CEA and AREVA R&D on HTR fuel fabrication and presentation of the CAPRI experimental manufacturing line

In the framework of the French V/HTR fuel development and qualification program, the Commissariat à l’Energie Atomique (CEA) and AREVA are conducting R&D projects covering the mastering of UO₂ coated particle and fuel compact fabrication technology. To fulfill this task, a review of past knowledge, of existing technologies and a preliminary laboratory-scale work program have been conducted with the aim of retrieving the know-how on HTR coated particle and compact manufacture:

• The different stages of UO₂ kernel fabrication GSP process have been reviewed, reproduced and improved.

• The experimental conditions for the chemical vapor deposition of coatings have been defined on dummy kernels and development of innovative characterization methods has been carried out.

• Former CERCA compacting process has been reviewed and updated.

In parallel, an experimental manufacturing line for coated particles, named GAIA, and a compacting line based on former CERCA compacting experience have been designed, constructed and are in operation since early 2005 at CEA Cadarache and CERCA Romans, respectively. These two facilities constitute the CAPRI line (CEA and AREVA PRoduction Integrated line).The major objectives of the CAPRI line are:

• to recover and validate past knowledge,

• to produce representative HTR TRISO fuel meeting industrial standards,

• to permit the optimization of reference fabrication processes for kernels and coatings defined previously at a laboratory-scale and the investigation of alternative and innovative fuel design (UCO kernel, ZrC coating),

• to test alternative compact process options and

• to fabricate and characterize fuel required for irradiation and qualification purpose.

This paper presents the status of progress of R&D conducted on HTR fuel particles and compact manufacture by early 2005 and the potential of the laboratory-scale HTR fuel CAPRI line.     

SEMER: a simple code for the economic evaluation of nuclear and fossil energy-based power production systems

The code system, SEMER, was recently developed to evaluate the economic impact of various nuclear reactors and associated innovations. Models for nearly all fossil energy-based systems were also included to provide a basis for cost comparisons.Essentially, SEMER includes three types of model libraries: the global model, for a rapid estimation of various nuclear and fossil energy-based systems, the detailed models, for the finer cost evaluation of individual components and circuits in a PWR type of reactor and the fuel cycle models, for PWRS, HTRs and FBRs, allowing the cost estimations related to all the steps in the nuclear fuel cycle, including reprocessing and disposal.This paper summarises our on-going investigations on new developments in, and on the validation of, the SEMER system.Details of the modelling principles, and the results of validation carried out in the context of an EDF/CEA Joint Protocol Agreement, are also presented.First results of this validation are highly encouraging:

• Relative errors for the total kWh or overnight and investment costs are less than 5% for large PWR systems operating in France or other countries.

• These errors are less than 3% for small-sized compact PWRs and they are of the order of 4–7% for HTRs (as compared to IAEA estimations).

• For fossil energy-based power plants, the relative error, even with slightly different cost breakdown between SEMER and that of existing installations, is from 5 to 20%.

• Similarly, errors on the nuclear fuel cycle costs are about 1–4%, compared to published reference values.

The 2006 CHF look-up table

CHF look-up tables are used widely for the prediction of the critical heat flux (CHF). The CHF look-up table is basically a normalized data bank for a vertical 8 mm water-cooled tube. The 2006 CHF look-up table is based on a database containing more than 30,000 data points and provides CHF values at 24 pressures, 20 mass fluxes, and 23 qualities, covering the full range of conditions of practical interest. In addition, the 2006 CHF look-up table addresses several concerns with respect to previous CHF look-up tables raised in the literature. The major improvements of the 2006 CHF look-up table are:

• An enhanced quality of the database (improved screening procedures, removal of clearly identified outliers and duplicate data).

• An increased number of data in the database (an addition of 33 recent data sets).

• A significantly improved prediction of CHF in the subcooled region and the limiting quality region.

• An increased number of pressure and mass flux intervals (thus increasing the CHF entries by 20% compared to the 1995 CHF look-up table).

• An improved smoothness of the look-up table (the smoothness was quantified by a smoothness index).

A discussion of the impact of these changes on the prediction accuracy and table smoothness is presented. The 2006 CHF look-up table is characterized by a significant improvement in accuracy and smoothness.     

