The impact of azimuthally asymmetric carbon deposition upon pellet-clad mechanical interaction in advanced gas reactor fuel

Cracked nuclear fuel pellets were modelled in the r-θ plane with an azimuthally varying clad surface temperature boundary condition using the PELICAN set of fuel performance models for the commercial finite element software, Abaqus. The temperature boundary condition was assumed to represent heat transfer impairment due to an azimuthally asymmetric carbon deposit on advanced gas-cooled reactor pins. The model predicts the radial and azimuthal displacement of the idealised fuel fragments, together with the resulting elastic, creep and plastic strains in the cladding. These were compared to simulations assuming a uniformly hot or cold boundary condition. Apart from a short period during the return to power from reduced power (70%) operation and outages, the hoop stress in the simulation with an azimuthally varying clad surface temperature was bounded by that of models with a uniform hot or cold surface temperature. The reduced stress was proposed to be due to the greater ability of the fuel fragments to relocate in order to accommodate changes to the power level. As a result, the creep strains in the model with an azimuthally varying clad surface temperature were lower than assuming either a uniform hot or cold boundary condition

Preliminary modelling of crack nucleation and propagation in SiC/SiC accident-tolerant fuel during routine operational transients using peridynamics

Silicon carbide fibre in silicon carbide matrix composites (SiC/SiC) are a promising cladding for use in accident tolerant fuels (ATF) in current light water reactor (LWR) designs. However, as they are a radically different material from current metal clads, current thermomechanical simulation methods struggle to accurately predict their behaviour, especially regarding the potential development of cracks. Thus, a new peridynamic model for SiC/SiC cladding has been developed in the Abaqus finite element code. The material model was isotropic and considers matrix cracking and fibre pull-out. The thermal expansion, swelling and the degradation of the thermal conductivity are modelled under typical LWR irradiation conditions. The swelling on the outer surface is predicted to be greater than the inner surface due to the lower irradiation temperature, causing a tensile stress on the inside of the cladding; tension being more challenging for a ceramic than a metal. This stress increases during the decrease in power at the start of a typical pressurised water reactor refuelling outage and causes microcracking of the matrix on the cladding inner surface. In models without fibres, cracks would propagate through the cladding. If fibres are modelled, matrix cracking will extend to a depth of around 20% through the cladding from the inner surface, which is unlikely to be an acceptable design. If an inner monolith of SiC is additionally modelled, cracking propagates through the monolith and acts as a stress raiser for matrix cracking in the composite, and therefore does not constitute a design improvement. If an outer SiC monolith is modelled, fibre pull-out strain on the inner surface of the cladding was increased by just under 70%. No cracks are predicted in an outer monolith which may therefore remain gas-tight and thus a more suitable design. These predictions are consistent with experimental findings

Modelling of Weibull distributions in brittle solids using 2-dimensional peridynamics

Peridynamics is a continuum mechanics modelling method, which offers advantages over traditional continuum methods when modelling brittle fracture. Brittle fracture typically follows a Weibull fracture distribution, but this behaviour is not well represented in bond-based peridynamics using a single valued bond failure stretch. In order to recreate specific Weibull-type behaviour in bond-based peridynamics, consideration must be given to scaling the distribution to account for the size of peridynamics bonds. Care must also be taken to avoid (wherever possible) non-physical crack arrest, caused by the variations in fracture toughness in the model, distorting the distributions. In this work a method for recreating a variety of Weibull distributions is outlined, based on applying Weibull-type bond behaviour only to surface bonds, including a transition zone across one horizon. The method is shown to be insensitive to variations in mesh refinement

Density functional theory study of the magnetic moment of solute Mn in bcc Fe

An unexplained discrepancy exists between the experimentally measured and theoretically calculated magnetic moments of Mn in α-Fe. In this study, we use density functional theory to suggest that this discrepancy is likely due to the local strain environment of a Mn atom in the Fe structure. The ferromagnetic coupling, found by experiment, was shown to be metastable and could be stabilized by a 2% hydrostatic compressive strain. The effects of Mn concentration, vacancies, and interstitial defects on the magnetic moment of Mn are also discussed. It was found that the ground-state, antiferromagnetic (AFM) coupling of Mn to Fe requires long-range tensile relaxations of the neighboring atoms along ⟨111⟩ which is hindered in the presence of other Mn atoms. Vacancies and Fe interstitial defects stabilize the AFM coupling but are not expected to have a large effect on the average measured magnetic moment

