respectively. The DHC data obtained from the MPTs are comparable to the data published in the literature for full sized CANDU pressure tubes. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2009-04-24 12:55:36.917

Probabilistic assessment and life cycle management of engineering components and systems in a nuclear power plant is intended to ensure safe and efficient operation of energy generation over its entire life. The CANDU reactor core consists of 380-480 pressure tubes, which are like miniature pressure vessels that contain natural uranium fuel. Pressure tubes operate under severe temperature and radiation conditions, which result in degradation with ageing. Presence of flaws in a pressure tube makes it vulnerable to delayed hydride cracking (DHC), which may lead to rupture or break-before-leak situation. Therefore, assessment of flaws in the pressure tubes is considered an integral part of a reactor core assessment program. The main objective of the thesis is to develop advanced probabilistic and mechanical stress field models for the assessment of flaws. The flaw assessment models used by the industries are based on deterministic upper/lower bound values for the variables and they ignore uncertainties associated with system parameters. In this thesis, explicit limit state equations are formulated and first order reliability method is employed for reliability computation, which is more efficient than simulation-based methods. A semi-probabilistic approach is adopted to develop an assessment model, which consists of a mechanics-based condition (or equation) involving partial factors that are calibrated to a specified reliability level. This approach is applied to develop models for DHC initiation and leak-before-break assessments. A novel feature of the proposed method is that it bridges the gap between a simple deterministic analysis and complex simulations, and it is amenable to practical applications. The nuclear power plant systems are not easily accessible for inspection and data collection due to exposure to high radiation. For this reason, small samples of pressure tubes are inspected at periodic intervals and small sample of data so collected are used as input to probabilistic analysis. The pressure tube flaw assessment is therefore confounded by large sampling uncertainties. Therefore, determination of adequate sample size is an important issue. In this thesis, a risk informed approach is proposed to define sample size requirement for flaw assessment. Notch-tip stress field is a key factor in any flaw assessment model. Traditionally, linear elastic fracture mechanics (LEFM) and its extension, serves the basis for determination of notch-tip stress field for elastic and elastic-perfectly-plastic material, respectively. However, the LEFM solution is based on small deformation theory and fixed crack geometry, which leads to singular stress and strain field at the crack-tip. The thesis presents new models for notch and crack induced stress fields based on the deformed geometry. In contrast with the classical solution based on small deformation theory, the proposed model uses the Cauchy's stress definition and boundary conditions which are coupled with the deformed geometry. This formulation also incorporates the rotation near the crack-tip, which leads to blunting and displacement of the crack-tip. The solution obtained based on the final deformed configuration yields a non-singular stress field at the crack-tip and a non-linear variation of stress concentration factor for both elastic and elastic-perfectly-plastic material. The proposed stress field formulation approach is applied to formulate an analytical model for estimating the threshold stress intensity factor (KIH) for DHC initiation. The analytical approach provides a relationship between KIH and temperature that is consistent with experimental results.

Probabilistic assessment and life cycle management of engineering components and systems in a nuclear power plant is intended to ensure safe and efficient operation of energy generation over its entire life. The CANDU reactor core consists of 380-480 pressure tubes, which are like miniature pressure vessels that contain natural uranium fuel. Pressure tubes operate under severe temperature and radiation conditions, which result in degradation with ageing. Presence of flaws in a pressure tube makes it vulnerable to delayed hydride cracking (DHC), which may lead to rupture or break-before-leak situation. Therefore, assessment of flaws in the pressure tubes is considered an integral part of a reactor core assessment program. The main objective of the thesis is to develop advanced probabilistic and mechanical stress field models for the assessment of flaws. The flaw assessment models used by the industries are based on deterministic upper/lower bound values for the variables and they ignore uncertainties associated with system parameters. In this thesis, explicit limit state equations are formulated and first order reliability method is employed for reliability computation, which is more efficient than simulation-based methods. A semi-probabilistic approach is adopted to develop an assessment model, which consists of a mechanics-based condition (or equation) involving partial factors that are calibrated to a specified reliability level. This approach is applied to develop models for DHC initiation and leak-before-break assessments. A novel feature of the proposed method is that it bridges the gap between a simple deterministic analysis and complex simulations, and it is amenable to practical applications. The nuclear power plant systems are not easily accessible for inspection and data collection due to exposure to high radiation. For this reason, small samples of pressure tubes are inspected at periodic intervals and small sample of data so collected are used as input to probabilistic analysis. The pressure tube flaw assessment is therefore confounded by large sampling uncertainties. Therefore, determination of adequate sample size is an important issue. In this thesis, a risk informed approach is proposed to define sample size requirement for flaw assessment. Notch-tip stress field is a key factor in any flaw assessment model. Traditionally, linear elastic fracture mechanics (LEFM) and its extension, serves the basis for determination of notch-tip stress field for elastic and elastic-perfectly-plastic material, respectively. However, the LEFM solution is based on small deformation theory and fixed crack geometry, which leads to singular stress and strain field at the crack-tip. The thesis presents new models for notch and crack induced stress fields based on the deformed geometry. In contrast with the classical solution based on small deformation theory, the proposed model uses the Cauchy's stress definition and boundary conditions which are coupled with the deformed geometry. This formulation also incorporates the rotation near the crack-tip, which leads to blunting and displacement of the crack-tip. The solution obtained based on the final deformed configuration yields a non-singular stress field at the crack-tip and a non-linear variation of stress concentration factor for both elastic and elastic-perfectly-plastic material. The proposed stress field formulation approach is applied to formulate an analytical model for estimating the threshold stress intensity factor (KIH) for DHC initiation. The analytical approach provides a relationship between KIH and temperature that is consistent with experimental results.