First spinning cylinder test analysis using a local approach to fracture

In recent years, several experimental programmes on large-scale specimens have been organized to evaluate the capabilities of the fracture mechanics concepts employed in structural integrity assessment of pressurized water reactor pressure vessels. During the first spinning cylinder test, a geometry effect was revealed experimentally showing the difficulties of transferring toughness data from small-scale to large-scale specimens. An original analysis of this test, by means of a local approach to fracture, is presented in this paper. Both compact tension specimen and spinning cylinder fracture behaviour were computed using a continuum damage mechanics model developed at EDF. We confirmed by numerical analysis that the cylinder's resistance to ductile tearing was considerably larger than in small-scale fracture mechanics specimen tests, about 50%. The final crack growth predicted by the model was close to the experimental value. Discrepancies in J R curves seemed to be due to an effect of stress triaxiality and plastic zone evolution. The geometry effect inducing differences in resistance to ductile tearing of the material involved in the specimens can be investigated and explained using a local approach to fracture methodology.     

Development of a spinning cylinder facility for fracture studies

The design of a proposed fracture test facility for large areas of thick-section steel is outlined, in which the test specimen is a hollow cylinder which is rotated at high speed. The facility is capable of applying both primary and thermal stresses to the flawed cylinder. A small-scale version of the facility has been built and tested, in which hollow cylinders of upto 300 kg and outer diameter 0.55 m have been spun at speeds up to 7000 rpm giving stresses close to yield. Some of the advantages and difficulties of the technique are described.     

Finite element analysis of experiment on dynamic behavior of cylinder due to electromagnetic force

An experiment on the dynamic behavior of a cylinder resulting from a transient electromagnetic force was conducted. This experiment can be considered associated with the dynamic deformation of a first wall or a vecuum vessel of a controlled thermonuclear tokamak type reactor. The dynamic strain of the cylinder was measured under a transient strong magnetic field using a non-inductive strain gage and a shielding room. A finite element method was applied to the analysis of the experiment by solving Maxwell's equations and the equation of motion of the cylinder simultaneously. The numerical results are in good agreement with the experimental results.     

A structural analysis of the circular cylinder with multi holes under thermal loading

A structural analysis of the circular cylinder with multi holes is performed using the finite element analysis program . This structure is an analytical model of the capsule used for material irradiation tests. The temperature distributions of the cylinder due to gamma heating are obtained and various parameters, such as specimen size, quantity of specimens and gap sizes between the holder and the specimen are considered in the analysis to obtain the thermal and mechanical characteristics. To assess the structural integrity of the capsule, stress analysis under thermal loading is also performed. The analysis results show that, in all specimens, the peak temperature occurred, and is significantly dependent on gap sizes between the holder and the external tube or the specimen. The stress of the cylinder, under thermal loading, is lower than the allowable stress of the material used.     

Damage evaluation for structural reliability assessment

The paper discusses damage evaluation in structures and the desirability of periodic inspections. Due to the difficulty of mathematical modeling of complex structures, reliance should be made on (a) expert opinion, and (b) interactive rule-based system analysis.     

Inelastic structural analysis: Design implications and experience

The current status of inelastic structural analysis is reviewed relative to the needs and requirements for design of elevated temperature nuclear reactor components. The classes of inelastic problems that can be solved in a practical way are identified and the overall scope of ongoing validation programs is reviewed. Three classes of problems are identified where the further development of simplified analysis techniques is necessary to make them tractable for design application.     

Inelastic evaluation of mechanical and structural components using the generalized local stress strain method of analysis

A simple and systematic method for carrying out inelastic evaluations of mechanical components and structures on the basis of two linear elastic finite element analyses is presented in this paper. The degree of interaction between the local and remainder regions is characterized by studying the relaxation response on the generalized local stress strain (GLOSS) diagram.GLOSS analysis is applied to several problems of practical interest involving multiaxial stress relaxation, follow-up, low cycle fatigue, plastic collpase and issues pertaining to the classification of stresses in pressure components. The results generated by the finite element method compare favourably with those obtained by GLOSS analysis.     

Seismic failure probability evaluation of redundant fast breeder reactor piping system by probabilistic structural response analysis

The seismic failure probability and the correlation coefficient of the multiple failure mode of the heat transport system of a three-loop fast breeder reactor have been evaluated based on a probabilistic structural response analysis. It has been found that the most probable failure mode of the heat transport system has less impact on the core cooling capability than other modes. The correlation coefficient of the heat transport system loops is approximately 0.9. It is found that the correlation comes from the common structural properties rather than the common seismic input. The present approach is useful for quantifying the correlation coefficient and the seismic fragility of the redundant component failure that is used in the systems analysis.     

