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The damage induced pressurized thermal shock (PTS) may pose to a reactor pressure vessel (RPV) is a critical safety requirement assessed as part of the ageing management programme of pressurized water reactors (PWRs). A number of researches have studied PTS initiated mainly by postulated accidents such as loss of coolant accidents (LOCAs). However, investigations on PTS-induced threat on RPV caused by inadvertent actuation of the safety injection, a frequent anticipated transient, have not been thoroughly studied. In this paper, a simplified multistep analysis method is applied to study the thermomechanical status of a two-loop PWR under PTS loads caused by inadvertent actuation of the safety injection system. A direct-coupling thermomechanical analysis is performed using a three-dimensional (3D) RPV finite element model. A 3D finite element submodel (consisting of the highiest stress concentration area in the RPV) and an assumed crack are then used to perform fracture mechanics analysis. Subsequently, the critical integrity parameter-stress intensity factor (SIF) is estimated based on FRANC3D-M-integral method coupled in the multistep simulation. The material fracture toughness of the vessel is computed based on the master curve method with experimental fracture toughness data. The results obtained from the direct coupling stress analysis in comparison with sequential coupling approach demonstrate the effectiveness of the proposed multistep method. Also, comparing SIF results obtained with that calculated based on the conventional virtual crack-closure technique (VCCT) and extended finite element method (XFEM) show good agreement. This study provides a useful basis for future studies on anticipated transient-induced crack propagation and remaining service life prediction of ageing reactor pressure vessels. [ABSTRACT FROM AUTHOR]

The paper presents the results of the application of the refined calculation guidelines to the analysis of the stress-strain state and fracture resistance of the equipment elements of the NPP primary circuit system with WWER reactor, in particular, the cylindrical part and the zone of the reactor pressure vessel inlet nozzle, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft under the operating and emergency modes of thermomechanical loading. The calculation methodology is based on the use of the modern models and methods of solution to the nonlinear boundary tasks of non-isothermal thermal viscoplasticity and tasks of fracture mechanics using the refined mixed schemes of the finite element method with increased accuracy. They allow one to obtain reliable solutions to the tasks considering the deformation history of thermomechanical loading, modern concepts of fracture mechanics and approaches to the modeling of brittle-viscous fracture defects, irradiation swelling and creep of metal, as well as as the structural elements, under the conditions of elevated temperature, intensive neutron irradiation and nonstationary modes of thermomechanical loading. The authors obtained and analyzed the calculation results for the cylindrical part and zone of the inlet nozzle of the WWER-1000 reactor pressure vessel, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft using the proposed guidelines. The results imply the possibilities of the proposed recommendations and make it possible to analyze some general tendencies and features of the application of the refined calculation models to justify the strength and life extension of the NPP structural elements under investigation. [ABSTRACT FROM AUTHOR]

In the lifetime prediction and extension of a nuclear power plant, a reactor pressure vessel (RPV) has to demonstrate the exclusion of brittle fracture. This paper aims to apply fracture mechanics to analyse the non-uniform cooling effect in case of a loss-of-coolant accident on the RPV integrity. A comprehensive framework coupling reactor system, fluid dynamics, fracture mechanics, and probabilistic analyses for the RPVs integrity analysis is proposed. The safety margin of the allowed RTNDT is increased by more than 16°C if a probabilistic method is applied. Considering the non-uniform plume cooling effect increases KI more than 30%, increases the failure frequency by more than 1 order of magnitude, and increases the crack tip constraint due to the resulting higher stress. Thus, in order to be more realistic and not to be nonconservative, 3D computational fluid dynamics may be required to provide input for the fracture mechanics analysis of the RPV. [ABSTRACT FROM AUTHOR]

The objective of this work is to find out the stress intensity and load confrontation of the axially cracked ASME pressure vessels so that the condition of the vessel will be branded how much more the life of the vessel wall would come if the crack is generated during operating conditions. The background of this work is based on the failures often occurring in the oil, gas and chemical plant industries. Process equipments are having its own standard design procedures and operating life's according to its material properties. Some of the equipments need frequent refurbishment as well as proper maintenance during operations due to the various working conditions. The code practices that process equipments need to be designed for time span of 20 to 25 years. However failures occurring during operations are unpredictable but it is diagnosable. It may be due to various reasons such as malfunctioning of components and wrong operations. In this paper the work is such that if the crack is generated axially inside due to load or corrosion, how much more operation the vessel would sustain. If the cracks grow continuously due to frequent loads how long the un-cracked thicknesses would withstand the internal pressure loads. ASME based designed pressure vessel has been considered for this study. The typical pressure vessel crack has been modeled internally in axial directions. The operating load has been applied and the behavior of cracks and its load confrontations were simulated using finite element technology and the results were presented. [ABSTRACT FROM AUTHOR]

