Stress analysis of pierced regions for prestressed concrete reactor vessels

The analysis of prestressed concrete vessels for nuclear reactors and, in particular, the design of the perforated end-caps increasingly calls for better analytical techniques. A method is proposed by which the distribution of stress in the perforated end-caps may be defined, assuming constant elevated temperature and radial prestress. If required, more complex operating conditions can be incorporated. A special feature of the proposed analysis is the method by which an elastic solution can be modified to take account of the time-dependent effects such as creep and shrinkage at ambient and elevated temperatures. The elastic solution is based on a two-dimensional initial strain finite element displacement analysis using triangular plate elements. After obtaining the initial elastic state of stress, a complete elastic, thermoelastic creep and shrinkage solution is achieved in a step-by-step manner based on the ‘rate of creep’ approach and using small time intervals during which the stresses are assumed constant. The strains are known quantities or may be defined at the end of the interval considered.The technique was used to analyse slab models tested and the results have been reported elsewhere. It was shown that the proposed method estimates the deformational behaviour of the models with an acceptable degree of accuracy. The distribution of stress as a result of thermal creep predicted by the method also agreed well with the cracking pattern of the models.     

An analytical method for three-dimensional non-linear responses of prestressed concrete nuclear reactor vessels

This paper describes the results of an investigation to develop an analytical method for assessing the non-linear behaviour and strength of three-dimensional concrete structures such as prestressed concrete nuclear reactor vessels (PCRVs) under monotonically increasing internal pressure. This three-dimensional finite element method uses a proposed material model for the non-linear response of concrete under a multiaxial stress state. Three numerical examples were analysed to investigate the feasibility of the analysis. The first was the calculation of the two-dimensional response of Kupfer's plain concrete. The second involved the analysis of a small-scale axisymmetric PCRV test model with a solid end slab. The third was the analysis of a three-dimensional PCRV test model with penetrations in the end slab. Good agreeement between experimental and analytical results was obtained.     

超大拱式变截面渡槽收缩徐变影响研究

以跨径200m的超大跨径变截面拱式渡槽的结构设计为例,通过建立有限元模型,对渡槽主拱圈的分段分环施工全过程进行了收缩徐变分析。结果表明,徐变收缩可引起较大的后期变形,对渡槽竖向位移影响显著。建议在超大跨拱式渡槽预拱度设计时,应充分考虑混凝土的收缩徐变对变形的影响,采取分段分环施工并在拱脚处使用微膨胀混凝土以减小收缩徐变的影响,并采取相应措施控制渡槽线形。     

Some issues in life assessment of longitudinal seam welds based on creep tests with cross-weld specimens

In order to reduce production costs, it is of great interest to use longitudinal seam welds when manufacturing large diameter pipes. The cost reduction can be as high as 30%. However, severe inservice accidents for this type of pipes working in the creep regime have occurred mainly due to mismatch in weldment creep properties.

In many cases, creep tests of cross-weld specimens, taken from the seam weld, are used to predict the behaviour of the seam weld, assuming that the creep behaviour of specimen and weldment is equivalent. Experiences of this procedure indicate that further knowledge is required before translation between specimen and component can be made.

In the present paper, both full scale seam welded pipes and cross-weld specimens are studied with the damage mechanics concept using finite element, FE, technique. The same mechanical model of multiple material zones is used for the two components. Both the influence of differences in creep properties between the weldment constituents and the size effect of the cross-weld specimen, are studied.

It is found that the cross-weld test results can not directly be translated to the full scale component. Factors such as the creep properties and the relative geometry of the weldment constituents and the size of the cross-weld specimen have to be considered when performing creep life assessment.     

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.     

Some problems associated with the behaviour of structures in the plastic range

When structures are tested beyond the elastic limit there are difficulties in comparing the actual behaviour with that predicted by idealised theoretical models, particularly for cyclic loading. These are mostly due to creep and change of geometry. The case of a cylinder-sphere vessel under internal pressure is discussed as an example, and some ideas put forward which may be useful in experimental work and for design.     

Modelling crack growth for creep and fatigue loading

Estimates of creep crack growth in engineering components under steady load conditions are usually based on the application of fracture mechanics concepts. In particular the creep parameter C* has become widely used together with creep crack growth data obtained from laboratory tests. There are now a number of practical methods to utilise experimental data. For high temperature components, which are subjected to cyclic (fatigue) as well as creep loading, the estimation of the fracture mechanics parameters becomes much more difficult, and consequently the extent to which the growth of pre-existing cracks grow by creep and fatigue is difficult to quantify. In this paper the response of Type 316L stainless steel is examined. This material progressively strain hardens under reversed cyclic loading, and the creep behaviour also changes. Using uniaxial fatigue and creep results, fracture parameter maps are developed to establish the appropriate regimes for creep-fatigue crack growth. Using the maps a model is developed which can predict the combined effect of fatigue and creep on crack growth. The implications of the model are discussed in relation to the limitations of obtaining results from laboratory tests at short times, and the assessment of practical engineering components.     

