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.     

On relating redistributed elastic and inelastic stress fields

The classical lower bound theorem in plasticity states that the load required to create equilibrium stresses in a structure that are below yield will always be less than or equal to the collapse load. Recent advances in determination of lower bound limit loads involve repeating elastic analyses after systematic modification of elastic moduli. The intention is to obtain lower bound limit loads from stress fields that would progressively approach a state similar to one at plastic limit. The gradual transformation of statically admissible stress fields from elastic to limit state can be compared to those corresponding to power-law creep indices, ranging from one to infinity. This paper attempts to investigate the possibility of establishing such relationships on a one-to-one basis, by considering standard component configurations.     

Modification of the bree diagram in presence of primary transient loads

The design of Class 1 LMFBR components operating at elevated temperature is accomplished in accordance with ASME III and Code Case N-47-28.

The main problem encountered in the design of components at elevated temperature is the satisfaction of strain limits according to the requirements of Test No. B-1, in the presence of significant seismic loads with very short duration (<40 s).

These transient primary loads in Test No. B-1 are treated like steady primary loads, and very often Test No. B-1 is not passed, causing more complex analyses to be performed for component strain limits satisfaction.

New formulae for calculating the residual stress distribution in the elastic core (core stress) and the effective creep stress parameter Z have been proposed to take into account the transient nature of seismic loads.

A comparison between results obtained in calculating Z according to Test No. B-1 or using the new formulae is presented in this paper; the new method for Z calculation appears to be more accurate and to give less conservative results than previous approaches.     

Numerical schemes for defining reference stress in components containing defects

In R6 and R5, the standards of integrity assessments of components containing defects established by the former Central Electricity Generating Board (CEGB) in the UK, the basic procedure in calculating the crack driving force parameters, J-integration and C*-integration is to define the reference stress, σ_ref, on the defective section. Three methods of directly defining the reference stress, σ_ref [multiple steady-state creep analysis (MSCA) method, creep module-modified iteration (CMMI) method and elastic module-modified iteration (EMMI) method], are suggested in this paper, differing from the common methods in which the limit loads of the components are first calculated and then the σ_ref is convertibly determined. The basic conceptions and calculational steps of these methods are discussed and compared in the context, and the validity is demonstrated by several examples.     

Design of a steam-heated sterilizer based on finite element method stress analysis

A steam-heated sterilizer is a pressure vessel of rectangular cross section externally reinforced by members welded to the flat surfaces of the vessel. These members are pressure vessels too with rectangular cross section. The ASME code provides alternative rules (Division 2) for the design of pressure vessels based on a Design By Analysis route. The stresses on the sterilizer were computed by the finite element method followed by the calculation of the stress fields according to the classification established in the ASME code. Structural members with shell intersections (as in the present case) present difficulties due to problems of linearisation and categorisation. In the present work the shell stress resultants were used instead of smoothed stresses. The operating conditions of the vessel involve cyclic application of loads requiring design based on fatigue analysis.     

A comprehensive stress analysis of BWR discharge lines subjected to high frequency fluid-dynamic excitation

Dynamic structural analysis has become one of the most extensive engineering efforts in the nuclear industry. Of particular concern is the dynamic structural analysis of complex piping systems. The present paper reports on such an analysis by summarising what has been done to account for dynamic loading associated with Safety/Relief Valve Discharge (S/RVD) and other loads such as weight, thermal effects and seismic loads in a Main Steam Line (MSL) with attached S/RVD lines. The analysis, which included the entire portion of the piping, involved the application of a modal approach up in to the high frequency region.

The various dynamic analysis techniques used in the assembled system, in substructures and at selected parts of the structure were the response spectrum method, generalised response analysis and selective modal time-history analysis, respectively. All dynamic results have been super-imposed on the static loads in the full model which contains all nodes. Stresses have then been evaluated in the entire system according to the rules set out in the ASME Boiler and Pressure Vessel Codes for Class 2 components.

The computation includes the application of known analysis techniques, its novelty lying in the substructuring and the subsequent superimposing of all dynamic results on the static loads. This substructuring, which was decided on following a thorough analysis of all relevant vibration mode shapes, allowed essential cost reduction, since the effects of high frequency fluid-dynamic excitation could be localised to one-third of the structure. The work demonstrates that comprehensive analysis of a rather complex system containing 1200 degrees of freedom can be performed with the modal analysis method applied locally up to a frequency as high as 120 Hz. The solution method proved to be fast and fairly reliable. By assembling results from available techniques (such as multi-level analysis, the generalised response method, selective modal time-history analysis and study of mode shapes) a reduction in conservatism has been possible and a heavily loaded complex system has been qualified with a fairly simple linear-elastic model.     

