Two-fluid model and hydrodynamic constitutive relations

Two-fluid formulation for two-phase flow analyses is presented. A fully three-dimensional model is obtained from the time averaging, whereas the one-dimensional model is developed from the area averaging. The constitutive equations for the interfacial terms are the weakest link in a two-fluid model because of considerable difficulties in terms of experimentation and modeling. However, these are of supreme importance in determining phase interactions. In view of this, the interfacial transfer terms have been studied in great detail both for the three- and one-dimensional models. New interfacial area, drag, virtual mass, droplet size and entrainment correlations are presented. In the one-dimensional model, a number of serious shortcomings of the conventional model have been pointed out and new formulations to eliminate them are presented. These shortcomings mainly arose due to the improper consideration of phase distributions in the transverse direction.     

Development of constitutive equations for nuclear reactor core materials

A set of strain rate dependent constitutive equations has been described which is capable of predicting deformation behavior of anisotropic metals under complex loading conditions with or without the presence of a neutron flux. The important feature of the constitutive equations is that they describe history dependent plastic deformation behavior of anisotropic metals under three-dimensional stress states. Since the analytical model accounts for the effect of prior deformation history at all times, it is capable of handling consecutive or simultaneous loading histories, such as post-irradiation loading, in-pile loading, etc. It is demonstrated that the general form of the constitutive relations is consistent with experimental observations made for Zircaloys under both unirradiated and irradiated conditions.     

Time-dependent inelastic analysis of metallic media using constitutive relations with state variables

A computational technique in terms of stress, strain and displacement rates is presented for the solution of boundary value problems for metallic structural elements at uniform elevated temperatures subjected to time varying loads. This method can accommodate any number of constitutive relations with state variables recently proposed by other researchers to model the inelastic deformation of metallic media at elevated temperatures. Numerical solutions are obtained for several structural elements subjected to steady loads. The constitutive relations used for these numerical solutions are due to Hart. The solutions are discussed in the context of the computational scheme and Hart's theory.     

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.     

Nonlinear elastic constitutive law for granular materials applicable to pebble-bed core

Assuming a granular material to consist of a random assembly of spheres in contact, a nonlinear but elastic constitutive law is derived. Use is made of the nonlinear force-displacement relationships of the contact loads in the normal and tangential directions. The Lamé constants of this isotropic continuum, which is not necessarily homogeneous, depends on the elastic constants of the spheres, the density of the array and either the mean pressure or the volumetric strain.     

The role of vaporization studies and mass spectrometry in the thermodynamics and phase relations of nuclear materials

The thermodynamics and phase relations of nuclear materials can be conveniently and powerfully studied by high-temperature vaporization investigations, especially if mass spectrometric techniques are incorporated. This paper discusses the physical principles of importance in high-temperature vaporization experiments and the use and limitations of conventional and mass spectrometric techniques. A vaporization study gives thermodynamic information about condensed materials and gases if equilibrium exists during the measurements. The course of a vaporization study leading to equilibrium values is described. The mass spectrometer has not been excelled for the identification of species, for rapid measurements of abundances, and for measurements of the temperature coefficients of the intensities of all the species. The instrument may be used for the investigation of vaporization reactions, for the study of reactions involving only gases in equilibrium with one another, and for the measurement of the chemical potentials of the individual components in a chemical system throughout wide composition ranges.     

Assessment of the constitutive properties from small ball punch test: experiment and modeling

An assessment of the true stress-true strain relationship has been done by means of tensile and small ball punch tests on austenitic and tempered martensitic steel at room temperature. A finite element model was developed and validated to calculate the force-deflection curve obtained from the ball punch experiment. The effects of the specimen thickness and material properties on the overall shape of the ball punch test curve are discussed. The constitutive behavior assigned to the specimen for the calculations was determined from the tensile test but we showed that assumptions have to be done to extend it to large strains as those arising during the punch tests. Using an inverse methodology, it was possible to show that a linear strain-hardening stage takes place at large strains. The potential for evaluating the evolution of the strain-hardening capacity after irradiation is outlined.     

