Evaluation of flawed piping under dynamic loading

This paper describes analytical studies of several of the large-scale flawed pipe experiments conducted for the International Piping Integrity Research Group (IPIRG), including detailed discussion of the test with the longest loading duration. Dynamic excitation with increasing load amplitude leads to failure of the piping at a predesignated test section containing a large manufactured flaw. Here, elastic analysis is shown to describe the system dynamic response reasonably well, provided that an appropriate value of structural damping can be selected. A simplified two degree-of-freedom model displays sensitivity to damping and is used to help select the optimal damping value for use in subsequent finite element calculations. The total damping for the IPIRG piping system is caused by a combination of structural damping from the support conditions and from plastic deformation at highly-stressed locations, such as at the degraded cross section itself or at the long-radius elbows. Effective, calculated damping values for the IPIRG tests varied by an order of magnitude, with low values of 0.5 to 1% associated with short-duration dynamic response and 5% or more for the long-duration test. The discussion includes comparisons of the calculated IPIRG results with ASME Code-suggested analysis damping values.     

Socket weld integrity in nuclear piping under fatigue loading condition

The purpose of this paper is to evaluate the integrity of socket weld in nuclear piping under the fatigue loading. The integrity of socket weld is regarded as a safety concern in nuclear power plants because many failures have been world-widely reported in the socket weld. Recently, socket weld failures in the chemical and volume control system (CVCS) and the primary sampling system (PSS) were reported in Korean nuclear power plants. The root causes of the socket weld failures were known as the fatigue due to the pressure and/or temperature loading transients and the vibration during the plant operation. The ASME boiler and pressure vessel (B & PV) Code Sec. III requires 1/16 in. gap between the pipe and fitting in the socket weld with the weld leg size of 1.09 × t₁, where t₁ is the pipe wall thickness. Many failure cases, however, showed that the gap requirement was not satisfied. In addition, industry has demanded the reduction of weld leg size from 1.09 × t₁ to 0.75 × t₁. In this paper, the socket weld integrity under the fatigue loading was evaluated using three-dimensional finite element analysis considering the requirements in the ASME Code. Three types of loading conditions such as the deflection due to vibration, the pressure transient ranging from P = 0 to 15.51 MPa, and the thermal transient ranging from T = 25 to 288 °C were considered. The results are as follows; (1) the socket weld is susceptible to the vibration where the vibration levels exceed the requirement in the ASME operation and maintenance (OM) code. (2) The effect of pressure or temperature transient load on socket weld in CVCS and PSS is not significant owing to the low frequency of transient during plant operation. (3) ‘No gap’ is very risky to the socket weld integrity for the systems having the vibration condition to exceed the requirement specified in the ASME OM Code and/or the transient loading condition from P = 0 and T = 25 °C to P = 15.51 MPa and T = 288 °C. (4) The reduction of the weld leg size from 1.09 × t₁ to 0.75 × t₁ may induce detrimental effect on the socket weld integrity.     

Non-destructive detection and analysis of residual and loading stresses in thick-walled components

Components and systems are designated to withstand loads. These loads are primarily mechanical ones, additionally thermal, chemical and other ones. The constructed part has to support these loads with safety margins. Additionally, peak values for stresses have to be avoided. During the last ten years the theoretical background as well as the numerical evaluation were developed and introduced in practice. Especially finite-element methods at least for loading stresses are the common aid of the designing engineer. The experimental verification of calculated stresses and stress distributions fails up to now. There is no experimental measurement of stress at all. For strain measurements - restricted to elastic strains and to the surface region, not exceeding some ten micrometres - only the X-ray technique allows static and dynamic measurements. Strain variations by changes of loads or stresses can be measured with strain gages, optical holographical interferometry and other methods - also restricted to the surface only. Nothing is known about the volume-distribution of strains and stresses, and for scientists and engineers it is a surprising phenomenon how practicians here rely on theories and calculations. During the last five years several approaches were developed as non-destructive methods for strain/stress-measurements not only on the surface but in the interior, too. The state of the art is described in this contribution covering ultrasonic as well as micromagnetic methods. Examples are given from research results and applications in practice. The most important literature differentiated referring to physics, review contributions and applications is listed in an appendix.     