The paper deals with an optimization problem related to axisymmetric membrane shells made of homogeneous, linear and isotropic materials and subject to a cyclic internal pressure. The optimization problem considers the possible crack growth in the shell as a structural constraint, which is accounted for by the well-known Paris law, and hence obeys the Linear Elastic Fracture Mechanics (LEFM) principles. The design variables are the meridian shape and the thickness distribution along the axis of the shell. After recalling the general background on the mechanics of thin-walled shells, the optimization problem is stated, formulated and solved in closed form by means of Pontryagin's Principle, showing two LEFM-based design criteria capable to help the designer in selecting the desired elastic performance through which the shell undergoes. It is shown that the derived optimal solutions are ellipsoids with variable thicknesses, whose distributions depend on the mass constraint and the applied pressure. Nevertheless, the optimal shapes guarantee the uniformity of either the meridian or the hoop stress, and such uniformity has been verified within a numerical example by an accurate finite element analysis. • The maximum volume problem for axisymmetric membrane shells is formulated. • The shells are subject to cyclic pressure and mass constraints. • The membrane theory of shells and Paris law are taken into consideration. • Optimal shapes are derived analytically by means of Pontryagin's Principle. • Two design criteria are given for uniform meridian and hoop membrane stresses. • The finite element method confirms the theoretical stress behavior. [ABSTRACT FROM AUTHOR]

The paper starts from concerns expressed by Sir Alan Cottrell, in the early 1970s, related to the safety of the pressurized water reactor (PWR) proposed at that time for the next phase of electrical power generation. It proceeds to describe the design and operation of nuclear generation plant and gives details of the manufacture of PWR reactor pressure vessels (RPVs). Attention is paid to stress-relief cracking and under-clad cracking, experienced with early RPVs, explaining the mechanisms for these forms of cracking and the means taken to avoid them. Particular note is made of the contribution of non-destructive inspection to structural integrity. Factors affecting brittle fracture in RPV steels are described: in particular, effects of neutron irradiation. The use of fracture mechanics to assess defect tolerance is explained, together with the failure assessment diagram embodied in the R6 procedure. There is discussion of the Master Curve and how it incorporates effects of irradiation on fracture toughness. Dangers associated with extrapolation of data to low probabilities are illustrated. The treatment of fatigue-crack growth is described, in the context of transients that may be experienced in the operation of PWR plant. Detailed attention is paid to the thermal shock associated with a large loss-of-coolant accident. The final section reviews the arguments advanced to justify ‘Incredibility of Failure’ and how these are incorporated in assessments of the integrity of existing plant and proposed ‘new build’ PWR pressure vessels. [ABSTRACT FROM PUBLISHER]

For a reactor pressure vessel steel 15Kh2MFA(III) experiments and calculations have been carried out to study the factors that have an influence on the increase of the lower-shelf fracture toughness in the temperature dependence diagrams upon warm prestressing. Stereoscopic fractography and numerical investigation have demonstrated that after the warm prestressing the crack tip remains blunt. This reduces the stress singularity during subsequent loading and raises the material fracture toughness. The paper gives the calculated data on residual stresses and crack-tip opening displacement during warm prestressing and upon relief. The calculated results are shown to agree well with the known analytical relations and experimental data. [ABSTRACT FROM AUTHOR]

• The ASME formula used for calculating stress intensity factor for nozzles were verified by linear elastic fracture mechanics finite element analysis. • Five Taiwan domestic RPV nozzles were considered for finite element stress and fracture mechanics analysis. • ASME formula provides conservative results for circular-shape nozzle corner crack but underestimates for elliptical-shaped crack. • The adjusted magnification factors were proposed for the elliptical-shaped nozzle corner crack. Due to the structural discontinuity of geometry having higher stress concentration, the nozzles may dominate the structural integrity of reactor pressure vessel (RPV) system, even the material radiation embrittlement is insignificant. The nonmandatory Appendix G in Section XI of the ASME Boiler and Pressure Vessel code provides a fracture mechanics-based methodology using magnification factors to calculate the stress intensity factor of reference crack tips as long as the stress distribution through the nozzle section is available. This paper establishes various three-dimensional finite element models of Taiwan domestic RPV nozzles to conduct a series of stress and linear elastic fracture mechanics analyses to estimate the stress intensity factors. The circular and elliptical reference corner cracks with depths of one-fourth and one-tenth thickness of the vessel wall along the 45° path are considered. Two evaluation results using the ASME method and the finite element linear elastic fracture mechanics analysis are compared. It is found that the ASME method produces conservative values of stress intensity factor at crack tips of circular corner cracks but underestimates the elliptical corner cracks. Finally, an adjusted magnification factor formula is proposed to obtain more accurate stress intensity factors for elliptical-shaped nozzle corner cracks. [ABSTRACT FROM AUTHOR]

