S.R. MacEwen

Calculations of irradiation growth in zirconium

Abstract Reaction rate theory is used to calculate the dimensional changes in zirconium that result from the annihilation of irradiation-induced point defects at internal sinks. The available data on point defect parameters and the microstructures produced by irradiation are reviewed in an effort to provide a reasonable, justifiable basis for the calculations. In accordance with the experimental evidence, the microstructure for the calculations is assumed to contain two main classes of sinks: dislocations with (a) -type Burgers vectors and grain boundaries. The growth strain results from a net flux of interstitials annihilating at edge dislocations and a corresponding vacancy flux arriving at the grain boundaries. The study includes a discussion of the sensitivity of the growth calculation to the expressions chosen for the sink annihilation probabilities, to the sink concentrations and to anisotropy of the microstructure. Finally, a comparison is made between calculated growth rates and experimental data for cold-worked Zircaloy-2, irradiated at 550 K. Two models are used to describe the behaviour of screw dislocations, which receive a net flux of vacancies. In model 1, the screw dislocations act as perfect sinks, forming dislocation helices, while in model 2, the excess vacancies do not annihilate at the screw dislocations but migrate by pipe diffusion to the grain boundaries. The absolute magnitude of the growth rate in cold-worked Zircaloy at 550 K, calculated using model 2, is much closer to experimental values than that obtained with model 1, which greatly underestimates the growth rate.

In-reactor stress relaxation of selected metals and alloys at low temperatures

Sttess relaxation of bent beam specimens under fast neutron irradiation at 340 and 570 K has been studied for a range of materials, as follows: several stainless steels, a maraged steel, AISI4140, Ni, Inconel X-750, Ti, Zircaloy-2, Zr-2.5% Nb and Zr3 Al. All specimens were in the annealed or solution-treated condition. Where comparisons were possible, the creep coefficients derived from the stress relaxation tests were found to be consistent with other studies of irradiation-induced creep. The steels showed the lowest rates of stress relaxation; the largest rates were observed with Zr-Nb, Ti and Ni. For most materials, the creep coefficient at 340 K was equal to or greater than that at 570 K. Such weak temperature dependence is not easily reconciled with existing models of irradiation creep based on dislocation climb, such as SIPA or climb-induced glide. Rate theory calculations indicate that because the vacancy mobility becomes very low at the lower temperature, recombination should dominate point defect annealing, resulting in a very low creep rate compared to that at the higher temperature. It is shown that the weak temperature dependence observed experimentally cannot be accounted for by the inclusion of more mobile divacancies in the calculation.

〈c〉-Component dislocations in zirconium alloys

Abstract Dislocations with 〈c〉- component Burgers vectors have been found in abundance near deformation twins, and to a lesser extent near grain boundary junctions, in deformed Zircaloy-2 and Zircaloy-4. Both pure 〈c〉 and 〈c + a〉 dislocations have been identified by TEM contrast experiments. The segments of 〈c〉- component dislocations tend to be long, straight, and to lie on either basal or pyramidal planes. It is suggested that these dislocations are generated in order to maintain compatibility between crystallites which differ significantly in their ability to accommodate an imposed deformation by 〈a〉- slip . The manner in which 〈c〉- component dislocations can alter the partitioning of irradiation-produced point defects, and their influence on irradiation growth are discussed.

The bauschinger effect in Zircaloy-2

Abstract The Bauschinger effect in Zircaloy-2 has been investigated at room temperature using (a) specimens cut from the L and ST directions of a thick, rolled slab, and (b) specimens machined from swaged rod. The blocks of material, from which the slab specimens were cut, received compressive prestrains of up to 3.8%, in either the L or ST direction, prior to the tensile specimens being machined from them. The slab specimens were deformed in tension using a computerized Instron, while the swaged rod specimens were deformed in tension/compression using a prototype, MTS Alpha System. A large Bauschinger effect, manifested by a reduction in the yield stress and by permanent softening, was observed. The magnitude of the reduction in the yield stress depended on the magnitude and direction of the prestrain, and on crystallographic texture, and is clearly large enough to influence design and fabrication of reactor-core components. The data from (b) have been analyzed by four different techniques to obtain estimates of the mean back stress which is responsible for the Bauschinger effect in Zircaloy-2. From a comparison of those values with a theoretical estimate based on the analysis of Brown and Clarke, it is concluded that the second phase (Ni,Cr,Fe) particles in Zircaloy-2 are not responsible for the effects observed. It is suggested that the Bauschinger effect is a direct consequence of crystallographic texture and the limited number of deformation modes which can occur in hep zirconium alloys.

Irradiation creep in Zr single crystals

Abstract A single crystal of crystal bar Zr was irradiated, unstressed, at 570 K in a fast (> 1 MeV) neutron flux of 5.5 × 10 16 n/m 2 -s . After a dose of 6 × 10 23 n/m 2 a tensile stress of 25 MPa was applied during a period of steady reactor power. The loading strain was an order of magnitude smaller than that observed when an identical, unirradiated, crystal was loaded to the same stress. There followed a period of primary creep during which the creep rate decreased to a value of 5 × 10 −6 h −1 in the first 24 hours of the test. For the final 2000 hours of the test the specimen was observed to creep at a rate of 1 × 10 −6 h −1 when the reactor was at full power. During shutdowns, the creep rate decreased with time. The results will be discussed and compared with predictions from current theories for the mechanism of irradiation enhanced creep in light of the micro-structures observed.

