Numerical analysis of limit load and reference stress of defective pipelines under multi-loading systems

The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially in Nuclear Electric's (formerly CEGB) R5 and R6 procedures. The reference stress method has been proven to be successful in problems pertaining to creep growth, rupture damage, creep buckling, and more recently, elastic–plastic fracture toughness. An approximate method of reference stress determination relies on prior knowledge of limit loads for various configurations and loadings. However, determination of the limit loads for the problems with complicated geometric forms and loading conditions is not a simple task. In the present paper, a numerical solution method for radial loading is presented, the mathematical programming formulation is derived for the kinematic limit analysis of 3D structures under multi-loading systems, and moreover, a direct iterative algorithm used to determine the reference stress is proposed which depends on the evaluation of limit load. The numerical procedure is applied to determine the limit load and reference stress of defective pipelines under multi-loading systems. The effects of four kinds of typical part-through slots on the collapse loads of pipelines are investigated and evaluated in detail. Some typical failure modes corresponding to different configurations of slots and loading forms are studied.     

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.     

Analysis and experiments on the plastic limit pressure of elbows

This paper discusses the plastic limit pressure of elbows without defects and with local thinned area in the extrados. Finite element analysis (FEA) and experiments have been used. The results of FEA show that the limit load of elbows under internal pressure increases with increasing wall thickness and bend radius of the elbow. The results are consistent with the calculated results by the Goodall formula, the maximum error is 6.58%. By data fitting of FEA, an empirical formula for the limit load of elbows with local thinned area in the extrados has been proposed, which is validated by experiments.     

On relating the reference stress, limit load and the ASME stress classification concepts

This paper discusses the relationship between the concepts of reference stress, limit load and the ASME stress classification framework, as it applies to common mechanical components and structures. The relationship is based on the underlying notion of load-control.

The reference stress method, which has been used mainly in the UK, attempts to correlate creep deformations in a structure with the results of a uniaxial creep test. It has been observed that the reference stress is relatively insensitive to material parameters characterizing creep behaviour. The method has been widely used in the design and life assessment of nuclear as well as conventional components. Specifically, it has been applied to problems pertaining to creep growth, rupture damage, creep buckling, and more recently, elastic-plastic fracture toughness.

Determination of the reference stress is not always a simple task. An approximate method of its determination relies on prior knowledge of limit loads for various configurations and loadings. The drawback, of course, is that there is a reliance on the available catalogue of limit loads. Rather than attempting to ‘fit someone into a garment’, this paper discusses a new and a direct procedure for reference stress determination using the GLOSS R-Node method. The reference stress is determined for some pressure component configurations. The ideas are extended to the ASME stress classification framework, and the various stress categories are discussed.     

Limit load and J estimates of a centre cracked plate with an asymmetric crack in a mismatched weld

The limit load and J estimates of a centre cracked plate with an asymmetric crack in the tensile properties mismatched weld were investigated. A limit load expression was derived on the basis of a simplified slip-line field. A good agreement between the predictions of the expression and finite element (FE) results was found for ratios of half-weld width to the crack ligament, H/l, of less than 0.5. The equivalent stress–strain relationship method (ESSRM) was used to predict elastic–plastic J values. Results from FE analyses show that the ESSRM is accurate for the crack with asymmetry in the mismatched weld provided an accurate theoretical or numerical value of the limit load of the same specimen is available. Defect assessment methods are discussed, and it is found that the failure assessment diagram (FAD) of an asymmetrically cracked mismatched weld can be constructed from the equivalent stress–strain relationship for the same mismatched geometry with a symmetric crack. The effect of an asymmetric crack on the FAD may then be covered by the limit load solution for the asymmetrically cracked mismatched weld.     

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.     

