Interpreting and predicting irradiation creep by fuel element modelling

In order to provide quantitative predictions of the deformation in fuel element cladding it is necessary to take into account several coupled mechanisms. In particular void swelling and irradiation creep components can only be isolated if they are individually understood and modelled correctly. The fuel element modelling program FRUMP has been used to investigate the contribution from void swelling when an appropriately stress dependent model is used. The voidage strain can then be isolated and the remaining irreversible strains examined to give information on irradiation creep. It is emphasized that a proper understanding of the stress effects on void swelling is essential for this procedure.     

The evolutive masing model and its application to cyclic plasticity and ageing

The cyclic plastic behaviour observed in metals results from the existence and development of plastic heterogeneities inside the material. Starting from this constatation, a general scheme - the evolutive Masing model - is proposed and detailed in some special cases. After briefly describing the structure of the Masing model and its interpretation as an homogenized elastic perfectly plastic constitutive model, some microstructural results are presented, describing the plastic heterogeneities which may develop in a metal under cyclic loading. The evolutive Masing model is then introduced by adding a possible evolution of the local constitutive equations or of the heterogeneous structure. Different types of evolution are then analysed and a special emphasis is laid on the case of yield stress evolution, the effect of which is exemplified in different situations. As a conclusion the introduction of microstructural results in the model is discussed and its role to reconcile microstructure, internal variables and hereditary models is advocated.     

High temperature creep and cyclic deformation behaviour of AISI 316 L(N) austenitic steel and its modelling with unified constitutive equations

Creep tests at constant stress and low cycle fatigue (LCF) tests were performed with a view to investigating and modelling the deformation behaviour of AISI 316 L(N) austenitic stainless steel at 700 °C. All experiments were done on samples taken from two different sheets of the same batch of material.The creep stresses were selected from the high stress range. The results obtained from creep tests on samples from different sheets are compared with each other. The differences between them and the results of a creep test carried out at constant load are indicated.The LCF experiments were strain controlled. The effects of strain rate and strain amplitude on the cyclic hardening behaviour were investigated.The parameters of a set of constitutive equations are determined from these data. The quality of the parameter fit is discussed.     

Formulations and computational strategies for novel problems of plasticity and creep

This paper comprises results which have been obtained in the course of studies on a unified approach to a variety of current static and dynamic problems of inelastic solids and structures. The objective of the first part of the paper is to review some concepts of constitutive and finite element modelling for novel plasticity applications. The specific topics covered here are: large elastic-plastic strains with infinitesimal or finite elastic strain contribution, non-associated viscous and non-viscous plasticity as applied to void-containing metals, and temperature and creep effects. The discussion to follow is aimed at showing the great potential of finite-element time stepping schemes in solving problems of structural and mechanical engineering. The numerical illustrations encompass a diversity of large scale computations such as geometrically and materially nonlinear analysis of frames and shells and bifurcation analysis in void-containing metals.     

A unified approach for numerical calculation of space-dependent kinetic equation

A unified numerical method based on the factorization approach is developed to solve the space-dependent neutron kinetic equation. Various numerical methods for solving the space-dependent kinetic equation have been developed so far. These methods can be classified into two categories, i.e., the direct and the factorization methods. The factorization method is known as an effective numerical method. In the present study, a new factorization method named the multigrid amplitude function (MAF) method is developed. Unlike the improved quasi-static (IQS) method, an independent amplitude function is assigned for each spatial region and energy group in the MAF method. The MAF method is a generalization of conventional methods, e.g., the frequency transform, IQS, and Theta methods. To evaluate the amplitude function in the MAF method, the time-dependent coarse-mesh finite difference (TCMFD) method is developed. The MAF method is implemented into a space-dependent kinetic code on the basis of the analytical polynomial nodal method. In order to verify the effectiveness of the MAF method, the TWIGL, Langenbuch, Maurer, and Werner (LMW), and Laboratorium für Reaktorregelung and Anlagensicherung (LRA) benchmark problems are analyzed. The calculation results show the effectiveness of the present method.     

A phenomenological approach for the analysis of combined fatigue and creep

An approach is proposed for the life prediction, under cumulative damage conditions, for fatigue and for creep. An interaction effect is introduced to account for a modification in the material behavior due to previous loading. A predictive technique is then developed which is applied to several materials for fatigue and which could potentially be used for creep.With due consideration to the similarity of the formulation for both phenomena, the analysis for the combination of fatigue and creep is then carried out through a straightforward sequential use of the two damage functions. Several patterns are studied without and with an interaction effect.     