A look-up table for fully developed film-boiling heat transfer

An improved look-up table for film-boiling heat-transfer coefficients has been derived for steam–water flow inside vertical tubes. Compared to earlier versions of the look-up table, the following improvements were made:

• The database has been expanded significantly. The present database contains 77,234 film-boiling data points obtained from 36 sources.

• The upper limit of the thermodynamic quality range was increased from 1.2 to 2.0. The wider range was needed as non-equilibrium effects at low flows can extend well beyond the point where the thermodynamic quality equals unity.

• The surface heat flux has been replaced by the surface temperature as an independent parameter.

• The new look-up table is based only on fully developed film-boiling data.

• The table entries at flow conditions for which no data are available is based on the best of five different film-boiling prediction methods.

The new film-boiling look-up table predicts the database for fully developed film-boiling data with an overall rms error in heat-transfer coefficient of 10.56% and an average error of 1.71%. A comparison of the prediction accuracy of the look-up table with other leading film-boiling prediction methods shows that the look-up table results in a significant improvement in prediction accuracy.     

Characteristics of corium debris bed generated in large-scale fuel-coolant interaction experiments

The formation of corium debris as the result of fuel-coolant interaction (energetic or not) has been studied experimentally in the FARO and KROTOS facilities operated at JRC-Ispra between 1991 and 1999. Experiments were performed with 3–177 kg of UO₂–ZrO₂ and UO₂–ZrO₂–Zr melts, quenched in water at depth between 1 and 2 m, and pressure between 0.1 and 5.0 MPa. The effect of various parameters such as melt composition, system pressure, water depth and subcooling on the quenching processes, debris characteristics and thermal load on bottom head were investigated, thus, giving a large palette of data for realistic reactor situations.Available data related to debris coolability aspects in particular are:

• Geometrical configuration of the collected debris.

• Partition between loose and agglomerated (“cake”) debris.

• Particle size distribution with and without energetic interaction.

These data are synthesised in the present contribution.     

High performance light water reactor

The objective of the high performance light water reactor (HPLWR) project is to assess the merit and economic feasibility of a high efficiency LWR operating at thermodynamically supercritical regime. An efficiency of approximately 44% is expected. To accomplish this objective, a highly qualified team of European research institutes and industrial partners together with the University of Tokyo is assessing the major issues pertaining to a new reactor concept, under the co-sponsorship of the European Commission. The assessment has emphasized the recent advancement achieved in this area by Japan. Additionally, it accounts for advanced European reactor design requirements, recent improvements, practical design aspects, availability of plant components and the availability of high temperature materials. The final objective of this project is to reach a conclusion on the potential of the HPLWR to help sustain the nuclear option, by supplying competitively priced electricity, as well as to continue the nuclear competence in LWR technology. The following is a brief summary of the main project achievements:

• A state-of-the-art review of supercritical water-cooled reactors has been performed for the HPLWR project.

• Extensive studies have been performed in the last 10 years by the University of Tokyo. Therefore, a ‘reference design’, developed by the University of Tokyo, was selected in order to assess the available technological tools (i.e. computer codes, analyses, advanced materials, water chemistry, etc.). Design data and results of the analysis were supplied by the University of Tokyo. A benchmark problem, based on the ‘reference design’ was defined for neutronics calculations and several partners of the HPLWR project carried out independent analyses. The results of these analyses, which in addition help to ‘calibrate’ the codes, have guided the assessment of the core and the design of an improved HPLWR fuel assembly.

• Preliminary selection was made for the HPLWR scale, boundary conditions, core and fuel assembly design, reactor pressure vessel, containment, turbine and balance of plant.

• A review of potentially applicable materials for the HPLWR was completed and a preliminary selection of potential in-vessel and ex-vessel candidate materials was made.

• A thorough review of heat transfer at supercritical pressures was completed together with a thermal-hydraulics analysis of potential HPLWR sub-channels. This analytical tool supports the core and fuel assembly design.

• The RELAP5 and the CATHARE 2 codes are being upgraded to supercritical pressures. Thus they can be used to support the HPLWR core design and to perform plant safety analyses.

• Assessment of the HPLWR design constraints, based on current LWR technology was documented. This document stresses the various criteria that must be satisfied in the design (e.g. material, temperature, power, safety criteria, etc.) based on experience gained in the design of PWR.

• Preliminary economic assessment concluded that the HPLWR has the potential to be economically competitive. However, an accurate assessment can only be done after the HPLWR design has been fixed. A more accurate economic assessment may be performed after the conclusion of this project.