A new monitoring system for piping systems in fossil fired power plants

A CEC-funded project has been performed to tackle the problem of producing an advanced Life Monitoring System (LMS) which would calculate the creep and fatigue damage experienced by high temperature pipework components. Four areas were identified where existing Life Monitoring System technology could be improved:

1. 1. the inclusion of creep relaxation

2. 2. the inclusion of external loads on components

3. 3. a more accurate method of calculating thermal stresses due to temperature transients

4. 4. the inclusion of high cycle fatigue terms.

The creep relaxation problem was solved using stress reduction factors in an analytical in-elastic stress calculation. The stress reduction factors were produced for a number of common geometries and materials by means of non-linear finite element analysis. External loads were catered for by producing influence coefficients from in-elastic analysis of the particular piping system and using them to calculate bending moments at critical positions on the pipework from load and displacement measurements made at the convenient points at the pipework. The thermal stress problem was solved by producing a completely new solution based on Green's Function and Fast Fourier transforms. This allowed the thermal stress in a complex component to be calculated from simple non-intrusive thermocouple measurements made on the outside of the component. The high-cycle fatigue problem was dealt with precalculating the fatigue damage associated with standard transients and adding this damage to cumulative total when a transient occurred.

The site testing provided good practical experience and showed up problems which would not otherwise have been detected.     

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。     

The evaluation of weldment creep strength reduction factors by experimental and numerical simulations

The current design rules for welds are usually based upon the uniaxial creep rupture strength data. The effects of the stress multiaxility and the corresponding stress redistribution process of welded components are relatively ignored. As the present high-temperature testing techniques require large resources when testing welded components in full scale, the simulation of the effects will rely more on the numerical modelling. To evaluate the weldment joint efficiency this paper has proposed a general procedure in which the spatial distribution of constitutive parameters is determined by uniaxial testing while the creep process of components is simulated by numerical methods. Finite element methods are employed in the creep analysis of an AISI 316 butt-welded joint in pressurised tubes with a creep soft weld. To interpret the rupture behaviour of the tubes, different criteria are used to predict the rupture life. On the basis of the predicted structural rupture performance equations, the weldment creep reduction factors are evaluated for different design lifetimes. The reduction factors defined by the ASME code principle are found to be non-conservative in this case.     

Integrity assessment for a tubeplate using the linear matching method

A series of numerical procedures have been presented recently for the integrity assessment of structures based upon the Linear Matching Method. A typical example of a holed plate has been used to verify these procedures for the evaluation of plastic and creep behaviours of components. In this paper, a more complex 2D tubeplate at the outlet from a typical AGR heat exchanger is analysed for the shakedown limit, reverse plasticity, ratchet limit and creep relaxation based on the application of the Linear Matching Method for a thorough case study. Both a constant material yield stress and a temperature-dependent yield stress are adopted for the evaluation of the ratchet limit. For the evaluation of accumulated creep strains, flow stresses and elastic follow-up factors with differing dwell times at the steady cyclic state, a monotonic creep computation is performed, where the start-of-dwell stress is the rapid cycle creep solution at the beginning of the dwell period. An estimation of the tubeplate lifetime is then obtained by the evaluation of fatigue and creep endurances.     

Structures at elevated temperatures: How long will they last?

In principle, questions about the behaviour of high-temperature structures can be answered by analysis in conjunction with material creep properties. However, because of the wide range of geometries in use, simplified methods have been developed which avoid lengthy computations yet isolate the important factors controlling component behaviour. This paper describes one approach which is to define a reference stress such that the component life is equal to the life of a simple specimen tested at the reference stress. A substantial body of work has shown that the reference stress can often be established quite simply even for complex components containing cracks. The approach then provides a simple framework for assessing structures which operate at high temperatures.     

Three-dimensional stress analyses of mitred elbows

Three-dimensional elastic stress analyses of a mitred elbow have been performed by the application of the MARC finite element program. Seven basic unit load cases have been considered. Results of these reference load cases may be applied in any combination to stress analyses of the same elbow subjected to more complicated loading conditions.

According to results from these analyses, when a mitred bend is subjected to in-plane loads, it exhibits behaviour similar to that of a smooth elbow under the same loading conditions. Results from out-of-plane load cases show some deviation from the behaviour of a smooth bend. These discrepancies cast some doubts on the conventional method of stress analysis of a mitred bend.     

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.     

Determining local stress and limit load in a thick-walled tube with a hoop direction U-shaped notch under tension

This paper presents, in terms of the spherical section assumption, an effective method for determining the local stress and limit load of a thick-walled tube with an external hoop direction U-shaped notch under tension, and discusses the relationships of the stress concentration factor with notch depth t, radius of the notch root and the internal radius a₁ of the tube. Expressions for the elastoplastic local stress and limit load, which have not been considered by previous workers, are proposed. Comparison of the results of this paper with those of previous work for the case where a₁ = 0 shows that the method of this paper is simple and effective in engineering.     

