Creep in nickel bombarded with 17 MEV deuterons

Irradiation creep data have been obtained with an apparatus designed to measure the irradiation creep of material subjected to light ion bombardment. The experimental apparatus has the capability to remotely set and control ion flux, stress and temperature for the creep test. Creep data have been obtained from nickel, 152 μm thick, bombarded with 17 MeV D⁺ ions at 473 K. It is shown that this choice of ion energy and specimen thickness results in minimal error induced by the stress gradient effect. Results to date indicate a nonlinear stress dependence of the creep rate with a stress exponent ≈2.5. This result is in substantial agreement with that found by other investigators using light ion irradiations. Results also suggest that in the temperature and stress range being studied, a climb-glide creep mechanism is operative.     

Viscoplastic deformation of rotating thin-walled disks

It is assumed, that the total strain rate can be decomposed additively into a purely elastic and an inelastic part. The evolution of the inelastic strain rate tensor is governed by a viscoplastic constitutive model with internal state variables. A rotating disk of uniform thickness is considered. It is presupposed that the thickness is much smaller than the outer diameter of the disk. Then a state of plane stress can be assumed and a quasianalytical solution is derived which contains parameter integrals of functions of the inelastic strain rates. The inelastic constitutive model poses an initial value problem. Since the governing ordinary differential equations are not only highly nonlinear but also mathematically stiff special consideration has to be given to time integration. Therefore, an implicit time integration algorithm is presented which is unconditionally stable. A numerical solution is computed using Hart's model and it is compared with a finite element solution. Deviations between the quasianalytical and the finite element solution are discussed.     

On the multiaxial behaviour of concrete exposed to high temperature

An attempt is made to formulate a multiaxial constitutive model for concrete in the temperature range up to 800°C. The proposed model can be characterized as isotropic, elastic-viscoplastic-plastic in the compression region. Brittle failure is assumed in the tensile region.The thermal strain increment is assumed to be a function of both temperature and the current stress tensor. This assumption implies that the thermal strain may have deviatoric components.The volumetric thermal strain is used as a scalar damage measure instead of temperature itself. The corresponding softening function is obtained from isothermal, uniaxial tests. Also the elastic properties are taken as functions of the volumetric thermal strain.The response of the model is illustrated and compared with experimental results.     

U-10Mo/Zr单片式燃料元件堆内稳态热-力学性能研究

本文建立了U-10Mo/Zr单片式燃料元件的辐照性能模型以及热-力学本构关系,采用有限元方法进行非均匀辐照场中燃料元件稳态热-力学性能的数值模拟,获得并分析了U-10Mo/Zr单片式燃料元件温度、形变和应力的分布特点及变化规律。研究结果表明,燃料芯体厚度增量在芯体和包壳结合面附近达到最大,主要受到燃料辐照蠕变的影响;在较低燃耗条件下,燃料芯体高温辐照肿胀模拟结果与低温辐照肿胀试验结果相当;燃料芯体边角区域和包壳端面外侧区域存在应力集中。      

Constitutive relations for nuclear reactor core materials

A strain rate dependent constitutive equation is proposed which is capable of describing inelastic deformation behavior of anisotropic metals, such as Zircaloys, under complex loading conditions. The salient features of the constitutive equations are that they describe history dependent inelastic deformation behavior of anisotropic metals under three-dimensional stress states in the presence of fast neutron flux. It is shown that the general form of the constitutive relations is consistent with experimental observations made under both unirradiated and irradiated conditions. The utility of the model is demonstrated by examining the analytical results obtained for a segment of tubing undergoing different loading histories in a reactor.     

Calculation of Thermalization of Pulsed Neutrons by Few-Pole Expansion Method

The thermalization of pulsed neutrons has been numerically calculated with the application of the few-pole expansion method, which gives an approximate solution in the form of a superposition of pseudo modes (functions of energy) with pseudo decay constants (also functions of energy). The time dependent neutron flux, the Cd and Gd γ-activation responses, as well as the neutron temperature in a pulsed water assembly have been obtained as examples, and the results compared with experimental data, with calculations by direct time integration method, and with calculated time eigenvalues of the medium.

These examples attest to the efficacy of the few-pole expansion method, the adoption of only three pseudo modes having yielded accurate numerical solutions, with only a small fraction of the computing time required by other methods such as direct time integration.     