Results of irradiated cladding tests and clad plate experiments

Two aspects critical to the fracture behavior of three-wire stainless steel cladding were investigated by the Heavy-Section Steel Technology (HSST) Program: (1) radiation effects on cladding strength and toughness; and (2) the response of mechanically loaded, flawed structures in the presence of cladding (clad plate experiments).Postirradiation testing results show that, in the test temperature range from −125 to 288°C, the yield strength increased, and ductility insignificantly increased, while there was almost no change in ultimate tensile strength. All cladding exhibited ductile-to-brittle transition behavior during Charpy impact testing. Radiation damage decreased the Charpy upper-shelf energy by 15 to 20% and resulted in up to 28°C shifts of the Charpy impact transition temperature. Results of irradiated 12.5 mm-thick compact specimens (0.5TCS) show consistent decreases in the ductile fracture toughness, J_Ic, and the tearing modulus. Results from clad plate tests have shown that: (1) a tough surface layer composed of cladding and/or heat-affected zone has arrested running flaws under conditions where unclad plates have ruptured; and (2) the residual load-bearing capacity of clad plates with large subclad flaws significantly exceeded that of an unclad plate.     

A multi-tank storage facility to effect power control in the PBMR power cycle

This article presents the concept of a storage facility used to effect power control in South Africa's PBMR power cycle. The concept features a multiple number of storage vessels whose purpose is to contain the working medium, helium, as it is withdrawn from the PBMR's closed loop power cycle, at low energy demand. This helium is appropriately replenished to the power cycle as the energy demand increases. Helium mass transfer between the power cycle and the storage facility, henceforth known as the inventory control system (ICS), is carried out by way of the pressure differential that exists between these two systems. In presenting the ICS concept, emphasis is placed on storage effectiveness; hence the discussion in this paper is centred on those features which accentuate storage effectiveness, namely:

• Storage vessel multiplicity;

• Unique initial pressures for each vessel arranged in a cascaded manner; and

• A heat sink placed in each vessel to provide thermal inertia.

Having presented the concept, the objective is to qualitatively justify the presence of each of the above-mentioned features using thermodynamics as a basis.     

The EPR: A clear step forward in dose reduction and radiation protection

For the European Pressurized Water Reactor (EPR) a large effort was made to improve the plant design with respect to radiation protection using the experience gained during the design of former generations of pressurized water reactor (PWR) in France and Germany, and their current operation. Keeping the radiation exposure of personnel to an acceptable level is one of the main objectives of the EPR design. Both the individual and the collective doses are considered.Internationally comparable limits based on recommendations of the International Commission on Radiological Protection (ICRP) have been established for individual doses. These limits describe the framework within which the individual dose shall be kept as low as possible, applying the principles:

• Justification: No practice involving exposures to radiation should be adopted unless it produces sufficient benefit to the exposed individuals or to society to offset the radiation detriment it causes.

• Optimization: In relation to any particular source within a practice, the magnitude of individual doses, the number of people exposed, and the likelihood of incurring exposures where these are not certain to be received should all be kept as low as reasonably achievable (ALARA), economic and social factors being taken into account.

• Limitation: The exposure of individuals resulting from the combination of all the relevant practices is subject to dose limits.

The paper describes the design provision and measures introduced in the plant design to achieve the above described goals.They are in essence:

• measures to avoid or to reduce sources of radiation;

• layout aspects;

• provisions made in the component design with respect to ease of operation and maintenance management;

• improved possibilities of decontamination;

• use of operating experience for design improvements.

The radiation protection layout principles compiled on the basis of safe operating experience gained from the existing pressurized water reactors in France and Germany are used to develop an improved plant design with respect to radiation protection aspects and dose optimization.Summary: The European Pressurized Water Reactor is an evolutionary third-generation pressurized water reactor with a rating in the 1600 MWe class. Its development was started in 1992 by Framatome and Siemens, whose nuclear activities were combined in January 2001 to form Framatome ANP, now AREVA NP. Being the product of intense bilateral cooperation the EPR combines the technological accomplishments of the world's two leading PWR product lines—the French N4 reactors in operation at Chooz and Civeaux and the Konvoi reactors in operation at Neckarwestheim, Emsland and Isar in Germany. From the very start, development of the EPR was focused on improving plant safety and economics even further and also a large effort was made to improve the plant design with respect to radiation protection. Keeping the doses received by operating and maintenance personnel to a level far below the limiting values was one of the main objectives of the EPR design. Both the individual and the collective doses are considered in this article.     