A simplified analysis of creep crack growth using local approach

The use of Fracture Mechanics parameters (K, J, C^*) is subjected to serious limitations when viscoplastic strain appears in a cracked structure.It is therefore one of the cases where a local approach of fracture might be the only mean to help understand the complex mechanical phenomena which influence crack growth.Using a very simple local fracture law, called sudden damage model, various closed form solutions of creep damage zone growth are proposed. With the help of a Double Cantilever Beam (DCB) model to simplify the geometry of the cracked structure, crack initiation and growth are analytically studied.Points such as creep zone size, stress redistribution or influence of local fracture criterion are discussed using closed form solutions.     

A data-driven approach for predicting failure scenarios in nuclear systems

A data-driven approach is presented for the on-line identification of the system Failure Mode (FM) and the prediction of the available Recovery Time (RT) during a failure scenario, i.e., the time remaining until the system can no longer perform its function in an irreversible manner. The FM identification and RT prediction modules are linked in a general framework that recognizes the patterns of dynamic evolution of the process variables in the different system failure modes. When a new failure scenario develops, its evolution pattern is compared by fuzzy similarity analysis to a library of reference multidimensional trajectory patterns of process variables evolution; the failure mode of the developing scenario is identified by combining the modes of failure of the reference patterns, weighed by their similarity to the developing pattern; the similarity weights are then fed to the RT prediction module that estimates the time remaining before the developing trajectory pattern hits a failure threshold.     

A two-surface cyclic plasticity model consistent with fundamental stress-strain equations of the power-law type

A plasticity constitutive model which can describe primary features of stress-strain behaviors of cyclically loaded metallic materials under isothermal conditions is developed in the framework of the two-surface plasticity theory. A special plastic hardening modulus function, which is consistent with the power-law type stress-strain expressions frequently used for both monotonic and cyclic stable stress-strain curves, is introduced to represent cyclic hardening as well as saturated behaviors more realistically. The model is validated through its application to the simulation of uniaxial cyclic and biaxial behaviors of cyclic hardening materials. This model is then implemented into a general purpose finite element computer program and applied to the analysis of a notched plate subjected to cyclic loading.     

The viscoplasticity theory based on overstress applied to the analysis of beams under monotonic and cyclic creep loading

The viscoplasticity theory based on total strain and overstress can reproduce rate-dependent inelastic deformation without distinction between plastic and creep strain using two material functions. A viscosity function and an equilibrium stress-strain curve characterize rate-dependency and work hardening, respectively. The theory is used to analyze the creep and cyclic creep behavior of a beam subjected to a linearly increasing moment which is subsequently held constant.The analysis shows the existence of two possible states of equilibrium for creep deformation: termination of primary creep or secondary creep. They occur when the equilibrium stress-strain curve has positive or zero slope in the plastic range.The numerical experiments illustrate that the stress distribution at the end of the moment increase depends on the moment rate. The rate effects disappear with time when stress is redistributed. For practical purposes the equilibrium solution is obtained before 10⁷ s, when the material functions representing AISI Type 304 Stainless Steel at room temperature are used. The other equilibrium solution (secondary creep) is reached after primary creep when the constant moment is above the limiting equilibrium moment which corresponds to the plastic hinge moment of plasticity theory. The stress distribution during stationary creep is shown to be the solution corresponding to the Norton law of creep theory. The numerical experiments also illustrate the influence of various viscosity functions and equilibrium stress levels. A growth law for the equilibrium stress-strain curve is postulated and reversed loading as well as repeated loading are investigated.     

Merits and limits of thermalhydraulic plant simulations - towards a unified approach to qualify plant models

The paper describes the problems associated with building a Nuclear Plant Model for simulation of transients under the light of recent Spanish and Belgian experience and suggests an approach to qualify plant models based on post-processing and scaling techniques.     

A simpler approach for predicting LWR vessel failure during severe accident conditions

Using closed-form solution techniques, models were developed for assessing the thermal and structural response of light water reactor (LWR) vessels and penetrations during severe accident conditions. Results from models are displayed as failure maps, generally developed in terms of non-dimensional groups, so that a broader range of reactor design parameters and severe accident conditions can be considered. In this paper, failure maps are used to compare LWR vessel response to three accident conditions. Results discussed within this paper illustrate the importance of vessel and tube geometrical parameters and material properties for predicting which vessel failure mode occurs first.     

