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.     

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.     

Irradiation swelling, creep and thermal-stress analysis of LWR fuel elements, computer code isune-2

The irradiation swelling, creep, and thermal-stress analysis of light-water reactor (LWR) oxide (UO₂) fuel elements is analysed. The analysis is based on the basic physical and mathematical assumptions and the experimental data of the fuel and cladding (or canning) materials. In the analysis, the nuclear, physical, metallurgical, and thermo-mechanical properties of the fuel and cladding materials under irradiation environment are examined carefully. The objectives of the paper are mainly (1) to formulate and carry out the irradiation swelling, irradiation creep, and thermal-stress analysis of fuel elements for LWR power reactors, and (2) to develop a computer code which will facilitate the computations for fuel element design, safety analysis, and economic optimization of the power reactors. In a general procedure of the analysis, the irradiation swelling, irradiation creep, temperature distribution, etc. in the fuel and cladding of the oxide fuel elements during the reactor in operation are studied. Some theoretical models and empirical relations (on the basis of accepted experimental data) for irradiation swelling and creep in the fuel and irradiation creep in cladding materials are postulated and developed. Some analytical and empirical relations (based on test results) for heat generation and temperature distribution in the fuel during fuel restructuring are derived. The fuel restructure is, in general, divided into the central void, columnar grain, equiaxed grain, and unaffected grain zones (or regions) after a sufficiently long period for the fuel elements to be irradiated (or operated). From these relations derived for irradiation swelling, irradiation creep, and temperature distribution in the fuel and cladding, together with the well-known strain-stress, incompressibility, compatibility, and stress equilibrium equations, the irradiation swelling, creep, and thermal-stress analysis for the LWR fuel elements can be carried out.From the analytical results obtained, a computer code, ISUNE-2 (which is in the sequence of computer code ISUNE-1 and -1A developed and used previously for liquid-metal fast breeder reactor fuel element design and safety and economic analysis), can be developed. With some reliable experimental data (measured during fuel elements in operation) as input, the computer code may predict various cases of LWR (oxide or carbide) fuel elements in operation. The general scope and resulting contribution of this paper is to provide a realistic analysis and a reliable operating LWR fuel element code for use by nuclear power utilities to predict the fuel element behavior in power reactors. The fuel element design, safety analysis, and economic optimization depend largely on the fuel element behavior in the power reactors.     

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.     

Irradiation creep relaxation of void swelling-driven stresses

Swelling-driven-creep test specimens are used to measure the compressive stresses that develop due to constraint of irradiation void swelling. These specimens use a previously non-irradiated 20% CW Type 316 stainless steel holder to axially restrain two Type 304 stainless steel tubular specimens that were previously irradiated in the US Experimental Breeder Reactor (EBR-II) at 490 °C. One specimen was previously irradiated to fluence levels in the void nucleation regime (9 dpa) and the other in the quasi-steady void growth regime (28 dpa). A lift-off compliance measurement technique was used post-irradiation to determine compressive stresses developed during reirradiation of the two specimen assemblies in Row 7 of EBR-II at temperatures of 547 °C and 504 °C, respectively, to additional damage levels each of about 5 dpa. Results obtained on the higher fluence swelling-driven-creep specimen show that compressive stress due to constraint of swelling retards void swelling to a degree that is consistent with active load uniaxial compression specimens that were irradiated as part of a previously reported multiaxial in-reactor creep experiment. Swelling results obtained on the lower fluence swelling-driven creep specimen show a much larger effect of compressive stress in reducing swelling, demonstrating that the larger effect of stress on swelling is on void nucleation as compared to void growth. Test results are analyzed using a recently proposed multiaxial creep-swelling model.     