Elevated-temperature structural design evaluation issues in LMFBR licensing

This paper describes elevated-temperature structural design issues and concerns identified by the NRC licensing review of the Clinch River Breeder Reactor Plant for a construction permit. Major issues concern weldment evaluation, notch weakening, steam generator tubesheet evaluation, and the use of “average” rather than “minimum” material properties in inelastic analysis. Other questions concern seismic effects, elastic follow-up, creep fatigue evaluation, plastic strain concentration, and transition welds. All of the issues were resolved but several required CRBRP Project commitment to perform additional confirmatory programs.     

Modelling of the HFR-EU1BIS experiment and thermomechanical evaluation

Numerical modelling has been successfully applied during the design and evaluation of the HFREU1bis HTR fuel pebble irradiation experiment conducted by the Joint Research Centre Institute for Energy (JRC) in the HFR Petten, The Netherlands. HFR-EU1bis contains 5 HTR fuel pebbles that are placed in a graphite shroud. This assembly is placed in a containment tube, which is again placed in another containment, which is in contact with the HFR cooling water.The experimental requirement is to maintain a central temperature of 1250 °C for all pebbles throughout the irradiation time of 250 effective full power days (efpd). This was achieved by tailoring the gas gaps in the sample holder such that the axial heat generation profile is compensated. Determining the dimensions of the components of the experiment has been done using a thermomechanical finite element model. A combination of numerical and analytical techniques has been applied to minimise calculation times. The thermomechanical finite element model includes the thermal influence of changing gas gap dimensions due to expansion. Heat transfer by radiation through the gas gap has been modelled as well.Results of the model have been compared with measured temperatures. After some adjustments of the model parameters, good agreement has been found between calculated and measured temperatures. Additionally, the influence of irradiation on graphite thermal conductivity and thermal expansion has been included in the model. Due to irradiation damage the thermal conductivity of graphite decreases and thermal expansion generally increases, leading to increasing thermal stresses. Due to burn-up however, the heat flux decreases during irradiation, which leads to a decrease in thermal stresses. To evaluate the influence of these competing mechanisms, the thermal stress evolution during irradiation has been calculated and will be discussed.     

Probabilistic methods in plastic structural analysis

The redistribution of stresses in ductile structures, although beneficial from the safety viewpoint, introduces another source of uncertainty, which requires specific methods when the probabilistic approach to reliability evaluation is followed.Practicable procedures have been developed for structures that satisfy the classical assumptions of plastic limit analysis. In particular, two theorems that allow to find rigorous upper and lower bouds on the probability of full plastic collapse under given loads, are presented. Other methods for probabilistic limit analysis are also indicated, including in particular a specifically developed parametric simulation procedure.The last part of the paper is devoted to the reliability analysis of plastic structures subject to loads varying (slowly) in time.It is recalled first that probabilistic limit analysis can be easily extended to the shakedown—incremental collapse problem, provided the loads vary within a finite domain: however, the significance of such an approach for stochastically varying loads is questioned. In fact, as time increases, the probability also increases that the loads cross any given threshold. Therefore, it is more appropriate to speak of “plastic adaption” rather than “shakedown”, and to focus the attention on the probability of reaching, in any given time interval, a certain permanent deformation. Again, only approximate solutions (in the form of upper and lower bounds) can be found to this question, but this appears to be a more rational and promising approach to the problem.     

Interface between structural and system analysis

In this paper, a brief discussion of the relationship between system and structural reliability in complex technological systems is presented. Fuctionally, a structure is considered from two points of view, namely, as a part of operational system and as a part of standby safety system. For each case, load characteristics and the effects on and from the structure are explained using some examples.     

Review of studies on criticality safety evaluation and criticality experiment methods

Since the early 1960s, many studies on criticality safety evaluation have been conducted in Japan. Computer code systems were developed initially by employing finite difference methods, and more recently by using Monte Carlo methods. Criticality experiments have also been carried out in many laboratories in Japan as well as overseas. By effectively using these study results, the Japanese Criticality Safety Handbook was published in 1988, almost the intermediate point of the last 50 years. An increased interest has been shown in criticality safety studies, and a Working Party on Nuclear Criticality Safety (WPNCS) was set up by the Nuclear Science Committee of Organisation Economic Co-operation and Development in 1997. WPNCS has several task forces in charge of each of the International Criticality Safety Benchmark Evaluation Program (ICSBEP), Subcritical Measurement, Experimental Needs, Burn-up Credit Studies and Minimum Critical Values. Criticality safety studies in Japan have been carried out in cooperation with WPNCS. This paper describes criticality safety study activities in Japan along with the contents of the Japanese Criticality Safety Handbook and the tasks of WPNCS.     