The fatigue assessment of tube connections under cyclic pressure is discussed using four kinds of methods from ASME VIII-2 and EN 13445-3. FEA results are compared to the fatigue test, and some conclusions are obtained. Method 1 is the most widely used traditional method and can be used in both welded structures and unwelded structures. This method has simple operation, safety and reliability. Method 2 adopts the effective strain range to assess the fatigue for both the welded and the unwelded structure. This method is with high accuracy, good stability, safety and reliability, but the elastic–plastic analysis is very complicated. Method 3 adopts the equivalent structure stress to assess the fatigue of the welded, it is developed from fracture mechanics, and the procedure is also very complicated. Method 4 is a detailed assessment procedure for the welded and unwelded, and it is the most accurate, stable and reliable among the four methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper recalibrates the Weibull modulus and the threshold fracture toughness in a three-parameter Weibull stress model for the cleavage assessment of the pressure vessel steel reported in a European Union Project. The description of the near-tip stress field, which contributes to the primary force driving the unstable cleavage fracture, utilizes the conventional, mechanism-based strain gradient plasticity theory. The thus calibrated Weibull modulus and threshold toughness do not exhibit significant dependence on the material length scale. The calibrated Weibull stress model based on this plasticity theory predicts an increased probability of fracture compared to that based on the classical plasticity. [Copyright &y& Elsevier]

Abstract: Some spherical pressure vessels are manufactured from a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels, one needs to evaluate the stress intensity factors (SIF) distribution along the fronts of these cracks. In a recent paper by the authors, mode I SIF distributions for a wide range of lunular and crescentic internal, surface, radial cracks were evaluated for a typical spherical pressure vessel of an outer to inner radii ratio of η = Ro /Ri =1.1. The present analysis is aimed to determine the influence of the spherical vessel geometry in terms of its outer to inner radii ratio η = Ro /Ri on the prevailing SIFs. Mode I SIF distributions for a wide range of lunular and crescentic crack array configurations are evaluated. The 3-D analysis is performed by means of the FE method, employing singular elements along the crack front, for five geometries representing thin, moderately thick, and thick spherical pressure vessels with outer to inner radius ratios of η = Ro /Ri =1.01, 1.05, 1.1, 1.7, and 2.0. SIFs are evaluated for arrays containing n =1–20 cracks; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.95; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are affected considerably by the geometry of the spherical pressure vessel-η, and by the following parameters: the number of cracks in the array-n, the depth of the cracks-a/t, and their ellipticity-a/c. [Copyright &y& Elsevier]

Abstract: Weibull stress model represents a basic local approach model used in the ductile-to-brittle transition region for description and prediction of cleavage fracture for materials of both PWR and WWER reactor pressure vessels. In the Weibull stress model used most frequently until now , the parameters are determined by a calibration procedure using the fracture toughness values of high and low constraint specimens. In the present paper, the results of SEN(B) pre-cracked specimens of 10×20×120mm size, with deep and shallow cracks, are utilized. Specimens were made of material of WWER-1000 reactor pressure vessel, and were tested at Nuclear Research Institute Rez. Determination of Weibull stress was performed for both the case of including plastic strain correction into the Weibull stress formula and without it. [ABSTRACT FROM AUTHOR]

Abstract: Many spherical pressure vessels are manufactured by methods such as the integrated hydro-bulge forming (IHBF) method, where the sphere is composed of a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels one needs to evaluate the stress intensity factors (SIFs) distribution along the fronts of these cracks. However, to date, only two 3-D solutions for the SIF for one inner semi-elliptical crack in thin or thick spheres are available, as well as 2-D SIFs for one through-the-thickness crack in thin spherical shells. In the present paper, mode I SIF distributions for a wide range of lunular and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front, for a typical spherical pressure vessel with outer to inner radius ratios of η = Ro /Ri =1.1. SIFs are evaluated for arrays containing n =1–20 cracks; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.95; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem, and the following parameters: the number of cracks in the array-n, the relative crack depth a/t, and the crack ellipticity a/c. [Copyright &y& Elsevier]