基于格林函数的应力简化计算方法及试验验证研究

以格林函数为基础,开发了高温高压条件下管道应力影响函数,在实验室条件下选取管道壁面上的典型点,通过高温应变测量对该方法进行了验证。结果表明,基于格林函数的应力简化计算方法的计算结果与试验结果吻合较好,该方法可应用于核电厂关键设备和管道的强度及疲劳寿命的快速评价,亦可用于疲劳监测系统开发。     

Some analytical and numerical results for cladded fuel rods subjected to thermo-irradiation induced creep

Stresses and velocities are analyzed for a hollow cylinder of fuel encased in metallic cladding and subjected to high temperature and high neutron flux fields. The material is represented by a compressible nonlinear thermo-irradiation viscoelastic model. A stress function for axisymmetric plane strain is introduced, and the problem essentially reduces to solving a nonlinear ordinary differential equation in the interfacial contact pressure. Some analytical results are obtained for the case of material properties independent of position. For the case of temperature, flux and thus material properties dependent on position, an approximate formulation is employed whereby the cylinder is divided into discrete rings with constant properties.     

Kondo universality and energy scales in plutonium

The macroscopic properties of α and δ-plutonium were analyzed within the Fermi-liquid approach аs well as the properties of a few model rare earth-based systems. The following major parameters in Pu were estimated within the single-site approximation: the characteristic Kondo energy, the f-electron shell occupation number, the effective degeneracy of the ground f-multiplet, the crystal field splitting energy. The ground state in δ-plutonium is a quantum superposition of two atomic states Pu³⁺ and Pu²⁺. According to its macroscopic physical properties δ-Pu at low temperature is very close to the intermediate valence regime. The temperature dependence of the static magnetic susceptibility in plutonium was calculated. Since the universal Wilson criterion and the Kadowaki-Woods universal relation are valid in δ-Pu it can be considered as a Kondo system, while the position of α-plutonium in the general classification of solids remains a puzzle. The plutonium homology issue is discussed.     

A general one-dimensional model for conduction-controlled rewetting of a surface

A computer-oriented analytical method for predicting the rewetting rate of a hot dry wall is proposed. The wall, which is modeled as a thin flat plate with internal heat generation, receives a variable heat flux from one side while it is cooled from the other side. The model accounts for the large variations of the heat transfer coefficient near the wet front and for the temperature dependence of the thermal and physical properties of the wall. The one-dimensional heat-conduction equation is solved by dividing the quenching zone into small segments of arbitrary temperature increment and constant properties and heat transfer coefficient. A trial-and-error method is developed to predict the velocity of the wet front, the length of the quenching zone and the temperature profile. The one-dimensional models of other authors can be obtained as particular cases of the present model.     

Finite element analysis of mixed-mode thermoelastic fracture problems

This paper presents a rigorous hybrid finite element procedure for the analysis of the thermoelastic problems with mixed-mode cracks. The singular character of the temperature gradient which significantly affects the distribution of thermal stresses near the crack-tip is precisely described. The calculations of temperature and thermal stress fields are carried out by the finite element assemblage in which hybrid singular elements are used around the crack-tip and high-order isoparametric regular elements are taken elsewhere.To determine the mixed-mode stress intensity factors, both the direct extrapolation method based on the finite element solutions and the indirect method using the modified integrals accounting for thermal effects have been proposed. To avoid the underestimation of stress intensity factors obtained by quarter-point singular elements, the important role of the hybrid singular elements developed is also demonstrated.For verification purposes, several pure mode and mixed-mode problems are solved. Excellent correlations between the computer results and available referenced solutions are drawn.     

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.     

Extension to the integral transport equation of an iterative method

In this paper we describe an extension to the neutron integral transport equation of an iterative method. Indeed an iterative scheme is used for both energy and space including external iteration for the multiplication factor and internal iteration for flux calculations. The Monte Carlo method is used to evaluate the spatial transfer integrals. The results were compared with those obtained by using the APOLLO2 code for a cylindrical cell.     