Feasibility study of the cut and weld operations by RH on the cooling pipes of ITER NB components

The maintenance operations of ITER NB components inside the vessel - Beam Line Components (BLC's) involve the removal of the faulty component, its transport to the hot cell as well as the reverse operations of transport of the repaired/new component and its reinstallation inside the vessel. Prior to the removal of the BLC's the cooling pipes must be detached from the component following a procedure that applies to the cutting of the pipes and subsequent welding when the component is re-installed. The purpose of this study, conducted in the framework of EFDA, is to demonstrate the feasibility of the cut and weld operations on the water pipes of the BLC's using fully remote handling techniques. Viable technologies for the cut and weld operations have been identified within the study; in particular the following aspects will be presented in the paper:

• Different strategies can be pursued in the detachment of the components depending on the number of cut and weld operations to be performed on the pipes. The selected strategy will impact on the procedure to be followed likewise on important aspects as the requirements of the flexible joints assembled on the pipes.

• The existing cutting techniques have been examined in the light of the remotely performed pipe cutting at the NB cell. Modifications of commercial tools have been proposed in order to adapt them to the BLC's pipes requirements. The debris produced during the cutting process must be controlled and collected, therefore a cleaning system has been integrated in the adapted cutting tool referred above.

• The existing welding techniques have been also examined and compared based on different criteria such as complexity, reliability, alignment tolerances, etc. TIG welding is the preferred technique as it stands out for its superior performance. The commercial tools identified need to be adapted to the NB environment.

• The alignment of the pipes is a critical issue concerning the remote welding. A proper alignment system has been proposed taking into account the pre-selected welding technique.

Modular HTR confinement/containment and the protection against aircraft crash

Does an HTR need a containment – pressure resistant – or is it possible – licensable – to have only a so-called confinement.The answer depends on both the results of the safety analysis of the accidents considered in the design and the acceptance by the licensing authorities and the public of a safety approach only based on severe core damage exclusion.The safety approach to be developed for modular HTRs must describe the application of the defence in depth principle for such reactors. Whatever the requirements on the last confinement barrier could be, a convincing demonstration of the exclusion of any severe core damage is needed, relying on exhaustive and bounding considerations of severe core damage initiators and the use of non-questionable arguments.The paper presents the containment issues for HTRs based on German experience background and considerations for modern modular HTR safety approach including beyond design situations.

• For the German HTRs (designed in the 80s), it could be shown in the licensing procedures in Germany that there was no need for a pressure retaining and gas tight containment to enclose radioactive nuclides released from the nuclear heat source. Instead, the confinement envelope acted in conjunction with other barriers to minimize the release of radioactive nuclides and the radiological impact on the environment.

• The confinement envelope consisted of the reactor building, a sub-atmospheric pressure system, a building pressure relief system, an HVAC systems isolation and a filtration system.

• During a major depressurization accident, unfiltered releases were discharged to the environment. The analyses results show that the environmental impact was far below the dose limits according to the German Radiological Protection Ordinance, even when the effect of filters was not taken into account.

• The demonstration strongly relied on the assumptions made for the source term definition, e.g. the fuel particles failure rates (under irradiation and during accidental conditions), the diffusion data, the dust data and the deposition/lift-off mechanisms.

• For modern modular HTRs, the last confinement barrier performances will have to be determined in accordance with the set of accidents to be considered in the design including internal and external hazards and the limits targeted for the public and the environment protection.

Further more the paper presents an analysis of effects of a deliberate crash of a large commercial airliner on a former German HTR design.     

Pressure-tube and calandria-tube deformation following a single-channel blockage event in ACR-700

One postulated accident scenario for the Advanced CANDU Reactor (ACR-700™) is the complete coolant flow blockage of a single pressure-tube (PT). The flow is not monitored within each individual PT, thus during the early stages of this accident the reactor remains at full power and full pressure, resulting in rapid coolant boil-off and fuel overheating. Melting of the Zircaloy (Zry) components of the fuel bundle can occur, with relocation of some molten material to the bottom of the PT, which may cause failure of the PT and/or the calandria-tube (CT). We analyzed several key phenomena occurring after the blockage, including coolant boil-off, cladding heat-up and melting, dripping of molten Zircaloy (Zry) from the fuel pin, thermal interaction between the molten Zry and the PT, localized bulging of the PT, and interaction of the bulged PT with the CT. The main findings of the study are as follows:

(1) Most coolant boils off within 3 s of accident initiation.