A semi-empirical approach for predicting two-phase flow discharge through branches of various orientations connected to a horizontal main pipe

The subdivision of two-phase flow in branching conduits consisting of a large horizontal main pipe with upward, downward, or lateral branches of reduced diameter is of great interest in various technological fields. For example, these conduits are important in light-water nuclear reactors (LWRs) in the case of a small break loss-of-coolant accident (SBLOCA) in a leg of the reactor's primary coolant loops, as well as for breaks or valve malfunctions in a large pipeline. In these kinds of circumstances, the relevant phenomenology often involves phase stratification coupled with possible liquid entrainment or gas pool-through phenomena. Therefore, these phenomena were studied in depth to evaluate the pressure drop across conduit elements resulting from the redistribution of flow phases and the discharged mass among them. In the past, several experiments have been performed along with studies in flow modelling. As a result, several formulae and models for branch exit quality and consequent discharge mass flow rate predictions have been proposed.In recent years, we have been engaged in extensive research on this subject, resulting in a new semi-empirical formulation to express branch exit quality in terms of the physical processes taking place in the conduits, the operating parameters and the branch geometry. In this paper, we applied these correlations to representative sets of experiments previously reported in the literature, comprising a wide range of branch-to-main-pipe diameter ratios and operating pressures, which proved our formulation to be very accurate.     

Use of local approach for predicting fatigue cracks in sleeves subjected to repeated thermal shocks

In pressurized-water nuclear plants, certain parts of the circuits have special zone where, for construction reasons, there is a slot that causes a high concentration of stresses. This is the case in particular of nozzles, protected by sleeves, which are subjected to numerous transients and thermal shocks. Loop tests have been carried out on models to evaluate the risk of the initiation or propagation of cracks in these structures. These appear after a few hundred cycles (500) of 210°C amplitude and attain a depth of the order of one milli-metre at 3000 cycles. To analyse how these fatigue cracks begin, an original method based on local approach has been developed in France. A law giving the number of cycles to initiate a crack in terms of the stress σ_θθ has been determined experimentally by numerous rupture mechanics tests on samples. Concordance of calculation and tests has been very satisfactory and has validated this method for thermal shocks on axisymmetrical structures. It is however desirable that an analogous method should be developed and validated for situations in which the plasticity is not confined.     

Systematic approach to predicting corrosion of zirconium alloys in the water coolant of nuclear reactors

A method of semiempirical prediction of corrosion of cladding zirconium alloys as a function of the operating conditions and composition is presented. The laws of thermodynamics and chemical kinetics of the oxidation reactions of a multicomponent zirconium alloy form the physicochemical basis of the computational method. The method is based on a model developed at the All-Russia Research and Design Institute of Integrated Power Technology for the corrosion of commercial and experimental zirconium alloys in water media under autoclave and reactor conditions taking account of the composition of the alloy and the water chemistry. The model is verified on the basis of independent tests performed on a series of zirconium alloys under autoclave and reactor conditions. The method developed makes it possible to predict the corrosion of fuel-element cladding made from zirconium alloys with fuel burnup to 80 MW·days/kg under the conditions of one- and two-phase VVER and RBMK coolant.     

A solution procedure for thermo-elastic-plastic and creep problems

An effective solution procedure for finite element thermo-elastic-plastic and creep analysis with temperature-dependent material properties is presented. The material model employed is summarized, the basic iterative equations are developed and the solution procedure is theoretically analyzed and numerically tested for its stability and accuracy properties.     

Stress state dependence of in-reactor creep and swelling: Part I: Continuum plasticity model

Irradiation induced swelling of reactor core materials may jeopardize safe and reliable operation of fast reactors due to swelling-induced distortion and interference of core components. The principles of incremental continuum plasticity are used here to develop constitutive equations that can be used to conduct engineering evaluations of these potential problems. The equations are used in Part II to analyze previously unreported in-reactor creep and swelling data obtained ca. 1977-1979 as part of the US breeder reactor program. Results of this stress state experiment showed for the first time that a deviatoric stress can affect volumetric swelling. The constitutive equations developed here predict that, in the presence of significant swelling, deviatoric and volumetric strain rate components each are functions of both deviatoric and hydrostatic components of stress for both linear and non-linear creep.     

Bias factors for radiation creep, growth and swelling

Central to the present concepts of the origin of the radiation-induced creep, growth and swelling phenomena is the relative interaction of interstitials and vacancies with various sinks. Radiation-induced climb of dislocations, which figures in many theories of radiation creep and growth, requires the absorption of an excess of either vacancies or interstitials. On the other hand, radiation swelling requires the absorption of an excess of vacancies to effect void growth. These relative preferences are normally expressed in theoretical models by certain bias factors, or capture efficiencies, usually assumed to be constant. Several attempts have been made to estimate their magnitude theoretically but all are seen to involve errors or physically unrealistic assumptions. We present here a unified treatment in which these various bias factors are estimated in a self-consistent model which incorporates, for the first time, all the essential physics, i.e., defect production, interactions of both vacancies and interstitials with sinks and the presence of two types of sinks. We present quantitative evaluations for the SIPA creep model and for radiation swelling, and compare with previous estimates of these phenomena.