On the analogy between thermally and irradiation induced creep

Employing an analogy between thermally induced and irradiation induced creep, physical arguments are used first to deduce a one-dimensional constitutive relation for metals under stress in a high temperature and high neutron flux field. This constitutive relation contains modified superposition integrals in which the temperature and flux dependence of the material parameters is included via the use of two reduced time scales; linear elastic, thermal expansion and swelling terms are also included. A systematic development based on thermodynamics, with the stress, temperature increment and defect density increment as independent variables in the Gibbs free energy, is then employed to obtain general three-dimensional memory integrals for strain; the entropy and coupled energy equation are also obtained. Modified superposition integrals similar to those previously obtained by physical argument are then obtained by substituting special functions into the results of the thermodynamic analysis, and the special case of an isotropic stress power law is examined in detail.     

The effect of irradiation on diffusion controlled creep processes

At temperatures below about half the melting point and under moderate stress, below the post-irradiated yield stress, a metal will, in a fairly high fast neutron flux ($\text{/}$ > 10¹³ n/cm² sec), suffer an enhanced creep compared to an unirradiated control held at the same temperature and state of stress. Ever since Schoeck's initial suggestion that the excess vacancies introduced by irradiation should cause an acceleration of the diffusion-controlled climb of edge dislocations over obstacles in their glide paths, there has been lively discussion on what conditions must exist (or indeed if there are any conditions) under which irradiation-accelerated diffusion will lead to an enhancement of the creep rate. It is shown here, considering both vacancies and interstitials, that for irradiation-accelerated climb of edge dislocations to enhance creep two basic conditions are necessary. First, the climb must be followed by glide and only that deformation produced by the glide is increased by irradiation. Second, there must exist a net difference in the flux of irradiation-produced interstitials and vacancies into the dislocations. This difference must be provided by other sinks which preferentially absorb one type of defect. This difference cannot be simply caused by the interaction of dislocations of differing orientations with the applied stress field or a preferential attraction between one type of defect and the dislocations. Creep rates computed using a diffusion-controlled climb model are compared with creep rates of a zirconium-base alloy at 300 °C, measured both during and following fast neutron bombardment. The model is shown to be reasonably consistent with such measurements.     

The effect of diffusion anisotropy on dislocation bias and irradiation creep in cubic lattice materials

Point defect currents to straight edge dislocations in fcc and bcc lattices are calculated taking into account the strain-induced diffusion anisotropy (elastodiffusion) of point defects in combined strain fields from dislocations and external loads. The dislocation bias factors are shown to depend on dislocation orientation with respect to the lattice symmetry axes and the direction of external load. The implications of the orientational dependence of bias factors for the dislocation loop kinetics, swelling and irradiation creep in cubic lattices are discussed.     

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.     

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.     

Deuterium trapping by irradiation damage in tungsten induced by different displacement processes

The deuterium trapping behaviors in tungsten damaged by light ions with lower energy (10 keV C⁺ and 3 keV He⁺) or a heavy ion with higher energy (2.8 MeV Fe²⁺) were compared by means of TDS to understand the effects of cascade collisions on deuterium retention in tungsten. By light ion irradiation, most of deuterium was trapped by vacancies, whose retention was almost saturated at the damage level of 0.2 dpa. For the heavy ion irradiation, the deuterium trapping by voids was found, indicating that cascade collisions by the heavy ion irradiation would create the voids in tungsten. Most of deuterium trapped by the voids was desorbed in higher temperature region compared to that trapped by vacancies. It was also found that deuterium could accumulate in the voids, resulting in the formation of blisters in tungsten.     

Irradiation induced dislocation loop and its influence on the hardening behavior of Fe-Cr alloys by an Fe ion irradiation

Nano indentation analysis and transmission electron microscopy observation were performed to investigate a microstructural evolution and its influence on the hardening behavior in Fe-Cr alloys after an irradiation with 8 MeV Fe⁴⁺ ions at room temperature. Nano indentation analysis shows that an irradiation induced hardening is generated more considerably in the Fe-15Cr alloy than in the Fe-5Cr alloy by the ion irradiation. TEM observation reveals a significant population of the a₀<1 0 0> dislocation loops in the Fe-15Cr alloy and an agglomeration of the 1/2a₀<1 1 1> dislocation loops in the Fe-5Cr alloy. The results indicate that the a₀<1 0 0> dislocation loops will act as stronger obstacles to a dislocation motion than 1/2a₀<1 1 1> dislocation loops.     