(2) The Zry cladding starts to melt between 7 and 10 s after accident initiation.

(3) The very high heat-up rate typical of the flow blockage accident sequence ensures that the molten Zry would drip to the bottom of the PT.

(4) After contacting the molten Zry, the PT and CT bulge out radially under the effect of the reactor pressure.

(5) PT/CT failure occurs only if the postulated mass of molten Zry in contact with the PT is sufficiently large, i.e., >100 g. The characteristic time scales for this 100-g case are as follows:

- PT bulging starts within 3 s of Zry/PT contact;

- PT makes contact with the CT in another 3 s;

- CT bulging starts in approximately 1 s;

- CT failure occurs within another 6 s.

Thus, the duration of the PT/CT deformation transient is 13 s, which gives a total duration of the accident (from PT blockage to PT/CT failure) of 20–23 s.The relatively simple models developed in this study and the estimates generated with these models provide a solid physical framework for the key phenomena in the single-channel flow blockage event in ACR-700. As such, they can also assist in the interpretation and verification of future analyses of this event conducted with more sophisticated codes and tools.     

Corrosion issues in nuclear waste disposal

This paper summarized some corrosion issues specific to nuclear waste disposal and illustrates them by the French geological clay concept for the reliable prediction of container degradation rate and engineering barrier integrity over extended periods, up to several thousands years. Among the items, the following are included:

• The importance of the underground repository conditions.

• The necessity of developing comprehensive semi-empirical models and also predictive models that must be based on the mechanisms of corrosion phenomena.

• The use of archaeological artefacts to demonstrate the feasibility of long term storage and to provide a database for testing and validating the models.

Sea-water desalination with nuclear and other energy sources: the EURODESAL project

This paper summarises our recent investigations undertaken as part of the EURODESAL project on nuclear desalination, currently being carried out by a consortium of four European, and one Canadian, industrials and two leading EU R&D organisations.Major achievements of the project, as discussed in this paper are:

• Coherent demonstration of the technical feasibility of nuclear desalination through the elaboration of coupling schemes for optimum cogeneration of electricity and water and by exploring the unique capabilities of the innovative nuclear reactors and desalination technologies.

• Verification that the integrated system design does not adversely affect nuclear reactor safety.

• Development of codes and methods for an objective economic assessment of the competitiveness and sustainability of proposed options through comparison, in European conditions, with fossil energy based systems.

Results obtained so far seem to be quite encouraging as regards the economical viability of nuclear desalination options.Thus, for example, specific desalination costs ($/m³ of desalted water) for nuclear systems, such as the AP-600 and the French PWR-900 (reference base case), coupled to multiple effect distillation (MED) or the reverse osmosis (RO) processes, are 30–60% lower than the desalination costs for fossil energy based systems, using pulverised coal and natural gas with combined cycle, at low discount rates and recommended fossil fuel prices. Even in the most unfavourable scenarios for nuclear energy (discount rate=10%, low fossil fuel costs) desalination costs with the nuclear reactors are 7–20% lower, depending upon the desalination capacities. Furthermore, with the advanced coupling schemes, utilising waste heat from nuclear reactors, the gains in specific desalination costs of nuclear systems are increased by another 2–15%, even without system and design optimisation. A preliminary evaluation shows that desalination costs with the GT-MHR, coupled to a MED process, could still be much lower than the above nuclear options for desalting capacities≤43 000 m³ per day. This is because its design intrinsically provides “virtually free” heat at ideal temperatures for desalination (80–100 °C).     

A study of fuel behavior in PWR design basis accident: an analysis of results from the PHEBUS and EDGAR experiments

As part of the French PWR safety study programme, fuel behavior during a design basis accident has been investigated in three parallel directions:

• - separate effect tests in the EDGAR apparatus for developing and validating cladding deformation models,

• - integral tests in PHEBUS for verifying codes,

• - development of fuel behaviour codes for plant calculation after assessment against experimental results. After describing the objectives and content of each of these programmes, the main findings are highlighted and discussed.

