The effect of residual strain on the thermal conductivity of nuclear graphite

This report describes an investigation of the effect of residual strain caused by compressive pre-stressing on the thermal conductivity of nuclear graphite. The structural changes caused by the applied stress were investigated by measuring the alteration in bulk and nitrogen displacement densities. In the range of small residual strains, the thermal conductivity increases as do the bulk and nitrogen displacement densities. For larger values of the residual strain (after stressing up to ~90% of the fracture stress) the thermal conductivity decreases approximately to its original value, while the bulk and nitrogen displacement densities continue to increase. These observations are compatible with some degree of crack formation; however, other data do not entirely support this simple picture.     

The porosity correction factor for the thermal conductivity of ceramic fuels

The variation of the porosity correction factor, β, with temperature and pore shape was studied by using the Fricke equation for the thermal conductivity of a two-phase medium containing the second phase as randomly distributed ellipsoids. The temperature variation occurs via a parameter, γ, related to the conductivity of the pores. The effect of pore shape was determined via the axial ratio, ε, of oblate or prolate ellipsoidal pores. The results are presented graphically in curves showing the variation of β with γ and ε.     

The effect of stress levels on the coefficient of thermal expansion of a fine-grained isotropic nuclear graphite

Due to the fluctuation and non-uniform distribution of temperature within the core structure of high-temperature gas-cooled reactors (HTGRs), the thermal expansion behavior of graphite materials plays an important role in the design of graphite components, especially of large-scale components. In the present paper, in order to investigate the influence of stress levels on the coefficient of thermal expansion (CTE) of IG-110 graphite, the strain gauge method was used to measure the CTE on the cylindrical specimens under a series of loads applied using a universal tensile testing machine. In addition, a more precise measurement using a thermal dilatometer was employed to validate the tests using the strain gauge method. A good agreement has been obtained between the experimental results using these two methods. The results show that when the specimens were under compressive loads, the CTE along the loading direction of the specimens increased and that along the perpendicular direction decreased, with more changes in the former. The absolute changes of the CTE in the two directions increased with increasing applied load. When graphite specimens were subjected to a compressive load of 40 MPa, the axial CTE of specimens sectioned along the radial direction of the graphite brick as it is installed in the core structure increased from 4.13 × 10⁻⁶ to 5.35 × 10⁻⁶ K⁻¹, while the axial CTE of specimens sectioned along the vertical direction increased from 3.97 × 10⁻⁶ to 5.58 × 10⁻⁶ K⁻¹. Moreover, the residual change of the CTE, which was caused by the permanent residual strain after unloading, was observed. The change of the CTE with stress levels should be considered in the stress analysis and life prediction of the nuclear graphite components.     

The effect of RE-rich phase on the thermal conductivity of U-Zr-RE alloys

Thermal conductivity of RE-bearing U-Zr fuels was investigated. Under an assumption of a RE-rich phase forming a macroscopic mixture with the matrix, the thermal conductivity was estimated for U-Zr-RE alloy. It was evaluated that the thermal conductivity of the U-Zr fuels would be lowered by less than 5% due to the addition of RE. The measurement of the thermal properties of U-Zr-Ce supported the present estimation.     

Anisotropy of coefficient of thermal expansion of nuclear graphite under compressive stresses

The coefficient of thermal expansion (CTE) of nuclear graphite IG-110 and NBG-18 under compressive stresses of 20 MPa, 30 MPa and 40 MPa has been measured by strain gauge method and corresponding anisotropies of CTE under stresses were investigated. With the increasing compressive stresses, the CTE of IG-110 and NBG-18 parallel and perpendicular to the loading directions increased significantly and decreased gradually respectively. The corresponding CTE anisotropies of IG-110 and NBG-18 almost maintain below 1.05 and keep their original near-isotropic properties under compressive stresses maybe due to the homogeneous sensitivity of CTE to the stresses, perfect crystallites in the grains and homogeneous alignment of grains in graphite. The constant isotropic properties of graphite IG-110 and NBG-18 under stresses are beneficial for the integrity and safety of the graphite used in the reactor.     

The effect of temperature on the diffusion length and the scattering cross section of thermal neutrons in graphite

The effect of heating graphite on the diffusion length and effective scattering cross section of thermal neutrons was investigated. It was established that in the 15–350 °C range the diffusion length changes mainly in accordance with the law 1/v for the absorption cross section. The slight deviation from this law is due to the increase of 0.5 mb/deg in the scattering cross section with an increase in temperature.     

