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.     

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.     

螺旋盘管式换热器管板的分析设计

螺旋盘管式换热器的设计标准为ASMEⅧ-1-2010,本文对管板组件进行局部应力分析,按照ASMEⅧ-2进行分析评定。按照标准的规定将管板简化成当量实心圆平板,开孔区设置不同的等效参数。管板组件的应力分析采用两种方法进行,分别为：基于弹性应力分析的应力分类法与基于塑性失效准则的极限载荷分析法。本文旨在促进弹性分析法与极限载荷分析法的联合使用。     

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 notch root elasto-plastic stress–strain state for general loadings using an elastic solution

A method is proposed for the evaluation of the elasto-plastic notch root stress and strain states using an elastic solution for an isotropic and homogeneous structure subjected to general loadings. Materials of von-Mises type obeying a multilinear strain hardening rule are considered for the present study. The yield zone around the notch root is assumed to be well contained and the analysis is based on the incremental deformation theory. It is observed that, due to relaxation and redistribution of stresses at the notch root, a fraction of the total elastic strain energy density is conserved during inelastic deformation at the notch root. In the present study the fractional contribution is evaluated using a proportionality function, which is shown to be constant for a given linear hardening material, and independent of the loading and geometry of the structure. Moreover, it has been noted from the study that the proportionality function is a linear function of normalized tangent modulus for the plane stress case, whereas it is a quadratic function for plane strain. The stresses and strains evaluated using the proposed method are in close agreement with finite element solutions.     

Limit analysis based on elastic compensation method of branch pipe tee connection under internal pressure and out-of-plane moment loading

A new method of calculating the limit load of a structure via a sequence of incompressible elastic finite element calculations with variable Young's moduli converging to the rigid perfectly plastic problem is used to study the limit load of branch pipe tee connections. Several models of branch pipe tee connection are meshed with shell elements and submitted to internal pressure with end axial load effect or out-of-plane moment. Results are compared with lower and upper bound analytical solutions and experimental results reported in the literature. Computations with 20 noded cubic elements are also proposed to validate shell studies. The J integral is also calculated by a simplified method with the limit load, using an example of a defective branch pipe tee connection.     

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.     

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.     

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.     

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.     

Evaluation of effective material properties of spiral wound gasket through homogenization

In this paper, a homogenization methodology is proposed to determine the material properties of spiral wound gaskets (SWGs) using finite element analysis through representative volume elements (RVE) of the gaskets. The constituents of this RVE are described by elasto-plastic material properties. The RVE are subjected to six load cases and the volume averaged responses are analyzed simultaneously to predict the anisotropic properties. The mechanical behaviour is simplified to an orthotropic material model with Hill’s plasticity model and the properties are verified with micro-mechanical simulation and experimental results available in the literature. Reasonable agreement is obtained between the results. Formulae for elastic properties are also derived by a simplified analytical method based on lamination theory and compared with those obtained from homogenization.     

轴向排汽凝汽器真空力平衡装置稳定性评估方法

根据轴向排汽凝汽器真空力平衡装置基本原理,选定合适的压杆稳定性经典计算模型,同时由于真空力平衡装置压杆为新型结构,并无可参考稳定安全系数,先取定安全系数等于6完成单个压杆选型计算,后利用ANSYS WORKBENCH软件建立真空力平衡装置整体压-弯杆系的极限载荷分析模型,应用欧盟EN13445-3压力容器分析设计标准的...     

