The effect of bi-directional loading on fatigue assessment of pressurized piping elbows with local thinned areas

An elastic–plastic finite element study is conducted to determine the effect of bi-directional loading on the fatigue characteristics of pressurized 90° piping elbows with local thinned areas. The analysis is conducted on pressurized piping elbows considered previously in the literature, but analyzed only for in-plane loading. Considering also the out-of-plane loading the present analysis seeks to simulate simultaneous horizontal and vertical seismic actions. A validation study is first conducted in which the present results obtained for in-plane loading are compared with previous results. Comparisons are made for deformation patterns, hoop strain histories, and reaction forces. The relative in-plane to out-of-plane load intensities to be adopted for the combined loading case is determined next. Results considering bi-directional loadings are then found for the pressurized piping elbow for a total of 23 cases of local area thinning. Finally conclusions are drawn about the significance of considering the additional out-of-plane loading.     

Evaluation of local thinned pressurized elbows

Erosion, corrosion or mechanical damage may cause local thinned areas (LTA) in piping and degrade its integrity. Acceptability criteria for LTA are available for straight pipes. However, for elbows, there are few studies. In this paper, the finite element method (FEM) is used to calculate the collapse load of a local thinned pressurized elbow and to analyse the factors influencing the collapse load. Based on the solution of the collapse load of LTA straight pipe, the stress level in an elbow without defects, and finite element analysis results, an analytical solution of the collapse load of LTA pressurized elbow is presented. A method to assess the acceptability of LTA in an elbow is given and compared with FEM results.     

含局部减薄水电站压力钢管极限承载力计算公式研究

为了对在役含局部厚度减薄(简称局部减薄)水电站压力钢管进行安全评价,结合试验结果验证了局部减薄管道极限承载力分析方法的可靠性,遴选出极限承载力影响因素为管道跨度、材料强度参数和局部减薄几何参数,揭示了3种影响因素对极限承载力的影响规律,并结合一系列计算数据拟合了剩余强度系数与该影响因素之间的函数关系,建立了以材料强度、局部减薄几何参数为变量的含局部减薄水电站压力钢管极限承载力计算公式。结果表明,含局部减薄水电站压力钢管极限承载力计算公式较B31G-2009、DNV-101、GB/T 19624-2004等规范有更高的计算精度;含局部减薄管道跨度大于1.5倍管道直径时,跨度对管道极限承载力的影响可忽略;局部减薄深度、减薄轴向长度和减薄环向长度对管道极限承载力的影响依次减弱。     

Experimental study of low-cycle fatigue of pipe elbows with local wall thinning and life estimation using finite element analysis

Low-cycle fatigue tests were conducted using elbow specimens with local wall thinning. Local wall thinning was machined on the inside of the elbow in order to simulate metal loss from erosion corrosion. The local wall thinning was located in three different areas known as the extrados, crown and intrados. The elbow specimens were subjected to cyclic in-plane bending under displacement control without internal pressure. In addition, three-dimensional elastic-plastic analyses were also carried out using the finite element method. As a result, the crack penetration area and the crack growth direction were successfully predicted by the analyses. The fatigue lives estimated by the analyses were close to those obtained by the experiments.     

Leak-before-break qualification of primary heat transport piping of 500 MWe Tarapur atomic power plant

The advent of Leak-Before-Break (LBB) concept has now replaced the traditional design basis event of the Double-Ended-Guillotine-Break (DEGB) to design the Primary Heat Transport (PHT) system piping of the Pressurised Heavy Water Reactor (PHWR) and Pressurised Water Reactor (PWR). This approach is being adopted to design the PHT system piping of 500 MWe Indian PHWR to be built at Tarapur (Tarapur Atomic Power Plant 3 and 4). The LBB concept basically demonstrates through fracture mechanics analysis that there is negligible chance of any catastrophic break of PHT pipes without prior indication of leakage. There are several steps in this work of LBB qualification, namely, evaluation of loads on the piping components, generation of tensile and fracture properties of PHT pipe base and weld material, determination of leakage size crack (LSC) and the elastic–plastic fracture mechanics (EPFM) and limit load analysis of the piping components with postulated LSC to evaluate the critical load at unstable ductile tearing and the limit load, respectively. The paper deals with the fracture analysis of the straight pipes and elbows of three pipe lines in the PHT system of TAPP 3 and 4. Three crack configurations are considered in the analysis. These are throughwall circumferential crack at the weld location of straight pipe and extrados of the elbow and throughwall axial crack at the elbow crown. In all the cases, necessary factor of safety with respect to the anticipated safe shutdown earthquake (SSE) load and LSC are shown to be more than the minimum required values for LBB qualification.     

Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.     

The interaction of pressure, in-plane moment and torque loadings on piping elbows

This study concerns the load interaction behaviour of 90° smooth piping elbows with circular cross-section and long straight tangent pipes. The finite element method is used for stress analysis of elbows having a wide range of bend and pipe factors. The main aim of the study is to establish the first yield interaction behaviour when an elbow is subjected to a combination loading of in-plane bending, torsion and internal pressure. The study shows that load interaction is influenced by pipe factor, bend radius and load coupling effect, with thinner elbows being affected to a larger degree.     