Concentration of plastic strains in steel liners due to concrete cracks in the containment wall

A substantial part of nuclear containments in US and Europe are designed with an outer bearing concrete structure and an inner sealing consisting of a tight-welded steel liner. The liner constitutes the ultimate leak-barrier, which prevents leakage at high internal pressure loads. The purpose of this paper is to show which influence a through-wall concrete crack may have on the strain level in the liner. A non-linear bar model is used to evaluate the liner behavior. It is shown that the effect from friction between the concrete and liner could be significant and cause high concentration of plastic strain. The influence of friction on the liner is verified by an experimental program presented in this paper. One of the conclusions is that concentrations of strain due to friction increase with decreasing liner thickness. This is important to consider when results from scale tests are interpreted. Scale models, which have thinner liners, could get significantly higher liner strain than the actual full-scale containment.     

Analysis of creep in a welded ‘P91’ pressure vessel

The present work considers the uniaxial and multiaxial creep behaviour of the tempered martensite 9%Cr 1%Mo steel ‘P91’ and the creep behaviour of welds in a P91 pressure vessel. The microstructure of a base metal/weld metal transition in a thick section pipe was analysed by means of optical microscopy and hardness measurements. Special emphasis was given to three microstructural states: the base metal (BM), the weld metal (WM) and the intercritical heat affected zone material (IC-HAZ). A significant difference between these three microstructures was their subgrain size, which was measured in the transmission electron microscope and was found to be smallest for the weld metal and largest for the intercritical heat affected zone material. The uniaxial creep behaviour of the three material states was analysed and it was shown that the creep strength increased with decreasing subgrain size. The elastic modulus of P91 was measured and the uniaxial creep behaviour of the three material states was characterized and represented by (i) the Norton law and (ii) in terms of the Robinson model. A welded pressure vessel was creep tested and hoop and axial strains were measured for three welds in the vessel. A creep stress analysis of the welded pressure vessel was performed based on (i) Norton's law and (ii) the Robinson model concentrating on the accumulated hoop and axial strains in the welds. Measured and calculated axial and hoop strains were found to be in good agreement.     

Continuum mechanics simulations of NiO/Ni–YSZ composites during reduction and re-oxidation

Repeated reduction–oxidation (redox) cycles on Ni-based solid oxide fuel cells (SOFC) have been experimentally well investigated and are known to be detrimental to the thermomechanical stability of the composites, especially on anode supported structures. In the present work the mechanistic analysis of the internal factors leading to the dimensional changes and the thermomechanical instability have been addressed, to our knowledge for the first time, using continuum mechanics simulations. The two intertwined percolating phases, YSZ and NiO/Ni, interact and the driving force for the dimensional change arises from the volumetric change related to the phase change NiO ? Ni. The measurable change in bulk length is given by the ceramic YSZ backbone as a response to the stress created by the chemical strain. The different subprocesses described in the model for YSZ were elastic and anelastic expansion, diffusional creep, grain boundary sliding (GBS) and microcracking due to excessive stress. In the Ni/NiO phase, nonelastic strains in terms of diffusional and power law creep were implemented, and additionally for NiO deformation due to microcracking and/or pseudoplasticity. Semi-empirical correlations were employed for creep limiting grain growth of Ni and NiO, particle coarsening of Ni and particle growth in NiO during the oxidation. Seven experimental cases of high temperature redox dilatometry were simulated. The model shows good qualitative agreement with the measurements. The different processes of importance for the dimensional behaviour are discussed.     

A TEMPERATURE-CREEP THEORY FOR PRESTRESSED CONCRETE CONTINUUM AND BEAM STRUCTURES

The paper describes a creep analysis for prestressed concrete structures subjected to sustained or cyclically varying temperatures; cracking is not taken into account. Theory is presented for the general continuum problem and for continuous beam structures, ft is in such a form that the initial elastic and thermoelastic solutions, and the limiting or steady-state solution for creep, are obtained from the use of a single matrix equation. The solution at all stages of the problem is therefore ideally suited to a computer analysis. The calculation procedures are direct and time-step solutions are not required. The examples presented illustrate the combined influence of creep and nonuniform temperatures, and demonstrate the need to include a steady-state stress analysis at the design stage if long-term serviceability of prestressed concrete structures is to be assured. It is concluded that Codes of Practice should include sufficient information relating to temperature to permit an evaluation of long-term structural behavior to be made.     

Cyclic loading of thick vessels based on the Prager and Armstrong–Frederick kinematic hardening models

The aim of this paper is to relate the type of stress category in cyclic loading to ratcheting or shakedown behaviour of the structure. The kinematic hardening theory of plasticity based on the Prager and Armstrong–Frederick models is used to evaluate the cyclic loading behaviour of thick spherical and cylindrical vessels under load and deformation controlled stresses. It is concluded that kinematic hardening based on the Prager model under load and deformation controlled conditions, excluding creep, results in shakedown or reversed plasticity for spherical and cylindrical vessels with the isotropy assumption of the tension/compression curve. Under an anisotropy assumption of the tension/compression curve, this model predicts ratcheting. On the other hand, the Armstrong–Frederick model predicts ratcheting under load controlled cyclic loading and reversed plasticity for deformation controlled stress. The interesting conclusion is that the Armstrong–Frederick model is well capable to predict the experimental data under the assumed type of stresses, wherever experimental data are available.     