The effect of neutron flux on dislocation climb

The effect of temperature, flux, stress and sub-grain size on the enhancement of dislocation climb during irradiation has been evaluatedusing solutions to Poissons equation for a single dislocation located at an arbitrary position within a sub-grain. As the distance from the dislocation to the boundary is decreased the climb velocity decreases, but its temperature dependence remains unaltered. The temperature and flux dependence of in-reactor creep are found to be in agreement with the corresponding dependencies of enhanced climb, giving support to a climb plus glide model for in-reactor creep. It is shown that the flux exponent p ue5fc dlnV/d In o can have values ranging from 0.5 to 1.0 depending on flux and sub-grain size and that the Arrhenius plot of climb velocity can show three distinct regions. At high temperature the activation energy is that for self diffusion, while at low temperatures it equals one half the vacancy migration energy; intermediate is a region in which the climb velocity shows little or no temperature dependence.

Zr-Fe intermetallic precipitates and Fe partitioning in Zr-2.5 at% Nb

Abstract Impurity or elemental additions may have a significant effect on hydrogen uptake in zirconium alloys. Neutron diffraction of as-extruded Zr-2.5 at% Nb pressure tube material revealed interplanar spacings corresponding to the α-, β- and ω-Zr phases, and three lines which could not be correlated with the above phases. Analytical Electron Microscopy (AEM) of this alloy revealed particles 20 to 60 nm in diameter containing Zr and Fe, without detectable Nb. Other particles having a similar morphology were also found, and were identified as β-Zr. Electron microdiffraction patterns taken from the particles were consistent with the Zr2Fe phase, with a bet structure of a = 0.66 nm , and c = 0.56 nm . The extraneous neutron diffraction lines, corresponding to d- spacings of 0.2338 nm, 0.2135 nm, and 0.2027 nm were from the {220}, {202} and {031} planes of Zr2Fe respectively. Fe was observed in β-phase using X-ray microanalysis in the AEM, and the presence of Zr2Fe intermetallic particles was supported by room temperature Mossbauer spectroscopy using deconvolution techniques. The partition coefficient for Fe, defined as the fraction of Fe in β-Zr relative to α-Zr, was determined to be about 1.5 to 2.0 using both techniques.

Point defect production and annihilation in neutron-irradiated zirconium

High-purity Zr has been irradiated to a dose of 2.2 × 1021 n/m2 (E < 0.1 MeV) using the pulsed spallation source at IPNS. Electrical resistivity was monitored continuously during irradiation. The saturation resistivity, found from a linear extrapolation of the damage-rate curve between four and five nΩ.m, is found to be 35 nΩ.m. However, comparison with data from the literature shows that the normalized damage-rate curves from five experiments at different temperatures (≤ 77 K) and with different neutron spectra, all fall on the same common curve. A saturation resistivity of 100 nΩ.m is found from the high-dose, linear part of this curve. A spontaneous recombination volume in the range 280 to 400 atomic volumes is found using the theory of Dettmann, Leibfried and Schroeder and the saturation resistivity of 100 nΩ.m. Post-irradiation annealing has been done up to 300 K using stepped, isochronal anneals. The recovery spectrum is in reasonable agreement with previous work, showing a large peak near 100 K, and two smaller peaks at 160 K and 250 K.

Flow stress and dynamic strain-ageing of β-transformed Zircaloy-4

Abstract The 0.2% yield stress of β-transformed Zircaloy-4 was found to be independent of prior-β grain size but varied as the inverse of the transformed β plate width. A dislocation loop expansion model originally proposed by Langford and Cohen [7] for cold-drawn iron wires is used to explain the inverse plate width dependence. Both air-cooled and water-quenched samples exhibited dynamic strain-ageing effects in approximately the same temperature range of 573 to 673 K: (a) a local minimum in strain-rate sensitivity is associated with a peak or an inflection point in the temperature dependence of the 0.2% yield stress for water-quenched or air-cooled samples respectively, and (b) yield drops were observed in strain rate change tests.

Solute effects on radiation-induced creep and growth

Abstract The effects of solute on radiation-induced creep and growth are discussed on the basis of their effects on the defect precipitation rates on extended defect sinks such as dislocations, grain boundaries and interfaces. Some simple relations between defect formation, defect precipitation and dimensional changes are derived. Results of model calculations are presented on the effects of defect trapping on immobile and on mobile solute traps on the deformation rate during irradiation. The calculations indicate moderate reductions of the radiation creep rate resulting from trapping and from the modified bias interactions. A qualitative discussion of the potential effects on radiation creep and growth resulting from radiation-induced solute redistribution is also given. These effects include pinning of dislocations by radiation-induced solute clouds and precipitates, depletion of the matrix of solute, and precipitate re-distribution in poly-phase material.