Phase-field modeling of gas bubbles and thermal conductivity evolution in nuclear fuels

A phase-field model was developed to simulate the accumulation and transport of fission products and the evolution of gas bubble microstructures in nuclear fuels. The model takes into account the generation of gas atoms and vacancies, and the elastic interaction between diffusive species and defects as well as the inhomogeneity of elasticity and diffusivity. The simulations show that gas bubble nucleation is much easier at grain boundaries than inside grains due to the trapping of gas atoms and the high mobility of vacancies and gas atoms in grain boundaries. Helium bubble formation at unstable vacancy clusters generated by irradiation depends on the mobilities of the vacancies and He, and the continuing supply of vacancies and He. The formation volume of the vacancy and He has a strong effect on the gas bubble nucleation at dislocations. The effective thermal conductivity strongly depends on the bubble volume fraction, but weakly on the morphology of the bubbles.     

Decontamination of nuclear graphite

Graphite is used in gas-cooled reactors (e.g. AGR, MAGNOX, HTR) and Russian RMBK reactors as a moderator and reflector. About 250,000 Mg of irradiated graphite (i-graphite) has to be considered as radioactive waste in the next few centuries. Fission products and activation of impurities in the graphite contaminate this graphite during reactor operation. Key nuclides for waste management are Co-60 during decommissioning, if decommissioning is performed immediately after reactor shutdown, and the long living radionuclides ¹⁴C and ³⁶Cl for long-term safety in the case of direct disposal. Most radioisotopes can, in principle, be removed by using the purification methods already applied during the manufacture of nuclear graphite. However, due to the same chemical behaviour as ¹²C, this does not seem to be applicable to ¹⁴C.Contaminated graphite cannot be stored in low-level surface disposal facilities such as Centre de L’Aube, in France, due to the long half-life of ¹⁴C [Millington, D.N., Sneyers, A., Mouliney, M.H., Abram, T., Brücher, H., 2006. Report on the International Regulation as regards HTR/VHTR Waste Management, Deliverable D-BF1.1 of the Raphael Project, EC Contract 516508, Confidential report]. Furthermore, the ¹⁴C activity of the graphite reflectors from the two German HTR reactors (AVR and THTR) would amount to more than 90% of the total ¹⁴C activity licensed for the underground disposal site Konrad in Germany for non-heat-generating radioactive waste [Brennecke, P., October 1993. Anforderungen an endzulagernde radioaktive Abfälle (Vorläufige Endlagerbedingungen, Stand: April 1990 in der Fassung vom Oktober 1993) - Schachtanlage Konrad -, BfS-ET-3/90-REV-2, Salzgitter, p. 51].The burning of nuclear graphite would be an efficient method for volume reduction, but would not be accepted by the public as long as all the ¹⁴C were emitted into the atmosphere in the form of CO₂. The required separation of the ¹⁴C from the off-gas is difficult and not economic because this carbon isotope has the same chemical properties as the ¹²C from the graphite matrix. The solidification of the whole amount of CO₂ would cancel out the volume reduction advantage of burning.Thus, a process is required which benefits from the inhomogeneous distribution of the ¹⁴C in the graphite matrix leading to ¹⁴C-enriched and ¹⁴C-depleted off gas streams (Schmidt, P.C., 1979. Alternativen zur Verminderung der C-14-Emission bei der Wiederaufarbeitung von HTR-Brennelementen, JÜL-1567].Tritium and other radioisotopes, including ³⁶Cl and ¹²⁹I, can be removed from graphite by thermal treatment. Even significant parts of the ¹⁴C inventory can be selectively extracted because most of the ¹⁴C may be adsorbed on the surface of the crystallites in the pore structure and not integrated into the crystal lattice. This has recently been demonstrated in principle by the HTR-N/N1 project. As an accompaniment to thermal treatments, steam reforming is an alternative method for decontaminating graphite from radionuclides. The decontamination rates are even higher in comparison to pure thermal treatment in an inert atmosphere, as was first evidenced by basic experiments in the HTR-N/N1 project.     