The available design formulas for flat heads and blind end closures in the ASME Code, Section VIII, Divisions I and 2 are based on bending theory and do not apply to the design of thick flat heads used in the design of high pressure vessels. This paper presents new design formulas for thickness requirements and determination of peak stresses and stress distributions for fatigue and fracture mechanics analyses in thick blind ends. The use of these proposed design formulas provide a more accurate determination of the required thickness and fatigue life of blind ends. The proposed design formulas are given in terms of the yield strength of the material and address the fatigue strength at the location of the maximum stress concentration factor Introduction of these new formulas in a nonmandatory appendix of Section VIII, Division 3 is recommended after committee approval. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, some of the older and newer Charpy-fracture toughness correlations have been examined and new correlations have been developed for predicting the ASTM E-1921 standard reference temperature, T 0. The results have been applied to some selected new steels and compared with measured T 0, where available. It is found that the predicted reference temperature from the new procedure gives reliable and acceptably conservative engineering estimate of T 0. Predicted values of reference temperatures under dynamic conditions from these T 0 using Wallin’s strain rate shift equation agree well with measured dynamic values for a few steels giving added support to the new procedure. [Copyright &y& Elsevier]

The radial second mode of sloshing in a circular cylindrical oil storage tank induces an out-of-plane deformation of the floating roof deck. The radial contraction of the deck due to this out-of-plane deformation contains modal components with circumferential wave numbers 0 and 2, thereby causing an elliptical deformation of the pontoon, which encloses the deck. In a previous paper, the stress caused by this elliptical deformation was analyzed by regarding the radial contraction of the deck as an enforced displacement of the whole pontoon. This paper presents an improved method for this stress analysis by considering the radial contraction of the deck as an enforced displacement of the joint between the deck and the pontoon. First, the effectiveness of the previous method in estimating the hoop membrane stress at the joint with the deck is confirmed by comparing the results obtained from the previous and improved method. Next, the improved method is used to predict also the other stress components in each portion of the pontoon. Numerical results reveal that the bending stresses are magnified locally near the joint with the deck and that the hoop membrane stress in the outer portion of the pontoon sensitively depends on the geometry of the cross-section of the pontoon. It is found that the hoop membrane stress near the joint between the outer rim and the top (or bottom) of the pontoon can be significantly reduced by increasing the slope of the top (or bottom) of the pontoon. [ABSTRACT FROM AUTHOR]

In order to calculate the fatigue life of cylinders subjected to internal pressure using the fracture mechanics approach, the stress intensity factors (SIFs) for internal semi-elliptical cracks are needed. Nowadays, the most accurate procedure for fatigue life calculation consists in starting from a postulated internal semi-elliptical crack and updating the flaw aspect ratio during the crack propagation. In this sense, assuming a semi-elliptical shape during crack propagation, SIFs both at the deepest crack point and at the surface point must be calculated in order to update the crack aspect ratio through its fatigue propagation. This continuous crack shape updating cannot be done using the conventional tabulated solutions, as those provided in the main design codes and SIF handbooks. This paper presents a number of closed-form equations, which very accurately fit the tabulated results in ASME Boiler and Pressure Vessel Code, Section VIII, Division 3, to calculate the SIF for internal semi-elliptical cracks in cylinders subjected to internal pressure. These equations can be used to avoid the use of the tabulated solutions, and, as a consequence, an automatic numerical integration of the propagation law can be done. [ABSTRACT FROM AUTHOR]

Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME code (Sec. VIII, Div. 3) and 2008 and 2009 Addenda, and these are now a part of the 2010 code. There is now a local damage-mechanics based strain-exhaustion limit, including the well-known global plastic collapse limit. Moreover, Code Case 2564 (Sec. VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement-controlled and short-duration dynamic pressure loading is given. This instability condition is evaluated for six plastic and viscoplastic constitutive relations. The role of strain rate sensitivity on the instability point is investigated. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared with the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain rate sensitivity on the instability strain depends on the form of the constitutive relation assumed. [ABSTRACT FROM AUTHOR]

A study is made of the dependence of the time of propagation of a fracture front in thick-walled vessels subjected to internal pressure on the wall thickness and the employed version of kinetic theory of creep. The stress intensity is taken to be the equivalent stress. Recommendations on using the results in computational applications are formulated. [ABSTRACT FROM AUTHOR]