Mechanisms of radiation induced creep and growth

Irradiation creep occurs primarily because the applied stress causes the evolving microstructure to respond in an anisotropic fashion to the interstitial and vacancy fluxes. On the other hand, irradiation growth requires the response to be naturally anisotropic in the absence of applied stress. Four fundamental mechanisms of irradiation creep have been conjectured: stress induced preferred absorption (SIPA) of the point defects on the dislocations, stress induced preferred nucleation (SIPN) of point defects in planar aggregates (edge dislocation loops), stress induced climb and glide (SICG) of the dislocation network and stress induced gas driven interstitial deposition (SIGD). These mechanisms will be briefly outlined and commented upon. The contributions made by these mechanisms to the total strain are not, in general, mutually separable and also depend on the prevailing (and changing) microstructure during irradiation. The fundamental mechanism of irradiation growth will be discussed: it is believed to arise by the preferred condensation of point defects and climb of dislocation loops and network on certain crystallographic planes. The preferred absorption and nucleation is thus a consequence of natural crystallographic anisotropy and not due to any external stresses. Again the effectiveness of this mechanism depends on the prevailing microstructure in the material. In this connection attention will be particularly drawn to the significance of solute trapping, segregation at grain boundaries, dislocation bias for interstitials and transport parameters for an understanding of irradiation growth in materials like zirconium and its alloys; the relevance of recent simulation studies of growth in such materials using electrons to the growth under neutron irradiation will be discussed in detail and a consistent model of growth in these materials will be presented.     

Microstructure dependence of irradiation creep and growth of zirconium alloys

Zirconium alloys exhibit both irradiation creep and irradiation growth. The mechanisms governing these processes determine the sensitivity of their rates to variables such as temperature, stress, neutron flux, and microstructure. In this paper I compare the observed relationships between creep and growth of zirconium alloys and dislocation density, grain structure, and crystallographic texture with the predictions of theoretical models. The approximately linear dependence of growth on dislocation density and its dependence on texture and grain shape are consistent with a model in which there is a net flux of interstitials to edge dislocations, and vacancies arrive at grain boundaries by pipe diffusion down screw dislocations. The insensitivity of irradiation creep to dislocation density and its dependence on texture are consistent with a climb-plus-glide model in which dislocations climb out of sub-boundaries and glide across the subgrains.     

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.     

In-situ observation of the effect of the precipitate/matrix interface on the evolution of dislocation structures in CLAM steel during irradiation

The key factor that affects the irradiation resistance of a material is its structure such as grain size and precipitates. Two types of China Low Activation Martensitic (CLAM) steels with a different number density of MC phase were pre-ion implanted and subsequently irradiated by electrons using ultra-high voltage electron microscope (HVEM). The effect of MC phase on the growth behavior of dislocation loops and the stability of pre-existing precipitates were investigated in situ and this may give some hints on the way to increase the ability against irradiation damage. The results show that a high number density of the fine MC phase improves the strength of the material and also helps to inhibit the fast growth of dislocation loops. The interface between the precipitate and the matrix acts as an effective sink to trap radiation induced point defects, which can possibly result in an improvement of irradiation resistance to some extent. However, the coarsening of precipitates because of radiation enhanced diffusion is another issue that needs to be seriously considered when developing a nuclear material.     