The feasibility of small size specimens for testing of environmentally assisted cracking of irradiated materials and of materials under irradiation in reactor core

Environmentally assisted cracking (EAC) or, in other words, stress corrosion cracking (SCC) of in-core materials has become an increasingly important reason for the downtime and maintenance costs of nuclear power plants (NPPs). Use of small size specimens for stress corrosion testing of irradiated materials is necessary because handling of high dose rate materials is difficult and the availability of these materials is limited. A drawback of using small size specimens is that they do not in some cases fulfil the requirements of the relevant testing standards and sometimes their limited load-bearing capacity prevents corrosion fatigue tests and tests with static loading at reasonable K_I values. The test results show that the ductile fracture resistance curves of a Cu–Zr–Cr alloy are, to some extent, independent of the specimen geometry and size. However, the curves of small specimens deviate from the curves of larger specimens at high J values (large plastic zone relative to the remaining ligament) or when the crack growth exceeds about 30% of the remaining ligament. The size dependency of the tested Cu–Zr–Cr alloy seems to be a consequence of decreasing stress triaxiality as the size of the specimen is decreased. The results of the SCC tests of sensitized SIS 2333 stainless steel (equal to AISI 304) specimens in simulated boiling water reactor (BWR) water show that the plastic deformation of the remaining ligament of the specimen has no significant effect on the environmentally assisted crack growth rate. This indicates that stress corrosion testing is not limited by the specimen size. The size dependency in SCC tests should be further studied by conducting tests using various specimen sizes.     

An investigation of the constitutive relations for intersubchannel transfer mechanisms in horizontal flows as applied in the ASSERT-4 subchannel code

In this paper, the influence that the constitutive relations used to represent some of the intersubchannel transfer mechanisms has on the predictions of the ASSERT-4 subchannel code for horizontal flows is examined. In particular the choices made in the representation of the gravity driven phase separation phenomena are analyzed. This is done by comparing the predictions of the ASSERT subchannel code with experimental data on void fraction and mass flow rate, obtained for two horizontal interconnected subchannels. ASSERT uses a drift flux model which allows the two phases to have different velocities. In particular ASSERT contains models for the buoyancy effects which cause phase separation between adjacent subchannels in horizontal flows. This feature, which is of great importance in the subchannel analysis of CANDU reactors, is implemented in the constitutive relationship for the relative velocity. In order to isolate different intersubchannel transfer mechanisms, three different subchannel orientations are analyzed. These are the two subchannels at the same elevation, the high void subchannel below the low void subchannel, and the high void subchannel above the low void subchannel. It is observed that for all three subchannel orientations ASSERT does a reasonably good job of predicting the experimental trends. However, certain modifications to the representation of the gravitational phase separation effects which seem to improve the overall predictions are suggested.     

Evaluation of inelastic constitutive models under plasticity-creep interaction for steel at 600°C

Uniaxial tests to identify plasticity-creep interaction in steel at 600°C were carried out as the Benchmark Project by the Subcommittee on Inelastic Analysis and Life Prediction, JSMS. The purpose of this paper is to present recent experimental data and predictions of constitutive models obtained in the project. Ten types of constitutive models were utilized to compare analytical predictions to sixteen benchmark experiments which are grouped into four categories: (I) tensile and creep tests under monotonic loading, (II) mixed mode tests under plastic and creep loading, (III) ratcheting deformation tests under program loads, and (IV) cyclic deformation tests under the combination of different strain rates. The benchmark tests in Group IV are used to estimate the creep-fatigue life of steel; the results will be published in a separate paper.     

Research and development at the structural materials information center

The U.S. Nuclear Regulatory Commission has initiated a Structural Aging Program at the Oak Ridge National Laboratory to identify potential structural safety issues related to continued service of nuclear power plants and to establish criteria for evaluating and resolving these issues. One of the tasks in this program focuses on the establishment of a Structural Materials Information Center where long-term and environment-dependent properties of concretes and other structural materials are being collected and assembled into a data base. These properties will be used to evaluate the current condition of critical structural components in nuclear power plants and to estimate their future performance during the continued service period.     

A high-resolution small animal SPECT system developed at Tsinghua

An SPECT system dedicated to small animal imaging shall be of a millimeter spatial resolution or even better.This study was aimed at achieving 0.5-mm spatial resolution for a small animal SPECT system at low cost.It was developed from a single-head clinical SPECT scanner,with a seven-pinhole collimator and a four-degree-offreedom motion control stage.Several key techniques were developed,including high-resolution image reconstruction algorithm,high accuracy geometrical calibration method,and optimized system matrix derivation scheme.The system matrix was derived from Monte-Carlo simulation and de-noised by fitting each point spread function to a two dimensional Gaussian function.Experiments of point source and ultra micro hot rod phantom were conducted.With a spatial resolution of 0.5-0.6 mm,this system provides a practical way for low-cost high-resolution animal imaging on a clinic SPECT system.