Limit loads for piping branch junctions under internal pressure and in-plane bending—Extended solutions

The authors have previously proposed plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on finite element (FE) limit loads resulting from three-dimensional (3-D) FE limit analyses using elastic–perfectly plastic materials [Kim YJ, Lee KH, Park CY. Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending. Int J Press Vessels Piping 2006;83:645–53]. The solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and for the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0. Moreover, the solutions considered the case of in-plane bending only on the branch pipe. This paper extends the previous solutions in two aspects. Firstly, plastic limit load solutions are given also for in-plane bending on the run pipe. Secondly, the validity of the proposed solutions is extended to ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0. Comparisons with FE results show good agreement.     

Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending

The present work presents plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic–perfectly plastic materials. To assure reliability of the FE limit loads, modelling issues are addressed first, such as the effect of kinematic boundary conditions and branch junction geometries on the FE limit loads. Then the FE limit loads for branch junctions under internal pressure and in-plane bending are compared with existing limit load solutions, and new limit load solutions, improving the accuracy, are proposed based on the FE results. The proposed solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0.     

Shakedown and limit analysis of 90° pipe bends under internal pressure,cyclic in-plane bending and cyclic thermal loading

The Linear Matching Method is used to create the shakedown limit and limit load interaction curves of 90° pipe bends for a range of bend factors. Two load cases are considered i) internal pressure and in-plane bending (which includes opening, closing and reversed bending) and ii) internal pressure and a cyclic through wall temperature difference giving rise to thermal stresses. The effects of the ratios of bend radius to pipe mean radius (R/r) and mean radius to wall thickness (r/t) on the limit load and shakedown behaviour are presented.     

基于Solidworks的三岔形岔管有限元分析及优化设计

以辽宁省某输水工程沿线隧洞进口设置的三岔形岔管为例,采用Solidworks软件中的Solidworks Simulation模块对岔管进行了有限元分析与计算,提出了更为合理的三岔形钢岔管体型。结果表明,增加梁的内伸宽度、截面高度、厚度均可降低梁和管壳的应力,其中梁本身的应力降低效果比管壳明显;拉杆附近的管壳位移最大且集中;管壳与加强梁连接处应力较高且集中,尤其是靠近拉杆和U梁水平中线附近;对于对称式三岔形岔管,在一定的内水压力作用下,腰梁的应力均值大于U梁,主管的应力均值大于支管;对于自流式长距离输水工程而言,为减小水头损失,岔管的加强梁应与管壳内部大致平齐。     

内压环形管开孔补强分析

通过有限元方法,对内压环形管在沿管壁法向带接管的结构进行应力分析,研究在特殊位置,弯管法线方向开孔时环管及支管中的应力分布,并与直管开孔补强的结果进行对比,总结弯管中非特殊位置的结构开孔时应力分布特点,为弯管开孔补强设计提供参考。     

Limit loads and fracture mechanics parameters for thick-walled pipes

In this paper, information on plastic limit loads and both elastic and elastic-plastic fracture mechanics parameters is given for cracked thick-walled pipes with mean radius-to-thickness ratios ranging from two to five. It is found that existing limit load expressions for thin-walled pipes can be applied to thick-walled pipes, provided that they are normalized with respect to the corresponding un-cracked thick-walled pipe values. For elastic fracture mechanics parameters, FE values of the influence functions for the stress intensity factor and the crack opening displacement are tabulated. For elastic-plastic J, it is shown that existing reference stress based J estimates can be applied, provided that a proper limit load for thick-walled pipes is used.     

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.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part I: stress intensity factor and limit load solutions

The J-integral and the crack opening area are the main parameters required for a leak-before-break evaluation of a piping system. Stress intensity factor and limit load solutions have been widely used for evaluating these parameters in a simplified way. Solutions for the stress intensity factor and limit load for a pipe with a circumferential through-wall crack subjected to axial and bending loads are reviewed and compared in this study. Based on the comparisons, recommendations are then made on expressions for calculating these parameters.     

面内弯矩下焊制管道三通的塑性极限载荷

基于极限分析的观点，推导了工业中焊制管道三通在面内弯矩工况下的极限载荷估算式，实验数据验证和与基于ASME规范及Billington经验公式的比较表明，极限载荷估算式对管道三通的塑性极限弯矩估算有较高的精度，在工程应用中具有参考价值。图6表1参10。     

A comparative study of usefulness for pad reinforcement in cylindrical vessels under external load on nozzle

The main purpose of this paper is to perform a comparative study of strength behavior for cylindrical shell intersections with and without pad reinforcement under out-of-plane moment loading on nozzle. Three pairs of full-scale test vessels with different d/D ratios were designed and fabricated for testing and analysis. A three-dimensional nonlinear finite element numerical analysis was also performed. The maximum elastic stress for each vessel under per unit moment on nozzle is provided. The plastic limit moment on nozzle is obtained by load–displacement and load–strain curves for each test vessel. The results indicate that the effect of pad reinforcement on decreasing maximum elastic stress and increasing plastic limit load is obviously effective. The study results will serve as the available data for understanding the usefulness of pad reinforcements and as the basis for developing an advanced design method by limit analysis for pad-reinforced cylindrical vessels under external loads on nozzle.     

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.     

Effects of attached straight pipes on finite element limit analysis for pipe bends

The effect of the length of an attached straight pipe on the plastic limit load of a 90° pipe bend under combined pressure and bending is quantified, based on finite element (FE) limit analyses using elastic–perfectly plastic materials with the small geometry change option. Systematic FE limit analyses of pipe bends with various lengths of the attached pipe are performed. It is shown that the effect of the length of the attached straight pipe on plastic limit loads can be significant, and the limit loads tend to decrease with decrease of the length of the attached straight pipe. In the limiting case of no attachment, the limit loads are found to be close to existing analytical solutions.     