UMo/Al弥散燃料板内裂变气体肿胀的静压效应研究

将核燃料的裂变气体肿胀与静水压力计算相耦合,并考虑重要的辐照蠕变,编制了定义其复杂力学本构关系的子程序。将定义各部分材料热-力学本构关系的用户子程序引入ABAQUS软件,获得了燃料板细观尺度下辐照-热-力耦合行为的计算模拟方法,并计算分析了核燃料裂变气体肿胀的静压效应。与不考虑裂变气体肿胀静压相关性的计算结果对比发现,在裂变气体肿胀计算中引入静压的影响,将使得核燃料颗粒内的辐照肿胀应变显著减小,引起板内最高温度降低,并减弱燃料颗粒和基体间的力学相互作用,减小燃料颗粒内的等效蠕变应变,致使基体内最大Mises应力和第一主应力减小。     

Void swelling and irradiation creep relationships

Recent analytical and theoretical work on swelling enhanced irradiation creep and stress effects on swelling is reviewed. A proposed explanation for swelling enhanced irradiation creep involves consideration of the role of vacancy loops. Theoretical work leads to the development of a new relationship for swelling enhanced creep which predicts larger irradiation creep rates at high levels of swelling (>5%) than the original formulation. Consideration is given to an additional effect of stress on swelling which involves a stress effect on the incubation dose. A constitutive equation is presented to describe this phenomenon. Design related illustrations are presented for these high fluence irradiation induced phenomena.     

Analyses of a restrained growth graphite irradiation creep experiment

Graphite is used as a moderator, reflector and structural component in pebble bed and prism High Temperature Reactors (HTRs). It is fortunate to reactor designers that irradiated graphite shows remarkably high creep behaviour under the influence of fast neutron irradiation at temperatures far below those required for significant creep strains to be generated in unirradiated graphite. This creep behaviour is important in the design of nuclear graphite reactor cores because the self-induced shrinkage stresses generated in typical core components during irradiation can be relieved. However, there are no reliable data on high fluence irradiation creep and the mechanistic understanding of the irradiation creep is insufficiently developed to reliably extrapolate to the high fluences expected of graphite in future HTR designs. The understanding of irradiation creep is further complicated because it has been experimentally observed that irradiation creep strain in graphite modifies other properties in particular the coefficient of thermal expansion. In addition modified changes in Young's modulus in crept specimens have been reported and it has also been postulated that irradiation creep may also modify dimensional change. The assessment of irradiation creep in graphite components is based on empirical laws derived from data obtained from small samples irradiated in a materials test reactor. However, due to the complicated irradiation rigs required and the amount of dimensional and property measurements needed to be taken, constant stress irradiation creep experiments are difficult and very expensive to carry out successfully. However, restrained creep experiments are simple to implement, less expensive and can be easily included as part of other, more conventional irradiation graphite experimental programmes. However, in the past, the disadvantage of these experiments has been that the results have been difficult to interpret using the then available analytical methods. In this paper the restrained creep experiment is revisited and analysed numerically and the possible benefit of using a restrained creep experiment in future graphite irradiation experiments is investigated. It is shown that a numerical simulation of the restrained creep experiment behaviour would be an essential tool to ensure that the stress within the specimen remains within defined limits so that specimen failure can be avoided.     

Diametral strain of fast reactor MOX fuel pins with austenitic stainless steel cladding irradiated to high burnup

The C3M irradiation test, which was conducted in the experimental fast reactor, “Joyo”, demonstrated that mixed oxide (MOX) fuel pins with austenitic steel cladding could attain a peak pellet burnup of about 130 GWd/t safely. The test fuel assembly consisted of 61 fuel pins, whose design specifications were similar to those of driver fuel pins of a prototype fast breeder reactor, “Monju”. The irradiated fuel pins exhibited diametral strain due to cladding void swelling and irradiation creep. The cladding irradiation creep strain were due to the pellet-cladding mechanical interaction (PCMI) as well as the internal gas pressure. From the fuel pin ceramographs and ¹³⁷Cs gamma scanning, it was found that the PCMI was associated with the pellet swelling which was enhanced by the rim structure formation or by cesium uranate formation. The PCMI due to cesium uranate, which occurred near the top of the MOX fuel column, significantly affected cladding hoop stress and thermal creep, and the latter effect tended to increase the cumulative damage fraction (CDF) of the cladding though the CDF indicated that the cladding still had some margin to failure due to the creep damage.     