A local approach to creep fracture by slow crack growth in an MDPE: Damage modelling

Slow crack growth (SCG) behaviour has been investigated under creep conditions in a medium density ethylene–butene copolymer (MDPE) on both axisymmetrical Full Notched Creep Tensile (FNCT) and Double Edge Notched Tensile (DENT) samples tested at 60 °C. An attempt is made to predict the long-term failure of a component under creep loading conditions, using an incremental damage law. The experimental creep damage observations were compared to the creep stress–strain distributions calculated by finite element method. Such comparison can provide a damage evolution law as a function of the maximum principal stress and the creep strain. The failure criterion is expressed in terms of a critical creep damage over a critical distance. This model is applied to creep crack growth on the FNCT and DENT samples.     

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.     

Development and use of the R5 procedures for the assessment of defects in high temperature plant

The R5 procedures have been developed within the UK power generation industry to assess the integrity of nuclear and conventional plant operating at high temperatures. Within R5, there are specific procedures for assessing components containing defects. These are largely based on approximate reference stress techniques and are continuing to be developed. This paper describes the procedures for assessing the incubation and growth of defects at elevated temperatures and includes examples of both experimental and finite-element validation of these approaches. The use of these basic procedures is then illustrated by application to a typical high temperature plant component.Alternative methods for assessing incubation and the early stages of creep crack growth are currently being developed within the R5 procedures and this paper finally describes one of these, the time dependent failure assessment diagram (TDFAD) approach.     

Difficulties in interpreting data from creep crack growth tests on type 316H weldments

Abstract

Experimental creep crack growth data are generally obtained by following standard methods such as ASTM E1457-07 and subsequently characterised using the C* parameter. These data are then used in assessment procedures, such as R5, together with reference stress estimates of C* in the component, to predict creep crack growth behaviour. Some modifications to the ASTM E1457 creep crack growth testing and analysis methods have already been proposed following a previous analysis of data from long term creep crack growth tests on type 316H parent material. This paper reports the results of creep crack growth tests on type 316H heat affected zone material at 550°C using compact tension (CT) specimens manufactured from non-stress relieved thick section butt welds. It is shown that interpretation of the data from these weldment tests is complicated by both the discontinuous nature of the cracking process and the presence of significant residual stresses in the CT specimens. Further modifications to creep crack growth testing and analysis methods are proposed to address difficulties arising from the discontinuous nature of the cracking process, and further work is identified to investigate the influence of the residual stresses present in the specimens on the observed crack growth behaviour.     

Continuum damage mechanics analyses of type IV creep failure in ferritic steel crossweld specimens

A major high temperature failure mechanism for weldments in ferritic steel steam pipework is circumferential creep cracking within the region of the heat affected zone, adjacent to the parent material, that experiences the lowest temperatures during the welding process. This is commonly known as type IV cracking. In recent years a number of experimental studies have investigated the occurrence of type IV failure in laboratory test pieces, however, there have been few attempts at theoretical modelling of type IV failure to assist in the formulation of design and assessment procedures. This report discusses the use of the creep continuum damage mechanics method for the analysis of the deformation and failure of weldments that are known to fail within the type IV region.The creep behaviour of each of the material regions of a weldment is described with a set of physically based constitutive equations, which incorporate a number of state variables. The finite element creep continuum damage mechanics method is used, with the physically based constitutive equations, to analyse the deformation and failure of the welded testpieces. The computations are shown to be in good agreement with the experimental results. The implications of the analyses are discussed with reference to the assessment of weldments that are susceptible to type IV failure.     

Creep life assessment of an overheated 9Cr-1Mo steel tube

Crude oil heater 9Cr–1Mo steel tubes from a refinery plant were studied, after 24 years of service at nominally 650 °C and 27 MPa, to predict their remanent lives. The investigation included dimensional, hardness and tensile measurements in addition to accelerated stress rupture tests between 650 °C and 700 °C and microstructural examination. Tube specimens were taken from two sections, the overheated side and the side which only saw the nominal operating temperature. The method employed involved the prediction of the increase in temperature with increasing sediment deposition during the operating life times using an FEM model. In addition the predicted temperatures are used to derive appropriate creep properties at relevant temperatures in a 3D pipe FEM creep analysis to predict the pipe deformation rate. All compare well with the actual service exposed pipe measurements and layer deposition. The overheated side revealed a small loss of creep strength in a stress rupture test. A layer of sediment (appr. 10 mm thickness) consisting basically of sintered carbon (coke) spread over the inside of the tube was acting as a thermal barrier causing the temperature to rise above 650 °C. Analysis for the overheated side predicted an upper bound temperature of ≈800 °C and a life of about 50 h suggesting that failure by creep rupture could occur rapidly in the sediment region.