Reference stress method for evaluation of failure assessment curve of cracked pipes in nuclear power plants

In order to obtain a precise failure assessment curve (FAC) in the R6 defect assessment procedure, it is necessary to evaluate the J-value of cracked components. The reference stress method can be used for estimating J-values. However, the accuracy of estimation depends on the limit load used for evaluating the reference stress. In this study, the applicability of several limit load solutions was investigated through comparison with the results of elastic-plastic finite element analyses (FEA). A pipe containing a circumferential surface crack was analyzed under pure bending load. Six materials used in nuclear power plants were assumed. It was shown that the reference stress method is valid for FAC evaluation. The maximum non-conservativeness caused by using the reference stress method is less than 20% compared to the results obtained by FEA.     

Shakedown limit loads for elbows under internal pressure and cyclic in-plane bending

This paper presents elastic, shakedown and plastic limit loads for 90° elbows under constant internal pressure and cyclic in-plane bending, via finite element (FE) analysis. Effects of the elbow geometry (the bend radius to mean radius ratio and the mean radius-to-thickness ratio) and of the large geometry change are systematically investigated. By normalizing the in-plane bending moment by the plastic limit load solution of Calladine, the shakedown diagram is found to be close to unity up to a certain value of normalized pressure (normalized with respect to the limit pressure) and then to decrease almost linearly with increasing normalized pressure. The value up to which shakedown limit loads remain constant depends on the elbow geometry and the large geometry change effect. Effects of the elbow geometry and the large geometry change on shakedown diagrams are discussed.     

Plastic collapse moment of 90° long radius elbows with internal circumferential surface crack at intrados under in-plane bending

Piping elbows under in-plane bending moment are vulnerable to cracking. The crack initiates at the surface and eventually reaches through the thickness and may lead to failure. The structural integrity assessment requires knowledge of the limit load. Limit load solutions for elbows with through-wall crack configurations are available in the open literature. But solutions for surface crack are not available. This paper presents a closed form expression for the plastic collapse moment (PCM) of 90°, long radius elbows with circumferential surface cracks at the intrados, under in-plane bending moment. The expression is derived, based on the results of non-linear (geometric and material) FE analyses covering a wide range of geometries and crack sizes. These plastic collapse moments evaluated herein will help in structural integrity assessment.     

Pressure of Newtonian fluid flow through curved pipes and elbows

Under conditions of high temperature and high pressure, the non-uniformity of pressure loads has intensified the stress concentration which impacts the safety of curved pipes and elbows. This paper focuses on the pressure distribution and flow characteristic in a curved 90 o bend pipe with circular cross-sections, which are widely used in industrial applications. These flow and pressure characteristics in curved bend pipes have been researched by employing numerical simulation and theoretical analysis. Based on the dimensionless analysis method a formula for the pressure of Newtonian fluid flow through the elbow pipes is deduced. Also the pressure distributions of several elbows with different curvature ratio R/D are obtained by numerical methods. The influence of these non-dimensional parameters such as non-dimensional curvature ratio, Reynolds number and non-dimensional axial angle α and circumferential angle β on the pressure distribution in elbow pipes is discussed in detail. A number of important results have been achieved. This paper provides theoretical and numerical methods to understand the mechanical property of fluid flow in elbow pipes, to analyze the stress and to design the wall thickness of elbow pipes.     

Simplified Thermoelastoplastic Models for Determination of Global and Local Stress in Coke Drums

Coke drums as major pressure vessels in delayed coking process experience cyclic thermal and mechanical loading during operation. The elastic-plastic behavior of coke drums including global and local (hot and cold spot) stress distribution has been analyzed using finite element analysis (FEA) method in our previous study. Here, instead of using FEA simulations, simplified theoretical models (STM) for global and local stress determination are developed. The global stress model is developed based on a single cladded shell element with temperature and pressure loading cycle. The local stress model is built on an axisymmetric circular cladded plate experiencing a non-uniform temperature distribution history. With the same input data, stress and strain values estimated by the STM are consistent with those from the FEA. An ease-of-use software package with built-in STMs is developed. It is the objective of this paper to show that STM can be a very time- and cost-saving analysis tool for general industrial users compared to professional commercial FEA software.     

Plastic limit load of cylindrical shells with cutouts subject to pure bending moment

In this paper, the results of limit analyses of thin-walled cylindrical shells with a circular hole under the action of a pure bending moment are presented in dimensionless form for a wide range of geometric parameters. Analytical estimation of lower bound limit load is carried out using the feasible sequential quadratic programming (FSQP) technique. The finite element calculations of limit load consist of elastic–plastic and lower and upper bound predictions by elastic compensation methods. A testing device was made to perform experiments to obtain limit bending moment of cylinders with circular openings. The analytical and finite element calculations are compared with experimental results and their correlation is discussed. The finite element calculation results were found to be in good agreement with lower bound estimations by the nonlinear mathematical programming (FSQP) method and the formula proposed by Shu.     