The effect of Nb on the corrosion and hydrogen pick-up of Zr alloys

Abstract Zr-Nb alloys are known to perform better in corrosion and hydrogen pick-up than other Zr alloys but the mechanism by which this happens is not well understood. Atomistic simulations using density functional theory of both tetragonal and monoclinic ZrO2 were performed, with intrinsic defects and Nb dopants. The overall defect populations with respect to oxygen partial pressure were calculated and presented in the form of Brouwer diagrams. Nb is found to favour 5 + in monoclinic ZrO2 at all partial pressures, but can exist in oxidation states ranging from 5 + to 3 + in the tetragonal phase. Nb5+ is charge balanced by Zr vacancies in both phases, suggesting that contrary to previous assumptions, Nb does not act as an n-type dopant in the oxide layer. Clusters containing oxygen vacancies were considered, Nb2+ was shown to exist in the tetragonal phase with a binding energy of 2.4 eV. This supports the proposed mechanism whereby low oxidation state Nb ions (2 + or 3+) charge balance the build-up of positive space-charge in the oxide layer, increasing oxygen vacancy and electron mobility, leading to near-parabolic corrosion kinetics and a reduced hydrogen pick-up. Previous experimental work has shown that tetragonal ZrO2 transforms to the monoclinic phase during transition, and that during transition a sharp drop in the instantaneous hydrogen pick-up fraction occurs. The oxidation of lower charge state Nb defects to Nb5+ during this phase change, and the consequent temporary n-doping of the oxide layer, is proposed as an explanation for the drop in hydrogen pick-up during transition

The effect of Nb on the corrosion and hydrogen pick-up of Zr alloys

Abstract Zr-Nb alloys are known to perform better in corrosion and hydrogen pick-up than other Zr alloys but the mechanism by which this happens is not well understood. Atomistic simulations using density functional theory of both tetragonal and monoclinic ZrO2 were performed, with intrinsic defects and Nb dopants. The overall defect populations with respect to oxygen partial pressure were calculated and presented in the form of Brouwer diagrams. Nb is found to favour 5 + in monoclinic ZrO2 at all partial pressures, but can exist in oxidation states ranging from 5 + to 3 + in the tetragonal phase. Nb5+ is charge balanced by Zr vacancies in both phases, suggesting that contrary to previous assumptions, Nb does not act as an n-type dopant in the oxide layer. Clusters containing oxygen vacancies were considered, Nb2+ was shown to exist in the tetragonal phase with a binding energy of 2.4 eV. This supports the proposed mechanism whereby low oxidation state Nb ions (2 + or 3+) charge balance the build-up of positive space-charge in the oxide layer, increasing oxygen vacancy and electron mobility, leading to near-parabolic corrosion kinetics and a reduced hydrogen pick-up. Previous experimental work has shown that tetragonal ZrO2 transforms to the monoclinic phase during transition, and that during transition a sharp drop in the instantaneous hydrogen pick-up fraction occurs. The oxidation of lower charge state Nb defects to Nb5+ during this phase change, and the consequent temporary n-doping of the oxide layer, is proposed as an explanation for the drop in hydrogen pick-up during transition

The effect of Sn-VO defect clustering on Zr alloy corrosion

Density functional theory simulations were used to study Sn defect clusters in the oxide layer of Zr-alloys. Clustering was shown to play a key role in the accommodation of Sn in ZrO2, with the {SnZr:VO}× bound defect cluster dominant at all oxygen partial pressures below 10-20 atm, above which Sn Zr × is preferred. {SnZr:VO}× is predicted to increase the tetragonal phase fraction in the oxide layer, due to the elevated oxygen vacancy concentration. As corrosion progresses, the transition to Sn Zr × , and resultant destabilisation of the tetragonal phase, is proposed as a possible explanation for the early first transition observed in Sn-containing Zr-Nb alloys

Hydrogen accommodation in Zr second phase particles: Implications for H pick-up and hydriding of Zircaloy-2 and Zircaloy-4

Ab-initio computer simulations have been used to predict the energies associated with the accommodation of H atoms at interstitial sites in {\alpha}, {\beta}-Zr and Zr.M intermetallics formed with common alloying additions (M = Cr, Fe, Ni). Intermetallics that relate to the Zr2(Ni,Fe) second phase particles (SPPs) found in Zircaloy-2 exhibit favourable solution enthalpies for H. The intermetallic phases that relate to the Zr(Cr,Fe)2 SPPs, found predominantly in Zircaloy-4, do not offer favourable sites for interstitial H. It is proposed that Zr(Cr,Fe)2 particles may act as bridges for the migration of H through the oxide layer, whilst the Zr2(Ni,Fe)-type particles will trap the migrating H until these are dissolved or fully oxidised