汽轮机抗燃油管路三通断裂分析

某电厂抗燃油管路三通在服役过程中发生断裂,材质分析结果表明,三通材料的金相组织中有暴露于内壁表面的杂质带,还有晶间腐蚀倾向。断口分析表明,三通的断裂性质为高周疲劳断裂,断面上可见贝纹线和疲劳辉纹,裂纹起源于三通管内壁的材质缺陷处,在振动应力作用下,导致疲劳断裂。     

Effect of reinforcement on plastic limit loads of branch junctions

This paper provides effects of reinforcement shape and area on plastic limit loads of branch junctions under internal pressure and in-plane/out-of-plane bending, via detailed three-dimensional finite element limit analysis assuming elastic-perfectly plastic material behaviour. It is found that reinforcement is most effective when (in-plane/out-of-plane) bending is applied to the branch pipe. When bending is applied to the run pipe, reinforcement is less effective when bending is applied to the branch pipe. The reinforcement effect is the least effective for internal pressure.     

Limit and burst pressures for a cylindrical shell intersection with intermediate diameter ratio

This paper provides results of inelastic stress analysis for a vessel–nozzle intersection with intermediate diameter ratio (d/D=0.526) under increasing internal pressure loading from experimental and non-linear finite element methods. The determination of the limit load due to internal pressure is performed by an experimental study for comparison with finite element analysis. The spread of plastic area for the analytical model vessel is provided. Also a burst test of the model vessel is carried out to provide some data to justify the existing design method and the basis for developing an advanced design guideline for shell intersections under internal pressure loading.     

电站锅炉过热器、再热器集箱静压分布的数值研究

利用数值模拟的方法，研究了径向引入引出型分配、汇流集箱系统的静压分布规律。为了消除计算中伪扩散的影响，选用了QUICK格式。数值计算结果表明：在三通附近，气流的变化非常强烈，在远离三通的区域．气流逐渐平稳。在分配集箱进口三通的两侧存在2个涡流区，正对三通中心线的支管处静压最高，远离三通的区域，静压分布与轴向引入引出方式规律基本一致。利用该方法计算了某电厂锅炉末级再热器的流量分配和热偏差情况，与实测结果相吻合。图6表1参2     

Net-section limit load approach for failure strength estimates of pipes with local wall thinning

The net-section limit load approach is typically used in assessment of pipes with local wall thinning, based on which a maximum load carrying capacity is easily estimated from one equation that includes two terms associated with the effect of the defect geometry and the material's resistance (strength). To better understand the applicability of the net-section limit load approach to pipes with local wall thinning, four different limit load expressions for pipes with local wall thinning under pure bending are considered, together with two different definitions of the material's resistance. Estimated failure moments are then compared with full-scale pipe test data. It is found that the use of an appropriate limit load solution reduces not only the degree of conservatism but also the dependence of the assessment results on the wall thinning geometry, and thus gives the best results. Therefore, finding such solutions for pipes with local wall thinning is an important issue.     

内压下轴向穿透裂纹等强度异径三通K1的计算

本文以断裂力学为基础，采用有限元分析方法，借助ANSYS有限元分析软件，对含轴向穿透裂纹等强度异径三通进行了研究。选择单元SOLID95和单元SOLID45建立了含轴向穿透裂纹等强度异径三通的有限元模型，并以此计算了内压载荷下各几何尺寸和裂纹尺寸三通主管和支管的应力强度因子K1，进一步换算成形状因子F并拟合成公式。公式的拟合误差在10％以内，可以满足工程安全评定的要求。     

The effect of mechanical heterogeneity and limit load of a weld joint with longitudinal weld crack on the J-integral and failure assessment curve

According to the CEGB R6 (Rev.3) approach, the influence of strength mis-matching and the limit load of a weld joint with a longitudinal weld crack on the J-integral and failure assessment curve can be studied by using an elastic–plastic finite element method for Center-Cracked Panel (CCP) specimens. The results indicate that the values of the J-integral and the shapes and positions of the failure assessment curves are greatly affected by the strength mis-matching factor M, a ratio of weld metal yield strength to that of base metal. If the limit load of the base metal is adopted to normalize the applied load, then the greater the value of M, the larger the safe area is in the failure assessment curve (FAC). However, if the limit load of the weld metal is adopted to normalize the applied load, then the greater the value of M, the smaller the safe area is. Therefore, for the undermatched and evenmatched joints, it is safer to choose the limit load of the base metal as the normalized load, and for the overmatched joints, it is safer to choose the limit load of the weld metal as the normalized load. Moreover, when M is less than 0.8 for the former situation, the option 1 curve of the R6 is not a conservative assessment curve. Considering that there is no simple theoretical formula which is suitable for calculating the limit load of a mechanical heterogeneous weld joint under plane stress and a variety of crack geometries, it is recommended that no matter what the strength of the overmatched or undermatched weld joint is, it is safer to use the limit load of that metal which has the higher strength grade of base metal and weld metal as the normalized load.     

Limit loads for pipe bends under combined pressure and in-plane bending based on finite element limit analysis

Approximate plastic limit load solutions for pipe bends under combined internal pressure and bending are obtained from detailed three-dimensional (3-D) FE limit analyses based on elastic-perfectly plastic materials with the small geometry change option. The FE results show that existing limit load solutions for pipe bends are lower bounds but can be very different from the present FE results in some cases, particularly for bending. Accordingly closed-form approximations are proposed for pipe bends under combined pressure and in-plane bending based on the FE results.