Structural integrity evaluation of X52 gas pipes subjected to external corrosion defects using the SINTAP procedure

In the present study, the SINTAP procedure has been proposed as a general structural integrity tool for semi-spherical, semi-elliptical and long blunt notch defects. The notch stress intensity factor concept and SINTAP structural integrity procedure are employed to assess gas pipelines integrity. The external longitudinal defects have been investigated via elastic–plastic finite element method results. The notch stress intensity concept is implemented into SINTAP procedure. The safety factor is calculated via SINTAP procedure levels 0B and 1B. The extracted evaluations are compared with the limit load analysis based on ASME B31G, modified ASME B31G, DNV RP-F101 and recent proposed formulation [Choi JB, Goo BK, Kim JC, Kim YJ, Kim WS. Development of limit load solutions for corroded gas pipelines. Int J Pressure Vessel Piping 2003;80(2):121–128]. The comparison among extracted safety factors exhibits that SINTAP predictions are located between lower and upper safety factor bounds. The SINTAP procedure including notch-based assessment diagram or so-called ‘NFAD’ involves wide range of defect geometries with low, moderate and high stress concentrations and relative stress gradients. Finally, some inspired and advanced viewpoints have been investigated.     

Use of the reference stress method in estimating the life of pipe bends under creep conditions

The effect that the change of ovality of pipe bends, due to creep under internal pressure, has on the stationary-state stress state has been investigated using a reference stress approach. Attention has been focused on practical pipe bend geometries and loading conditions in power plant applications.Prediction of failure times based on stationary-state stresses, for cases in which ovality changes are neglected and in which ovality is included, indicate that the change of ovality can be very significant in some practical situations. Failure times obtained using a creep continuum damage mechanics approach have also been compared with those obtained using the stationary-state predictions with ovality changes included. These results indicate that even sophisticated damage mechanics analyses are inadequate unless the effects of the changing ovality which occurs are taken into account.     

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.     

Evaluation of the effect of metallurgical variables on materials behaviour and reference curves

An integral part of the safety assessment of nuclear pressure vessels and piping is the quantitative estimation of defect growth in both a stable and an unstable manner during service. This estimation is essential for determining whether any defect detected during inspection should be repaired or whether the size of the defect even after its expected growth is small enough to leave the integrity of the vessel unaffected.

The most important stable defect growth mechanism is that of environmentally assisted cyclic crack growth. Recent results indicate that it is markedly affected by sulphur content and/or manganese sulphide morphology and distribution. This implies that an essential improvement in component safety has been gained by currently applied steelmaking practices, which result in extra low sulphur content, generally below 0·010 wt.%, and in the round shape and small size of inclusions through, e.g. calcium treatment, hence considerably reducing the effect of the environment on crack growth rate. This further implies that the ASME Section XI reference curves for environmentally accelerated cyclic crack growth are conservative for steels produced by current steelmaking practices.

The ASME Section XI applies predominantly linear elastic fracture mechanics to assess the effects of cracks on the integrity of nuclear power plant components. Unstable linear elastic fracture often propagates by a cleavage mechanism. The cleavage fracture process has recently been shown to be of a statistical nature in both ferritic and bainitic steels. The carbide size distribution plays a dominant role in controlling the fracture toughness of these steels. A cleavage fracture model has been developed, by which both the expectance value and the probability limits of the fracture toughness, K_IC, can be predicted. The probability limits given by the model are shown to be consistent with the experimental observations. The application of the model to the data on which the ASME Section XI reference fracture toughness curve is based indicates that the reference curve is slightly unconservative.     

The effect of residual stress on the creep deformation of welded pipe

The finite element method has been used to study the creep deformation of pipe butt welds in the presence of an initial residual stress distribution. The study has used values for pipe dimensions, temperature (575°C) and internal pressure (70 bar) which correspond to the conditions being used in a pressure vessel testing programme which is investigating transverse weld metal cracking in CrMoV reheat pipe welds. Two sets of steady state creep data for the weld metal have been used, one to represent a weld weaker than the parent and the other one that was stronger. A residual stress distribution, consistent with experimental data, has been generated as àn initial condition for the analysis. The results are presented, discussing the effects of residual stress on both the total and creep strain accumulations for the two weld properties. The steady state creep laws used in the analysis do not allow for damage accumulation, but the possibility of such an effect is discussed using the Kachanov model. The results of the finite element analysis are compared with the experimental creep strain data from the pressure vessel testing programme.     

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.