Proposal of reference stress for a surface flaw on a cylindrical component from a review-with-comparison of the local metal loss assessment rule between API 579-1 and the p-M diagram method

The Remaining Strength Factor (RSF) approach in Part 5 of API 579-1/ASME FFS-1 is an assessment method for a cylindrical component with a local metal loss based on surface correction factors. Also, reference stress solutions that are applied in the Failure Assessment Diagram (FAD) method for a cylindrical component with a crack-like flaw are provided in Annex D using surface correction factors. In the recently-developed p-M diagram method, the reference stress solution for local metal loss evaluation in a cylindrical component is derived using bulging factors, which are similar but not identical to the surface correction factors used in API 579-1/ASME FFS-1. This paper describes the results of a comparative study among the RSF approach, reference stress solutions for the FAD method, and the p-M diagram method, in terms of plastic collapse evaluation of a cylindrical component. These results were compared with the FEA and experimental results to confirm how these estimated stresses could be validated. This study also involves recommended reference stress solutions for a cylindrical component with a crack-like flaw or a local metal loss, which should be adopted as fitness-for-service rules, and a discussion on the influence of the design margin of the construction code on allowable flaw depth.     

The linear matching method applied to the high temperature life integrity of structures. Part 1. Assessments involving constant residual stress fields

Design and life assessment procedures for high temperatures are based on ‘expert knowledge’ in structural mechanics and materials science, combined with simplified methods of structural analysis. Of these, R5 is one of the most widely used life assessment methods internationally with procedures based on reference stress techniques and shakedown calculations using linear elastic solutions. These have been augmented by full finite element analysis and, recently, the development of a new programming method, the linear matching method (LMM), that allows a range of direct solutions that include shakedown methods and simplified analysis in excess of shakedown. In this paper, LMM procedures are compared with calculations typical of those employed in R5 for cyclic loading problems when the assumption of a constant residual stress field is appropriate including shakedown and limit analyses, creep rupture analysis and the evaluation of accumulated creep deformation. A typical example of a 3D holed plate subjected to a cyclic thermal load and a constant mechanical load is assessed in detail. These comparisons demonstrate the significant advantages of linear matching methods for a typical case. For a range of cyclic problems when the residual stress field varies during the cycle, which include the evaluation of plastic strain amplitude, ratchet limit and accumulated creep strains during a high temperature dwell periods, the corresponding LMM and R5 procedures are discussed in an accompanying paper.     

碗米坡预应力闸墩三维有限元分析

应用三维有限元数值分析方法对坝基、坝体、闸墩、混凝土锚块及预应力锚索在内的整体模型进行应力和变形计算。研究结果表明，预应力闸墩具有整体稳定性，在各种荷载的组合效应下整个墩体的变形和应力分布满足设计要求。     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part III: estimation of crack opening area

Evaluation of the crack opening area (COA) plays a central role in the evaluation of the critical crack length for a detectable leak for piping systems. Simplified evaluation methods for the COA for a circumferential through-wall crack in a pipe subjected to axial and bending loading or their combination is reviewed in this paper. Elastic solutions are compared and recommendations are given. Plastic solutions by the reference stress method are compared with nonlinear finite element solutions. The reference stress method tends to overestimate the COA for medium or large crack angles. Considerable improvement is achieved by making empirical modifications to the limit load expressions used in the calculation of the reference stress.     

风电叶片子部件测试平台构建及拉挤板材力学特性研究

为探究风电叶片强度测试体系与拉挤板材力学行为,首先提出一种用于风电叶片金字塔结构测试技术,提出子部件试验新概念;其次进行子部件测试平台机械结构、液压系统及控制方案的设计,并利用有限元分析进行验证;最后基于所设计测试平台对子部件,即拉挤板材进行静力试验。结果表明：风电叶片金字塔结构的测试方案准确可行;部件试验设备最大应力发生在加载支架后梁,最大应力为242.5 MPa,最大位移为1.049 mm,未超其结构应力应变极限;拉挤板材破坏载荷为800 kN,失效变形形态包括弹性、屈服和断裂3个阶段,有限元分析数据与试验结果吻合较好,最终结果可为全尺寸叶片测试局部失效状况提供数据参考。     

利用部件整体耦合法分析柴油机气缸盖热机械强度

为提高气缸盖的热机械性能,采用部件整体耦合法对多缸柴油机气缸盖进行了三维非线性有限元分析。在考虑各部件接触关系的基础上,计算了气缸盖在螺栓预紧力、热载荷、最高燃烧压力多场耦合作用下的应力分布,确定了各影响因素在缸盖上造成应力集中的主要位置及原因,并与发动机实际运行后情况进行了对比,为结构改进提供了理论指导。     