Creep—fatigue test of a thick-walled vessel under thermal transient loadings

To improve the damage evaluation methods in the design code for Fast Breeder Reactors (FBRs), a series of creep—fatigue tests of structural models under thermal transient loadings are going on at Oarai Engineering Center of the Power Reactor and Nuclear Fuel Development Corporation (PNC). Test models are designed to incorporate representative structures of components and pipings used in FBRs and are subjected to severer cyclic thermal transients than those experienced in FBRs. The test is planned to be continued until failure occurs. This paper describes the creep—fatigue test results and their damage evaluation for the first test model.A 40 mm thick vessel model made of SUS304 austenitic stainless steel was subjected to cyclic thermal transients, in which sodium at 600°C and 250°C flowed repeatedly. The period of each transient was 2 h. Cracks were observed at seven test portions in the model after 1002 cycles of the thermal transients.Elastic and inelastic analyses were performed to evaluate creep—fatigue damage and crack propagation. The safety margins included in the creep—fatigue design methods based on elastic analysis as well as those based on inelastic analysis are discussed. Finally fracture mechanics analyses were performed to explain the observed crack growth.     

Crack growth under cyclic thermal shock loading

Experimental and theoretical results of fatique crack growth under cyclic thermal shock loading are presented. The experiments were done by cooling hot steel plates by a water jet. Linear elastic fracture mechanics is applied to predict fatigue crack growth theoretically. For this stress intensity factors of semi-elliptical surface cracks were calculated by use of the weight function method. Measured fatigue crack growth is compared with predictions from the theory.     

A structural analysis of the circular cylinder with multi holes under thermal loading

A structural analysis of the circular cylinder with multi holes is performed using the finite element analysis program . This structure is an analytical model of the capsule used for material irradiation tests. The temperature distributions of the cylinder due to gamma heating are obtained and various parameters, such as specimen size, quantity of specimens and gap sizes between the holder and the specimen are considered in the analysis to obtain the thermal and mechanical characteristics. To assess the structural integrity of the capsule, stress analysis under thermal loading is also performed. The analysis results show that, in all specimens, the peak temperature occurred, and is significantly dependent on gap sizes between the holder and the external tube or the specimen. The stress of the cylinder, under thermal loading, is lower than the allowable stress of the material used.     

Non-linear 3D piping analysis under stochastic dynamic loads

A new analytical method is presented for non-linear 3D piping systems subjected to stochastic dynamic loadings. First, the paper describes the development of an empirical formulation for the strength and deformation characteristics of piping systems based on a detailed finite-element shell analysis of various pipebends. Five structural parameters are selected to characterize a typical nuclear power piping design in the formulation. Second, the use of a simplified plastic hinge model is proposed in which the non-linear behavior of pipebends under stochastic loadings is accounted for by using an orthotropic biaxial hysteretic model. A numerical example and comparison with other methods are illustrated in terms of computational time and practicality of the method.     

Transient cavitation effects in fluid piping systems

An accurate prediction of pressure transients and associated loadings in nuclear power plant piping systems requires a treatment of cavitation. A technique for calculating this effect in a general fluid-hammer analysis by the method of characteristics is developed. Cavitation is treated by a modified column separation model and is assumed to be a local phenomenon occurring whenever the pressure drops below the vapor pressure of the fluid. While the model is a simplification of the actual phenomena it reproduces the essential features of transient cavitation. Computational results obtained for a variety of piping arrangements demonstrate the versatility of the approach, and clearly illustrate the fact that neglecting cavitation leads to erroneous pressure-time loadings in the piping systems. Comparisons of calculated results with available experimental data, for a simple piping arrangement, show good agreement and provide validation for the computational cavitation model.     

Stress analysis of non-uniform thickness piping system with general piping analysis software

Most general piping analysis software can only perform ASME design stage type code compliance analysis with uniform pipe wall thickness. However, non-uniform wall thickness, commonly on elbows or bends, can be found in many industrial applications. A typical example is thinned non-uniform thickness at bends or elbows caused by flow accelerated corrosion (FAC). In this paper, an analysis procedure is introduced to enable a general piping software to conduct ASME III class 1 piping analysis with non-uniform wall thickness. The demonstration is performed on CANDU (Canadian Deuterium Uranium) feeder pipes, which have been subjected to FAC caused wall thinning. The results are compared with both conventional uniform thickness piping analysis and non-uniform thickness solid finite element analysis. The comparison shows the validity of the proposed “average-minimum-average” approach by employing the general piping analysis software. The approach remains conservative compared to the benchmark solid finite element analysis results. Meanwhile it provides lower acceptable thickness than the conventional piping analysis.     