The influence of roughness on tribological properties of nuclear grade graphite

The influence of surface roughness on tribological properties of graphite IG-11 was investigated on a standard SRV tester. The experimental condition was selected as: 30 N normal load, room temperature and a 10 Hz frequency with different strokes. The experiments environments included helium and air. Five types of roughness were studied in the experiments. The experiments revealed that the surface roughness greatly affected the graphite friction behavior. When the friction surface was smooth, the friction coefficient was high because of intensive adhesion accompanied by many pits at the friction surface. When the friction surface was rough, the adhesion was very poor, but the wear was excessive and generated many graphite particles at the friction surface. These particles can separate the friction surfaces, which reduced the friction action between them. For very rough specimens, the friction coefficient decreased with sliding velocity at about 0.004 m/s and then increases gradually.     

Investigation of kinetic recovery process in low dose neutron-irradiated nuclear graphite by thermal annealing

To investigate the kinetic recovery process of low dose neutron-irradiated graphite, nuclear-grade isotropic graphite IG-110U and ETP-10 were neutron irradiated using the JMTR up to 1.38 × 10²³ n/m² (E_n > 1 MeV) at ~473 K. In-situ measurement of macroscopic length was conducted during the isothermal and isochronal annealing process from room temperature up to 1673 K. From room temperature to 773 K for IG-110U, and to 1023 K for ETP-10, macroscopic lengths, lattice parameters, and unit cell volumes of both specimens recovered to their pre-irradiation values, and this recovery process subdivided into two stages. The activation energies of macroscopic volume recovery at 523–673 K and 673–773 K were determined to be ~0.22 eV and ~0.57 eV for IG-110U, respectively; ~0.13 eV and ~2.59 eV at 523–923 K and 923–1023 K for ETP-10, respectively. The migration of not only single interstitials but also interstitials dissociated from submicroscopic interstitial groups along basal planes followed by vacancy-interstitial recombination play a dominant role in the first stage. The second stage is suggested to proceed via the motion of carbon groups along basal planes for IG-110U, and migration of single interstitials along the c-axis for ETP-10. During 773 K or 1023 K up to 1673 K, macroscopic length continuously shrank with decreasing shrinking rate, even with a turnaround to swell at 1173 K for IG-110U.     

Large-scale numerical simulation of mechanical and thermal properties of nuclear graphite using a microstructure-based model

The mechanical and thermal properties of nuclear graphite depend strongly on the microstructures. In this paper, a large-scale three-dimensional boundary element model is presented to study the relationships between the bulk effective properties and microstructure changes in nuclear graphite. Acceleration of the associated boundary element method (BEM) is achieved by use of a fast multipole method (FMM) in allowing large-scale numerical simulations of the model containing up to several hundred micro-structural pores to be performed on one desktop computer. The effects of several key micro-structural parameters such as the pore aspect ratio and the fractional porosity on the bulk mechanical and thermal properties of nuclear graphite are evaluated. The numerical results are compared with some experimental data due to oxidation and good agreement is observed. It is demonstrated that the presented method is potential for fundamental understanding of the bulk properties of nuclear graphite from micro-structural views.     

The various creep models for irradiation behavior of nuclear graphite

Graphite is a widely used material in nuclear reactors, especially in high temperature gascooled reactors (HTRs), in which it plays three main roles: moderator, reflector and structure material. Irradiation-induced creep has a significant impact on the behavior of nuclear graphite as graphite is used in high temperature and neutron irradiation environments. Thus the creep coefficient becomes a key factor in stress analysis and lifetime prediction of nuclear graphite. Numerous creep models have been established, including the visco-elastic model, UK model, and Kennedy model. A Fortran code based on user subroutines of MSC.MARC was developed in INET in order to perform three-dimensional finite element analysis of irradiation behavior of the graphite components for HTRs in 2008, and the creep model used is for the visco-elastic model only. Recently the code has been updated and can be applied to two other models—the UK model and the Kennedy model. In the present study, all three models were used for calculations in the temperature range of 280–450 °C and the results are contrasted. The associated constitutive law for the simulation of irradiated graphite covering properties, dimensional changes, and creep is also briefly reviewed in this paper. It is shown that the trends of stresses and life prediction of the three models are the same, but in most cases the Kennedy model gives the most conservative results while the UK model gives the least conservative results. Additionally, the influence of the creep strain ratio is limited, while the absence of primary creep strain leads to a great increase of failure probability.     

The effect of open porosity on the re-solution of fission gas from grain-edge bubbles

The model of fission gas release from UO₂ fuel during irradiation has been modified to include the effects of the presence of grain-edge porosity on the overall level of re-solution of gas atoms from grain boundaries. The consequence of this improvement is to enhance the predicted fractional gas release at high burn-up.