Limit load analysis using the reference volume concept

Limit load analysis is usually performed by the interpretation of stress redistribution using either linear elastic or inelastic methods. Several redistribution iterations are required to achieve an accurate estimate of the limit load. In this paper the reference volume method is illustrated and shown to be effective in finding the limit load using few linear elastic redistribution iterations. The reference volume is based on the concept of using a part of the volume of the component that is undergoing plastic deformation. The method is applied to a two-dimensional indeterminate beam and a full three dimensional model of an oblique nozzle. This illustrates different cases of reference volumes to verify the analysis procedure.     

柴油机气缸盖温度场数值模拟

采用有限元方法进行柴油发动机气缸盖的换热分析,详细考虑各种因素对气缸盖的影响,得出较为准确的温度分布。分析模型准确,简化较小;换热边界条件考虑详细,并用实测温度值反复修正计算边界条件,得出的温度场与试验测值误差小于3.5%。故本次温度场计算结果可为该机型的热评估及进一步强化提供参考。     

Limit loads of circumferentially flawed pipes and cylindrical vessels under internal pressure

Published limit load formulae for circumferential defects overestimate the burst pressure for penetrating defects in pipes by the factor two in the short crack limit, because they only consider axial stress. Therefore, a class of limit load solution is discussed which takes the triaxial state of stress into account. The solutions for pressure loaded crack faces are improved analytically. Primal–dual limit analysis with the finite element method is used to adjust all solutions to numerical results. Limit loads are obtained for circumferential cracks of all sizes in thick-walled cylinders.     

预负荷空心圆柱滚子轴承承载性能的有限元分析

利用有限元分析软件ANSYS对预负荷空心圆柱滚子(HCR)轴承的承载性能进行分析。主要计算预负荷空心圆柱滚子轴承的最底部滚子和次底部滚子的等效应力、接触应力和滚子内圈拉应力的分布情况,分析滚子空心度和过盈量对轴承应力和额定载荷的影响。通过分析和计算得到数据结果为预负荷空心圆柱滚子轴承的进一步优化提供参考依据。     

活塞组件接触分析流程自动化及接触面设计研究

基于活塞销与活塞销座表面型线几何型线及刚度的差异,在热载荷与机械载荷的作用下发生不协调形变,产生较大的局部接触应力,采用有限元法对某型船用柴油机活塞销孔结合面型线进行优化设计。通过对原活塞模型进行分析并与静载试验结果对比,找出应力集中位置;采用有限元软件和自行开发程序,实现活塞销-孔接触副型面的自动优化设计;最终从优化结果中选取最佳优化方案。优化后,活塞销孔型面应力集中显著降低,接触型面上最大Mises应力下降55.5%。     

汽油机活塞热力耦合强度分析

采用活塞、活塞销和连杆组合的三维模型对活塞三维温度场进行分析。并以此为基础,对活塞进行机械负荷和热负荷耦合分析,计算了活塞耦合应力场。全面了解活塞热负荷和机械负荷下的活塞强度,并与单纯机械负荷下的活塞进行对比,分析温度对活塞应力分布的影响,为活塞改进设计提供参考。     

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.     

汽车动力总成橡胶隔振器弹性特性的有限元分析

本文以汽车动力总成液阻悬置的橡胶主簧为研究对象，探讨了橡胶隔振器弹性特性的有限元分析方法。文中介绍了橡胶有限元分析的基本理论，论述了建立橡胶超弹性特性本构关系时试验数据的获取方法，并对由不同橡胶本构模型拟合试验数据的结果进行了分析。对一轿车发动机液阻悬置的橡胶主簧在三个垂直方向的力一位移特性进行了有限元分析，并和实测结果进行了对比分析，计算了橡胶主簧的静、动态应力，结果可用于其强度的分析，讨论了橡胶主簧静态弹性特性有限元分析计算结果与单元特性的关系。文中所述的方法也可用于其它橡胶产品的分析。