The behaviour of WB 35 piping material under dynamic loading in the high speed tensile test

For the determination of the strength-, deformation- and fracture behaviour of the material 17 MnMoV 6 4 (WB 35) which is used for piping components, tensile tests were carried out at different loading rates (monotonic and impact-type) on smooth and notched pipe strip specimens over a temperature range extending from − 30°C to 250°C.For the conduct of the tests a hydraulic high speed tensile machine having a free motion device was used; the velocity of impact was preset at ca. 7 m/s.With impact-type (dynamically) loaded specimens in general higher strength and deformation values were obtained than with monotonic (statically) loaded ones. In all of the specimens having low deformation values which were investigated microfractographically, ductile portions were found adjacent to the notch on the fracture surface.     

3D-FE-calculations of a pressure vessel under thermal shock loading

After concluding the cyclic thermal shock tests on the nozzle A2 and in the cylindrical area of the HDR-RPV, several institutions have conduced preliminary calculations on the long-term thermal shock test project using finite element method. These investigated the behaviour of the nozzle and the cylinder wall, each of which possessed a single crack. The comparison of the results (CMOD, J-integral) with particular reference to the cylinder wall, resulted in great differences partly due to the different discretisations, boundary conditions and crack geometries. The main influence, however, came from the different assumed material parameters.With the calculated J-integral values for the cylinder wall a stable crack propagation of about 1 mm was predicted.The crack in the cylinder wall does not reach the maximum opening by the test end. In contrast, the calculation on the nozzle shown a rapid opening of the crack at the beginning of the test with a subsequent gradual closing.     

Blowdown force analysis of piping system under LOCA conditions using BLOWDOWN code

The BLOWDOWN code was developed for blowdown force analysis of piping system under LOCA conditions. This is a post-processor of the thermal-hydraulic analysis code RELAP4/MOD6. The results obtained from the RELAP4/MOD6 code are converted into blowdown forces by the BLOWDOWN code.In the paper, the physics and algorithms of the BLOWDOWN code are outlined. Some numerical examples are also presented to show the effectiveness of the code.     

A study on the evolution of crack networks under thermal fatigue loading

The crack network is a typical cracking morphology caused by thermal fatigue loading. It was pointed out that the crack network appeared under relatively small temperature fluctuations and did not grow deeply. In this study, the mechanism of evolution of crack network and its influence on crack growth was examined by numerical calculation. First, the stress field near two interacting cracks was investigated. It was shown that there are stress-concentration and stress-shielding zones around interacting cracks, and that cracks can form a network under the bi-axial stress condition. Secondly, a Monte Carlo simulation was developed in order to simulate the initiation and growth of cracks under thermal fatigue loading and the evolution of the crack network. The local stress field formed by pre-existing cracks was evaluated by the body force method and its role in the initiation and growth of cracks was considered. The simulation could simulate the evolution of the crack network and change in number of cracks observed in the experiments. It was revealed that reduction in the stress intensity factor due to stress feature in the depth direction under high cycle thermal fatigue loading plays an important role in the evolution of the crack network and that mechanical interaction between cracks in the network affects initiation rather than growth of cracks. The crack network appears only when the crack growth in the depth direction is interrupted. It was concluded that the emergence of the crack network is preferable for the structural integrity of cracked components.     

Transient thermal hydraulic modeling and analysis of ITER divertor plate system

A mathematical model has been developed/updated to simulate the steady state and transient thermal-hydraulics of the International Thermonuclear Experimental Reactor (ITER) divertor module. The model predicts the thermal response of the armour coating, divertor plate structural materials and coolant channels. The selected heat transfer correlations cover all operating conditions of ITER under both normal and off-normal situations. The model also accounts for the melting, vaporization, and solidification of the armour material. The developed model is to provide a quick benchmark of the HEIGHTS multidimensional comprehensive simulation package. The present model divides the coolant channels into a specified axial regions and the divertor plate into a specified radial zones, then a two-dimensional heat conduction calculation is created to predict the temperature distribution for both steady and transient states. The model is benchmarked against experimental data performed at Sandia National Laboratory for both bare and swirl tape coolant channel mockups. The results show very good agreements with the data for steady and transient states. The model is then used to predict the thermal behavior of the ITER plasma facing and structural materials due to plasma instability event where 60 MJ/m² plasma energy is deposited over 500 ms. The results for ITER divertor response is analyzed and compared with HEIGHTS results.     