New material balance analysis method for abnormally high-pressured gas-hydrocarbon reservoir with water influx

Because of the strong stress sensitivity in abnormally high-pressure gas-hydrocarbon reservoirs, the calculation of aquifer volume is very difficult; it is hard to analyze the material balance equation (MBE) for the abnormally high pressured gas-hydrocarbon reservoirs with water influx. The traditional MBE is poorly reliable. Because the volume of the aquifer is corresponding to the dynamic reserves, the accuracy of aquifer volume calculation will be decisive to the reliability of material balance analysis. Therefore, the research of a new MBE method has been conducted to the abnormally high pressured gas-hydrocarbon reservoirs with water influx. This paper proposed a new concept to describe the rock elastic energy and water influx energy using the linear relationship of cumulative production, which simplifies the MBE and converts to a multivariate nonlinear equations. The equations were solved by iteration method. Furthermore, the water influx energy, water influx, and aquifer volume can be calculated by the linear relation coefficient of cumulative production. This method is adopted for calculating the results of several scenarios of numerical simulation and actual production data in a certain abnormally high pressured gas-hydrocarbon reservoir. The accuracy of the new method for calculating the dynamic reserves and drive index is validated. This method also avoids the error caused by calculating water influx energy or neglecting the rock elastic energy in abnormally high pressured gas-hydrocarbon reservoirs.     

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.     

Plastic collapse of pipe bends under combined internal pressure and in-plane bending

Plastic collapse of pipe bends with attached straight pipes under combined internal pressure and in-plane closing moment is investigated by elastic–plastic finite element analysis. Three load histories are investigated, proportional loading, sequential pressure–moment loading and sequential moment–pressure loading. Three categories of ductile failure load are defined: limit load, plastic load (with associated criteria of collapse) and instability loads. The results show that theoretical limit analysis is not conservative for all the load combinations considered. The calculated plastic load is dependent on the plastic collapse criteria used. The plastic instability load gives an objective measure of failure and accounts for the effects of large deformations. The proportional and pressure–moment load cases exhibit significant geometric strengthening, whereas the moment–pressure load case exhibits significant geometric weakening.     

A numerical method for lower bound limit analysis of 3-D structures with multi-loading systems

The determination of lower bound limit load of 3-D structures is by no means an easy task, especially for complex configurations and loading systems. In our previous work, a numerical method of upper bound limit analysis for 3-D structures with multi-loading systems was proposed. This method combines FEM and mathematical programming technique in an iterative procedure. In the present article, on the basis of the nature of the iterative procedure for upper bound limit analysis, the statically admissible stress fields, which satisfies the equilibrium equation and boundary conditions, are constructed using some intermediate variables obtained by upper bound limit analysis procedure. Moreover, a mathematical programming formulation is set up for the static limit analysis of 3-D structures under multi-loading systems and a direct iterative algorithm used to determine the lower bound limit load multiplier is proposed, which depends on the static theorem of plasticity. The numerical examples are given to demonstrate the applicability of the procedure.     

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.     

Non‐linear ultimate strength and stability limit state analysis of a wind turbine blade

According to the design codes for wind turbine blades, it is sufficient to evaluate the blade's limit states using solely a linear analysis. This study, however, shows the need of non‐linear analyses in blade design. Therefore, a geometrically non‐linear structural response of a 34 m blade under flap‐wise loading has been compared with a linear response to determine the blade's resistance in the ultimate strength and stability limit states. The linear analysis revealed an unrealistic failure mechanism and failure mode. Further, it did not capture the highly non‐linear response of the blade that was measured in an ultimate full‐scale test to failure and determined by a geometrically non‐linear analysis. A design evaluation in accordance with the least stringent Germanischer Lloyd (GL) requirements has been compared with non‐linear approaches proposed by GL and Eurocode, which require the application of an imperfection. The more realistic non‐linear approaches yielded more optimistic results than the mandatory linear bifurcation analysis. Consequently, the investigated blade designed after the lesser requirements was sufficient. Using the non‐linear approaches, considering inter‐fibre failure as the critical failure mode, yielded still a significant safety margin for the designer (7–28%). The non‐linear response was significantly dependent on the scaling of the imperfection. Eurocode's method of applying an imperfection appeared more realistic than the GL method. Since the considered blade withstood 135% of the design load at a full‐scale test to failure and the blade has operated successfully in the field, GL's safety factors combined with the imperfection size may be too conservative. Copyright © 2015 John Wiley & Sons, Ltd.     

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 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.