Employing industrial standards in software engineering for W7X

The stellarator W7X is a large complex experiment designed for continuous operation and planned to be operated for about 20 years. Software support is highly demanded for experiment preparation, operation and data analysis which in turn induces serious non-functional requirements on the software quality like, e.g.:

• high availability, stability, maintainability vs.

• high flexibility concerning change of functionality, technology, personnel

• high versatility concerning the scale of system size and performance

These challenges are best met by exploiting industrial experience in quality management and assurance (QM/QA), e.g. focusing on top-down development methods, developing an integral functional system model, using UML as a diagramming standard, building vertical prototypes, support for distributed development, etc., which have been used for W7X, however on an ‘as necessary’ basis. Proceeding in this manner gave significant results for control, data acquisition, corresponding database-structures and user applications over many years.As soon as production systems started using the software in the labs or on a prototype the development activity demanded to be organized in a more rigorous process mainly to provide stable operation conditions. Thus a process improvement activity was started for stepwise introduction of quality assuring processes with tool support taking standards like CMMI, ISO-15504 (SPICE) as a guideline. Experiences obtained so far will be reported.We conclude software engineering and quality assurance has to be an integral part of systems engineering right from the beginning of projects and be organized according to industrial standards to be prepared for the challenges of nuclear fusion research.     

Prediction of fuel channel—graphite gas-gap behaviour in RBMK reactors

To maintain thermal contact between the fuel assembly and the graphite moderator, RBMK design reactors employ graphite split rings, which are alternatively tight on the pressure tube or tight on the graphite brick central bore. The split in the graphite rings allows a helium/nitrogen gas mixture to flow up the fuel channel. This prevents oxidation of the graphite and can be sampled to detect pressure tube leaks. The initial clearance between the rings and pressure tube or graphite brick is approximately 2.7 mm (1.35 mm each side). Due to material property changes of the pressure tubes and graphite during operation of the reactor, the size of the clearance between the rings and the pressure tube/brick, called the “gas-gap”, varies. Closure of these gaps has been identified as a possible safety case issue by reactor designers and by independent reviews carried out as part of TACIS reviews and as part of the Ignalina Safety Analysis Report. The reasons for this are that gas-gap closure would cause the pressure tube to be tightly gripped by the graphite bricks via the split rings, which could lead to:

• Extra loading on the upper pressure tube zirconium/steel transition joint, particularly during shut down and emergency transients.

• Splitting of the graphite brick, leading to loss of thermal contact between the pressure tube and graphite. As approximately 5.6% of the heat in graphite-moderated reactor is generated within the moderator through neutron and gamma-heating, loss of thermal contact would result in higher graphite temperatures, accelerating the rate of graphite expansion and hence increasing the loading of the core radial restraint.

• Graphite debris may become lodged in inter-brick gaps, leading to increased axial pressure tube loading during shut down and emergency transients.

The authors have carried out deterministic assessments based on the Ignalina RBMK-1500 reactors in Lithuania, modelling the behaviour of the graphite under irradiation and have predicted graphite bore diameter changes that are in good agreement with the measurements of graphite bore diameters taken at Ignalina Nuclear Power Plant (NPP). A probabilistic model has been developed using the actual results of the deterministic calculations with non-linear graphite behaviour. Statistical analysis of the measurements of tube and graphite diameters taken from Units 1 and 2 at Ignalina NPP has been carried out. Further work has been carried out to try to determine the uncertainty inherent in the predictions of the gas-gap closure from the calculations. The overall objective of the studies is to aid prediction of the gas-gap closure process, and help to identify a suitable monitoring strategy for gas-gap closure that could be used for any RBMK reactor.     

Plastic collapse and LBB behavior of statically indeterminate piping system subjected to a static load

The plastic collapse and LBB behavior of statically indeterminate piping system were investigated in this study, compared with those of the statically determinate piping system. Special attention was paid to evaluate the crack opening displacement after a crack penetrated wall thickness. The main results obtained were as follows:

1. The reduction of ultimate strength caused by a crack was relatively small in the statically indeterminate piping system. The main reason is thought to be that a sufficient redistribution of the bending moment occurs in this system.

2. A method to evaluate the crack opening displacement after crack penetration in a pipe with a non-penetrating crack was proposed. From this method, it was known that the crack opening displacement could be evaluated by using the incremental plastic rotation angle.

3. The acceptable defect size considering the deformation of a pipe was estimated by comparing the plastic moment at the defective part and the gross yielding moment at the non-defective part.