螺旋管式直流蒸汽发生器壳侧流场数值模拟方法研究

铅冷快堆（LFR）采用一体化堆芯设计方案,其中的直流蒸汽发生器（OTSG）多采用螺旋管式结构以使整体结构小型紧凑。为研究LFR中螺旋管式OTSG壳侧铅铋冷却剂的流动传热特性,利用FLUENT软件,采用一种分区段计算方法,通过管壁热流密度拟合公式对螺旋管式OTSG壳侧进行了三维数值模拟。最终验证了该分段计算方法的正确性,分析了OTSG壳侧铅铋冷却剂的流动传热特性,获得了其速度、温度以及压力场的计算数据,为下一步OTSG流致振动分析和高温应力计算提供了依据。      

大气压下大功率等离子体炬的数值模拟

主要研究直流等离子体炬的数值模拟方法,通过求解等离子体弧社区域的能量守恒,动量守恒,质量守恒及电流连续性方程,得到不同边界条件下温度,速度,电流密度分布,计算了大气压下２００Ａ自由氩弧的温度分布,电势和电流分布,并与实验数据及现有的理论计算进行了比较,得到了较好的结果,在此基础上结合本实验室５０００Ａ大功率等离子体炬,讨论了有阴极喷口存在下的弧柱部分的数值计算,以及能量守恒方程中辐射项,焦耳热项的     

Mechanical modeling of creep, swelling and damage under irradiation for polycrystalline metals

A constitutive equation of creep, swelling and damage under irradiation for polycrystalline metals applicable to structural analyses in multiaxial state of stress is developed. After reviewing microscopic mechanisms of irradiation creep and swelling, the relevant theories proposed so far from the view point of metallurgical physics and their applicability are discussed first. Then a constitutive model is developed by assuming that creep under irradiation can be decomposed into irradiation-affected thermal creep and irradiation-induced creep. By taking account of the Stress-Induced Preferential Absorption (SIPA) mechanism, the irradiation-induced creep is represented by an isotropic tensor function of order one and zero with respect to stress, which is, at the same time, the function of neutron flux and neutron fluence. The volumetric part of the irradiation-induced creep is identified with swelling. The irradiation-affected thermal creep is described by modifying Kachanov-Rabotnov theory for stress-controlled creep and creep damage by incorporating the effect of irradiation. Finally irradiation creep and swelling of 20% cold-worked type 316 stainless steel at elevated temperature are predicted by the proposed constitutive equations, and the numerical results are compared with the corresponding experimental results.     

Finite element analysis of loaded structures at very high temperatures

At very high temperatures loaded metallic structures undergo creep deformations. The generated creep strains are connected with stress relaxations, stress redistributions and/or progressive deformations.In mainly load controlled situations the behaviour of the material can be described by a nonlinear viscous flow law (Norton power law).A stress-deformation analysis of complex structures can be carried out by finite element codes in which the mentioned constitutive equation is implemented. The code PERMAS-VISCOUS was used to analyse the stress state of a notched tension bar and the deformation behaviour of a tube under external pressure undergoing a creep collapse. The relation to experimental findings is also given.     

Identification and properties of the fundamental expansion functions for neutron transport in an infinite homogeneous medium

Starting from the basic expression for the neutron flux due to a point source in an infinite homogeneous scattering and absorbing medium, the first few fundamental expansion functions corresponding to successive collisions are identified, and their analytic properties are presented, in spherical and plane geometry. Various representations of the functions are obtained in the form of power series, an expansion in a series of exponential integrals, and other integrals. The adequacy of traditional asymptotic forms is considered.     

Creep rupture at superimposed non-stationary stress and temperature loading

For superimposed stress and temperature loading the conditions are analysed for which the combined loading can be considered as the result of an independent superposition of the individual loading types. Superimposed time linear ramp loading as well as superimposed cyclic (triangle) loading is treated as a special case. In general, as far as one loading type strongly dominates as being the most life time consumpting type, the same will essentially determine the life time for the superimposed loading. In that case the loading types can be considered as mutually independent. However, the differences between the results of rigorous calculations based on the life fraction rule and approximate estimate (independent superposition) as shown for the case of Zircaloy-4 may be within the limits of reproducibility of usual stress rupture tests. The calculations are compared to experiments performed on Zircaloy-4. At loading conditions for which the grain structure remains constant very good agreement is achieved between calculated and measured life times.     

Mechanical and temperature contact in fuel rod and cladding

This paper presents a method of analysis for nuclear fuel rods. The paper concentrates on the interaction between fuel and cladding and between cracked surfaces. Both temperature and mechanical contact are considered. For the temperature contact an analysis model for the heat transfer conditions at fuel and cladding is presented. The most attention of the interaction problem is focused on the constitutive modelling of the mechanical interaction. A constitutive relation between contact stresses and the slip between fuel and cladding is presented. The paper presents a finite element solution of the proposed model. For assumed elastic material properties results from the proposed interaction models are presented. The effect of different contact conditions on contact stresses, stress intensities, etc. are presented.