Fracture mechanics issues for irradiated blanket structures

This paper reviews some of the factors that will affect fracture behavior of fusion reactor structures and summarizes some component life predictions based on linear elastic fracture mechanics analysis. The review includes discussion of the environments to which the components will be subjected, the response of materials to these environments, the time dependent nature of the structural response, and the fracture related failure mechanisms.Radiation environments and complex loading conditions in a fusion reactor cause a variety of material phenomena. These phenomena include irradiation swelling and creep, strength changes due to matrix hardening, helium embrittlement, and surface effects such as sputtering and blistering.The interaction of thermal creep, irradiation creep, and swelling results in complex time, temperature, and neutron fluence dependent stress histories in first wall and blanket structures. These effects reduce compressive thermal stresses during the burn portion of a reactor operating cycle and result in residual tensile stress during the non-burn portion of the cycle. The cyclic nature of these stresses, particularly in a tokamak reactor, and the presence of undetected flaws provide a basis for the application of fracture mechanics. Linear elastic fracture mechanics analysis techniques have been applied to predict component life for several conceptual tokamak fusion reactor designs. These analyses show that the structural life may be limited by growth of initial flaws to a coolant leakage. Results indicate that for neutron wall loadings below 2 to 3 Mw/m², life is likely to be controlled by stresses during the burn period and, at higher wall loadings, by residual stresses during the non-burn period.Fracture toughness properties tend to be reduced by irradiation. Therefore, brittle fracture will be a potentially critical failure mode. Fatigue crack growth and fracture characteristics of the design will affect the operating mode of a reactor and influence the performance of different types of reactors. Tests are currently planned to develop material crack growth and fracture toughness data [1] for candidate alloys because these properties have been shown to be important.     

A third stage of irradiation creep involving its cessation at high neutron exposures

As swelling approaches 5–10% in AISI 316, the creep rate appears to rapidly decline and eventually vanish. There may be some correlation between this phenomenon and concurrent changes in failure mode that also appear to be related to void swelling. For some fusion-relevant applications, creep correlations derived from fast reactor data may lead to an overprediction of the creep strain.     

The temperature dependence of irradiation creep

The stress induced absorption mechanism (SIPA) of irradiation creep will be discussed by developing a new application of rate theory which emphasizes particularly the significance of the vacancy loops formed from the displacement cascades during fast neutron irradiation. A simple analytic result for the expected creep strain rate and various related numerical results will be discussed. The relation between irradiation creep and void swelling will be emphasized, particularly in relation to the significance of the vacancy emission processes from the vacancy loops.     

SAMURA—A fast computer code for reactor fuel pin performance modelling and analysis

A very fast integral numerical computer code for the modelling of transient and steady-state thermal and mechanical behaviour of Zircaloy-clad UO₂ fuel pins in water reactors has been developed. The computational technique which determines the stress and deformation state of the fuel pin is based upon an extremely efficient finite difference scheme, i.e. the non-linear terms in the constitutive equations which produce a non-linear system of equations have been linearised using a Taylor expansion technique coupled with a very sophisticated error minimization algorithm and then solved with great accuracy. An improved numerical method has also been developed for the fast and efficient solution of the transient heat conduction equation. In this way a very stable and economical one-dimensional code (with appropriate provisions made for its conversion to a quasi two-dimensional code) has been obtained. The physical processes included are thermo-elastic deformation, thermal and irradiation creep, plasticity, fission gas swelling and release, formation of cracks in the fuel, hot pressing, densification, pore migration and dish or central void filling. Here the mathematical basis of SAMURA is presented along with some preliminary calculations and benchmarkings. It is concluded that SAMURA is quite fast indeed, converges to accurate results and within the margins of the error criterion chosen has very reasonable computer demands. It is also stable under all conditions tested.     