An evaluation of structural failure modes for prestressed concrete containments

Prestressed Concrete Containment Vessels (PCCVs) refer to a popular type of containment used in the United States for Pressurized Water Reactors (PWRs).This paper presents analytically predicted ultimate pressures and seismic levels for PCCVs, considering various modes of failures. Results for six containments are presented, and correlated with the available test data.The analytical methods use either classical techniques or finite element analyses. The ultimate capacity calculations are based upon conservative deterministic estimates of strength of the structure, under both internal pressure and earthquake loads.The results indicate the following: internal pressure capacities of PCCVs built in the US are almost uniformly equal to 2.5 times the design pressure; seismic capacities are at least two times the design level, but they vary widely among the PCCVs depending on the foundation characteristics; seismic capacity of a PCCV decreases with internal pressure; and a PCCV is expected to contribute very little to the overall seismic risk of a nuclear power plant.     

Trends in the evaluation of the structural integrity of RPVs

The aim of this paper is to review recent trends, improvements and validations of methodologies for the assessment of reactor pressure vessel (RPV) integrity against the risk of leak or catastrophic failure, mainly deriving from the possible presence of crack-like defects at critical locations in the vessel wall.The first part of the work gives an overview of the input parameters, namely loading conditions, material properties and possible crack shape and dimensions, which are needed for a comprehensive fracture analysis of RPVs, discussing recent findings and still open questions about them.The next two sections are concerned with reviews of the presently available fracture approaches, related to both brittle and ductile fracture behaviour, and of probabilistic fracture mechanics methodologies.As conclusion, present limitations of methodologies for evaluation of RPV structural integrity and areas which need further improvements are outlined.     

Finite element analysis of inelastic structural behaviour

The paper examines computational aspects of the numerical solution of dissipation and diffusion problems which describe inelastic mechanical processes and transport mechanisms of transient environments. Both phenomena are rate processes which lead in general to a system of coupled first order differential equations after finite element idealization of the spatial dependence.     

Deflection-based method for seismic response analysis of concrete walls: Benchmarking of CAMUS experiment

A number of shake table tests had been conducted on the scaled down model of a concrete wall as part of CAMUS experiment. The experiments were conducted between 1996 and 1998 in the CEA facilities in Saclay, France. Benchmarking of CAMUS experiments was undertaken as a part of the coordinated research program on ‘Safety Significance of Near-Field Earthquakes’ organised by International Atomic Energy Agency (IAEA). Technique of deflection-based method was adopted for benchmarking exercise. Non-linear static procedure of deflection-based method has two basic steps: pushover analysis, and determination of target displacement or performance point. Pushover analysis is an analytical procedure to assess the capacity to withstand seismic loading effect that a structural system can offer considering the redundancies and inelastic deformation. Outcome of a pushover analysis is the plot of force–displacement (base shear–top/roof displacement) curve of the structure. This is obtained by step-by-step non-linear static analysis of the structure with increasing value of load. The second step is to determine target displacement, which is also known as performance point. The target displacement is the likely maximum displacement of the structure due to a specified seismic input motion. Established procedures, FEMA-273 and ATC-40, are available to determine this maximum deflection. The responses of CAMUS test specimen are determined by deflection-based method and analytically calculated values compare well with the test results.     

Survey of advanced structural design analysis techniques

An extensive survey, critical review and basic development of linear elastic analysis methods for one-, two-, and three-dimensional continua is presented. For each of the continua the basic variation principles, significant for the development and understanding of the fundamentals of the structural analysis are given, and their use in deriving the basic equations is demonstrated. In some instances the results presented are original and in some cases they are given in a novel form. The detail intermediate steps are omitted to keep the basic picture as sharp as possible.

An attempt is made to select out of the tremendous number of various proposed finite elements, the ones that are adequate for engineering applications in machine design and are not too complicated to make their used cumbersome or uneconomical.

No discussion of computer programs is presented, however, it is understood that many present structural analysis problems are solved by the use of a computer. References cited in the discussion of various theories contain discussion and outline of computer programs utilizing the respective theories.