Observations on the low-temperature creep properties of uranium carbide under irradiation

The creep behaviour of 97% dense hyperstoichiometric UC has been examined during irradiation in three-point bend tests carried out at 450°C up to a dose of $\text{1.65 × 10}{}^{26}\text{fissions/m}{}^3$. A rapid decrease in measured strain rate with dose was observed at each stress level, nominally steady-state creep being established above $\text{≈ 1 × 10}{}^{26}\text{fissions/m}{}^3$ when the creep rate was a factor of 8 lower than that observed in UO₂ irradiated under identical conditions. Creep rates were found to be directly proportional to stress at high doses. Comparison of results from this test with data from other experiments up to $\text{2 × 10}{}^{25}\text{fissions/m}{}^3$ in compression and tension indicates little variation in the radiation-creep constant between 450°C and 800°C. The creep rate for UC, much lower than that observed in UO₂, is consistent with recently reported determinations of the effective uranium self-diffusion coefficients under irradiation in those materials.     

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.     

Radiation induced creep and growth of zirconium alloys

The strain under irradiation of zirconium and its alloys is calculated within a simple rate theory approach. Network dislocations and interstitial dislocation loops with their Burgers vector oriented parallel to the crystal basal plane are assumed to climb by preferentially attracting interstitials with respect to vacancies, while the grain boundaries act as neutral sinks and absorb therefore more vacancies than interstitials. This same theory has been applied by Fainstein-Pedraza, Savino and Pedraza for modelling the irradiation growth of cold worked zirconium alloys. It is now extended by including the effect of vacancy traps and the stress induced preferential bias for interstitials of those dislocations favourably oriented with respect to an external or internal stress field. In addition, a model which allows to correlate the deformation of the individual grains with the strain of the polycrystalline specimen where they pertain is developed. The stresses induced within the same grain while it deforms inside the textured crystal are also numerically calculated. Those stresses modify the grain strain via the SIPA mechanism and the stresses-strains are then coupled. The calculated crystal deformation is strongly dependent on texture. For tubes with the c axis oriented preferentially on an axial plane, a rapid increase of the longitudinal strain rate is predicted at high doses.     

Irradiation induced creep of ceramic nuclear fuels

This contribution gives a review of the experimental results and accompanying theoretical considerations. The mechanisms considered for irradiation creep are: relaxation of elastic stresses by fission spikes, promotion of dislocation slide by thermal spikes, preferential, stress-orientated nucleation of dislocation loops and preferential growth of dislocation loops. A survey over the irradiation creep rates attributed to steady-state creep shows $\text{ε}{}_{\mathrm{irr}}\text{~ σ · F}$ for oxide fuel in the stress and fission rate ranges of $\text{σ = 10–50}\text{MN/m}{}^2$ and $\text{F = 3 × 10}{}^{12}\text{–1 × 10}{}^{14}\text{f/cm}{}^3\text{· s}$ at burnups < 3%. There seems to be a continuous increase of the irradiation creep rate of oxide fuels with increasing temperature. However, that increase cannot be directly interpreted through a thermally activated process. It seems that the irradiation creep rate will also depend on fuel porosity, on plutonium distribution in mechanically blended UO₂-PuO₂, but not substantially on the plutonium content per se. Some results were already given for carbide and nitride fuels, which show the irradiation creep rate to be lower by about a factor of 10 than for oxide fuel under comparable conditions. Primary irradiation creep has been observed up to $\text{(3–5) × 10}{}^{19}\text{f/cm}{}^3$ and could prevail up to $\text{1 × 10}{}^{20}\text{f/cm}{}^3$.     

Anisotropy of irradiation creep of Zr-2.5wt%Nb and Zircaloy-2 alloys

Stress relaxation in bending tests have been used to determine the creep anisotropy of Zr-2.5wt%Nb and Zircaloy-2 alloys during fast neutron irradiation at 570 and 320 K. The ratios of creep rates from longitudinal and transverse sections were found to be larger in Zr-2.5wr%Nb materials than in Zircaloys at both temperatures, and larger at 320 K than at 570 K for both alloys. The creep anisotropy at 570 K for both alloys can be related to crystallographic texture by a model in which the strains are produced by slip of dislocations of the type $\text{1}\text{3}$〈1120〉, 65% on prism planes and 35% on basal planes; at 320 K the ratios of prism to basal slip are 84/16 in Zr-2.5wt%Nb and 73/27 in Zircaloy-2. The latter difference is attributed to alloying. An important implication of these results is that the reduction of elongation rates in CANDU¹ power reactors due to compressive end load is less than was previously believed.