Technical basis for swelling-irradiation creep opposition testing

Swelling and irradiation creep equations derived from EBR-II immersion density and pressurized tube data were used to predict swelling-irradiation creep opposition behavior (i.e., internal stress type of loading). The swelling-irradiation creep opposition predictions were made for single assembly bowing and slit tube behavior. The results show that an enhanced sensitivity is associated with the swelling-irradiation creep opposition application relative to immersion density and pressurized tube data. A direct relationship exists between single assembly swelling induced bowing and slit tube behavior; therefore, slit tube behavior represents a direct application of swelling-irradiation creep opposition behavior. This study provided the technical justification for a slit tube irradiation test designated WSA-60.     

Residual stress behavior in fast neutron irradiated SA AISI 304l stainless steel cylindrical tubing

Residual stress measurements were made on solution-annealed (SA) AISI 304L stainless steel (SS) irradiated in EBR-II over a temperature range from 402 to 524°C by axially slitting short sections of tubing. The data were analyzed by using SA AISI 304 SS physical properties and SA AISI 304L SS swelling and irradiation creep empirical equations to calculate the slit width change (δ) versus fluence (φt) curve. At temperatures equal to and above 445°C, δ versus φt calculations indicate that the stress effect on swelling is sufficiently large to reduce the swelling rate temperature gradient, and consequently the on-power stress gradient, to zero. This behavior is confirmed by void volume gradient measurements. At lower temperatures, δ versus φt calculations indicate that stress affected swelling is smaller and does not relax the swelling rate temperature gradient. Void volume gradient measurements confirm the presence of a swelling gradient. Calculations of the δ versus φt curve were made with four different empirical swelling equation fluence dependencies, and the best agreement with the δ versus φt data was obtained with a power form type swelling equation. The equations fit the immersion density data ($\text{ΔV}\text{V}{}_0\text{versus}\text{φt}$) within experimental scatter, but predict significantly different δ versus φt behavior. These results show that the slit tube results are very sensitive to the empirical swelling equation form.     

Effects of irradiation on ferritic alloys and implications for fusion reactor applications

This paper reviews the ADIP irradiation effects data base on ferritic (martensitic) alloys to provide reactor design teams with an understanding of how such alloys will behave for fusion reactor first wall applications. Irradiation affects dimensional stability, strength and toughness. Dimensional stability is altered by precipitation and void swelling. Swelling as high as 25% may occur in some ferritic alloys at 500 dpa.Irradiation alters strength both during and following irradiation. Irradiation at low temperature leads to hardening whereas at higher temperatures and high exposures, precipitate coarsening can result in softening. Toughness can also be adversely affected by irradiation. Failure can occur in ferritics in a brittle manner and irradiation induced hardening causes brittle failure at higher temperatures. Even at high test temperature, toughness is reduced due to reduced failure initiation stresses.Ferritic alloys should provide an attractive material for structural applications in a fusion reactor but the temperature regime over which they are used must be limited.     

On establishing constitutive equations for use in design of high-temperature fast-reactor structures

The presentation describes the approach being used to establish constitutive equations for wide use in the design of fast breeder reactor (FBR) components in the US. The approach combines exploratory experiments, constitutive model studies, studies of computational techniques, and tests of simple structural configurations. Short-time (elastic-plastic) behavior, long-time (creep) behavior, and their interactions are considered, and some of the background to equations now identified for use in current FBR design applications involving three structural alloys is discussed. Comments are also given on current efforts aimed at identifying improved constitutive equations for these alloys and on properties data required for design applications. References are cited which have addressed the status of the process at various times.     

Residual stress measurements in irradiated solution-annealed type 304 stainless steel tubing

Immersion density and residual stress measurements were made on solution-annealed type 304 stainless steel capsule tubing irradiated up to fluence levels of 9 × 10²² n/cm² (E > 0.1 MeV). The measured residual stress is dependent on the competition between differential swelling which builds up differential stresses, and irradiation creep which relaxes these stresses. The measurements were analyzed using a bilinear swelling equation formulated with swelling data from the same heat of material. The temperatures and fluence levels of the swelling and slit tube data were each calculated with the same computer code. At high fluence, when swelling was in the steady-state region, the effective irradiation creep rate increased by a factor of about three. Further analysis was made assuming that stress-enhanced swelling and swelling-enhanced irradiation creep were the enhanced relaxation mechanisms.