Structural evaluation of a piping system subjected to thermal stratification

Piping systems in nuclear power plants are often designed for pressure, mechanical loads originating from deadweight and seismic events and operating thermal transients using the equations in the ASME Boiler and Pressure Vessel Code, Section III. In the last few decades a number of failures in piping have occurred due to thermal stratification caused by the mixing of hot and cold fluids under certain low flow conditions. Such stratified temperature fluid profiles give rise to circumferential metal temperature gradients through the pipe leading to high stresses causing fatigue damage. A simplified method has been developed in this work to estimate the stresses caused by the circumferential temperature distribution from thermal stratification. It has been proposed that the equation for the peak stress in the ASME Section III piping code include an additional term for thermal stratification.     

Transient analysis of blowdown thrust force under PWR LOCA

The analytical results of blowdown characteristics and thrust forces were compared with the experiments, which were performed as pipe whip and jet discharge tests under the PWR LOCA conditions. The blowdown thrust forces were obtained by Navier-Stokes momentum equation for a single-phase, homogeneous and separated two-phase flow, assuming critical pressure at the exit if a crifical flow condition was satisfied.The following results are obtained:

1. (1) The node-junction method is useful for both the analyses of the blowdown thrust force and of the water hammer phenomena.

2. (2) The Henry-Fauske model for subcooled critical flow is effective for the analysis of the maximum thrust force under the PWR LOCA conditions. The jet thrust parameter of the analysis and experiment is equal to 1.08.

3. (3) The thrust parameter of saturated blowdown has the same one with the value under pressurized condition when the stagnant pressure is chosen as the saturated one.

4. (4) The dominant terms of the blowdown thrust force in the momentum equation are the pressure and momentum terms except that the acceleration term has large contribution only just after the break.

Fatigue design of nuclear class 1 piping considering thermal stratification

In ASME B&PV Code, Section III, Subsection NB-3600, thermal stratification is not taken into account to determine the peak stress intensity range for fatigue design of nuclear class 1 piping. Therefore, the effects of several parameters such as boundary layer thickness, temperature difference, stratification length, wall thickness, inner diameter and material properties on peak temperature and peak stress intensity due to non-linear temperature distribution of thermal stratification in a pipe cross-section are studied through the numerical parametric study. The results of the parametric study are closely examined and consolidated to introduce an additional term into the equation of ASME so that the modified equation can be used to determine the peak stress intensity range due to all loads including thermal stratification.     

Fracture mechanics investigations on cylindrical large scale specimens under thermal shock loading

To investigate the crack growth and crack arrest behaviour of primary circuit materials large scale experiments were conducted on component-like specimens under pressurized thermal shock loading at MPA Stuttgart. The material characteristics varied from high tough material to low tough material with higher nil ductility transition temperature to simulate EOL or beyond EOL-state. All tests started from in-service conditions and were cooled down to room temperature. The specimens showed both stable and unstable crack growth and partly crack arrest. The crack growth behaviour was verified by post test calculations and could be explained with the help of the multiaxiality of the stress state.     

The steamhammer problem: dynamic shock loading of critical reactor piping systems

In the course of both pre-operational testing and power operation of commercial nuclear power plants, relatively large amplitude transient vibrations of steam piping systems have been experienced with damage to the piping supports in at least one recent case. These transient vibrations result from ‘steamhammer’ or dynamic shock loading induced by pressure and momentum transient conditions generated in the piping by sudden changes to the flow conditions, such as are produced by sudden valve opening or closure. In particular, vibrations have been experienced in by-pass and discharge lines as a result of relief valve discharge, and in main steam lines as a result of sudden main stop valve closure. Piping in both BWR and PWR reactor systems has been found to be susceptible to these conditions.This paper is concerned with the evaluation of the pressure and momentum transients resulting from sudden valve operation, and the determination of the dynamic response of the piping to the induced transient loading. The characteristics of the transient conditions existing immediately following both sudden valve opening and closure as encountered in BWR and PWR plants are discussed. The procedures used to calculate the transient time history functions are outlined. The derivation of the loading induced in the piping by the pressure and momentum transients is discussed and the determination of the dynamic response of the piping is presented. The procedures described in the paper are illustrated by actual examples from BWR and PWR plants, and the significance of steamhammer effects relative to other loading conditions is discussed.     

Inelastic analysis methods for piping systems

The analysis of pipework systems which operate in an environment where local inelastic strains are evident is one of the most demanding problems facing the stress analyst in the nuclear field. The spatial complexity of even the most modest system makes a detailed analysis using finite element techniques beyond the scope of current computer technology. For this reason the emphasis has been on simplified methods. It is the aim of this paper to provide a reasonbly complete, state-of-the-art review of inelastic pipework analysis methods and to attempt to highlight areas where reliable information is lacking and further work is needed.