Limit moment of local wall thinning in pipe under bending

In engineering practice, pipe containing local wall thinning may be subjected to bending load. The existence of local wall thinning on pipe surface impairs the load-carrying capacity of pipe. In order to maintain the integrity of the pipe containing local wall thinning, it is very important to develop a method to evaluate such a pipe with local wall thinning under bending. In this paper, the limit moment of local wall thinning pipe under pure bending is computed employing 3D elastic–plastic finite element analysis. The results show that the limit moment of pipe is affected not only by the width of defect but also by the longitudinal length of defect. When the longitudinal length of defect overpasses some critical value, the results from net-section collapse criterion (NSC) are in very reasonable agreement with the results from finite element analysis. Therefore, the NSC formula can conservatively be used to assess the limit load-carrying capability of local wall thinning pipe under bending.     

A review of limit load solutions for cylinders with axial cracks and development of new solutions

Limit load solutions for axially cracked cylinders are reviewed and compared with available finite element (FE) results. New limit solutions for thick-walled cylinders with axial cracks under internal pressure are developed to overcome problems in the existing solutions. The newly developed limit load solutions are a global solution for through-wall cracks, global solutions for internal/external surface cracks and local solutions for internal/external surface cracks. The newly developed limit pressure solutions are compared with available FE data and the results show that the predictions agree well with the FE results and are generally conservative.     

Design by analysis versus design by formula of high strength steel pressure vessels: a comparative study

A comparative study for design by analysis and design by formula of a cylinder to nozzle intersection has been made using different finite element techniques. The cylinder to nozzle intersection investigated is part of a typical vertical pressure vessel with a skirt support. For the study the commonly used ductile P355 steel alloy and the high strength steel alloy P500 QT were considered. The comparative results clearly show disadvantages in terms of limit load capability when the design-by-formula procedures are used in the design of high strength steel pressure vessels. The FE results also clearly show advantages of the shell to solid sub-modeling technique, as it combines the accuracy of 3D-solid modeling with the affordable computing time of the 3D-shell modeling technique.     

630MW亚临界机组宽度滑压运行优化试验研究

介绍了某电厂630MW亚临界汽轮机组基于阀点滑压运行优化的试验情况,提出“宽度滑压优化”的概念,即在5个常规负荷点(535MW、473MW、410MW、347MW和300MW)基础上,增加目前省电网调度对600MW容量等级机组要求的深度调峰下限负荷点(240MW)。通过不同负荷不同运行方式下的滑压比对试验,发现高压缸效率、高排汽温等指标参数的变化规律,确定调峰范围内最优的机组运行方式,同时也获得优化后的滑压运行曲线,并给出了滑压曲线背压项修正公式。与原滑压曲线相比,优化后滑压曲线尤其在深度调峰下限负荷中的应用有效地降低了机组发电热耗率和供电煤耗率,提高了机组运行的经济性和调峰性能。     

Studies on gasketed flange joints under bending with anisotropic Hill plasticity model for gasket

The behavior of a gasketed flange joint under bending loads has been studied by three dimensional finite element analysis (FEA) and experiments. The in-plane and bending stiffness of spiral wound gaskets are considered using anisotropic Hill plasticity material model. The variation in bolt axial force of joints under bending load predicted by the finite element analysis compares well with the experimental results. The contact stress distribution obtained have significant variation in the pattern from the previous material models and consistent with the results of Bouzid [1] regarding flange rotation.     

Relevance of plastic limit loads to reference stress approach for surface cracked cylinder problems

To investigate the relevance of the definition of the reference stress to estimate J and C* for surface crack problems, this paper compares finite element (FE) J and C* results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface cracks and finite internal axial cracks are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) a local limit load, (ii) a global limit load, (iii) a global limit load determined from the FE limit analysis, and (iv) the optimised reference load. It is found that the reference stress based on a local limit load gives overall excessively conservative estimates of J and C*. Use of a global limit load clearly reduces the conservatism, compared to that of a local limit load, although it can sometimes provide non-conservative estimates of J and C*. The use of the FE global limit load gives overall non-conservative estimates of J and C*. The reference stress based on the optimised reference load gives overall accurate estimates of J and C*, compared to other definitions of the reference stress. Based on the present findings, general guidance on the choice of the reference stress for surface crack problems is given.     

The flat end to cylindrical shell connection—limit load and creep design

The influence of the shear force, acting at the cylinder–plate intersection, on the limit load pressure is shown, and graphs for the determination of the limit load pressure as well as the required plate thickness for a limit load design are given. The (ideal) plastic nonlinear viscoelastic analogue in generalized stresses for the determination of (highly nonlinear) creep results from given limit load results is described, and its usefulness and (technically satisfying) accuracy shown by means of two examples.