Michael Tonks

Void nucleation and growth in irradiated polycrystalline metals: a phase-field model

We present a phase-field model for void formation in polycrystalline metals with vacancy concentrations exceeding the thermal equilibrium values. By incorporating a coupled set of Cahn–Hilliard and Allen–Cahn equations, the model captures several relevant processes including vacancy annihilation and nucleation at grain boundaries (GBs), vacancy diffusion toward sinks (including GBs and void surfaces) as well as void nucleation and growth due to vacancy supersaturations occurring in the grain interiors. Illustrative results are presented that characterize the rate of annihilation of the vacancy population at the GB sinks, as well as the formation of void denuded zones adjacent to GBs in bicrystalline and polycrystalline samples, the width of which is found to depend on both the vacancy diffusivity and the vacancy production rate.

A quantitative comparison between C0 and C1 elements for solving the Cahn-Hilliard equation

The Cahn-Hilliard (CH) equation is a time-dependent fourth-order partial differential equation (PDE). When solving the CH equation via the finite element method (FEM), the domain is discretized by C^1-continuous basis functions or the equation is split into a pair of second-order PDEs, and discretized via C^0-continuous basis functions. In the current work, a quantitative comparison between C^1 Hermite and C^0 Lagrange elements is carried out using a continuous Galerkin FEM formulation. The different discretizations are evaluated using the method of manufactured solutions solved with Newtons method and Jacobian-Free Newton Krylov. It is found that the use of linear Lagrange elements provides the fastest computation time for a given number of elements, while the use of cubic Hermite elements provides the lowest error. The results offer a set of benchmarks to consider when choosing basis functions to solve the CH equation. In addition, an example of microstructure evolution demonstrates the different types of elements for a traditional phase-field model.

Development of a grain boundary pinning model that considers particle size distribution using the phase field method

In this work, we expand a grain boundary (GB) pinning model that considers a range of different spatial distributions of particles to also account for a distribution of particle sizes. We begin by developing a phase field model that describes GB and pore interactions and verify it by comparing to molecular dynamics simulations. We then develop an analytical pinning model that considers the impact of the particle size distribution, in terms of the mean and standard deviation of the particle radius. The analytical model is verified by comparing to simulation results of our phase field model and those of a simple Monte Carlo model. A significant finding from the model is that the mean value of the resistive pressure decreases with increasing standard deviation of the particle radius.

Demonstrating the Temperature Gradient Impact on Grain Growth in UO2 Using the Phase Field Method

Grain boundaries (GBs) are driven to migrate up a temperature gradient. In this work, we use a phase field model to investigate the impact of temperature gradients on isotropic grain growth. GB motion in 2D UO2 polycrystals is predicted under increasing temperature gradients. We find that the temperature gradient does not significantly impact the average grain growth behavior because the curvature driving force is dominant. However, it does cause significant local migration of the individual grains. In addition, the temperature dependence of the GB mobility results in larger grains in the hot portion of the polycrystal.

Fully-coupled engineering and mesoscale simulations of thermal conductivity in UO2 fuel using an implicit multiscale approach

Though the thermal conductivity of solid UO2 is well characterized, its value is sensitive to microstructure changes. In this study, we propose a two-way coupling of a mesoscale phase field irradiation model to an engineering scale, finite element calculation to capture the microstructure dependence of the conductivity. To achieve this, the engineering scale thermomechanics system is solved in a parallel, fully-coupled, fully-implicit manner using the preconditioned Jacobian-free Newton Krylov (JFNK) method. Within the JFNK function evaluation phase of the calculation, the microstructure-influenced thermal conductivity is calculated by the mesoscale model and passed back to the engineering scale calculation. Initial results illustrate quadratic nonlinear convergence and good parallel scalability.

Molecular dynamics simulations of He bubble nucleation at grain boundaries

The nucleation behavior of He bubbles in single-crystal (sc) and nano-grain body-centered-cubic (bcc) Mo is simulated using molecular dynamics (MD) simulations, focusing on the effects of the grain boundary (GB) structure. In sc Mo, the nucleation behavior of He bubbles depends on irradiation conditions. He bubbles nucleate by either clustering of He atoms with pre-existing vacancies or self-interstitial-atom (SIA) punching without initial vacancies. In nano-grain Mo, strong precipitation of He at the GBs is observed, and the density, size and spatial distribution of He bubbles vary with the GB structure. The corresponding He bubble density is higher in nano-grain Mo than that in sc Mo and the average bubble size is smaller. In the GB plane, He bubbles distribute along the dislocation cores for GBs consisting of GB dislocations and randomly for those without distinguishable dislocation structures. The simulation results in nano-grain Mo are in agreement with previous experiments in metal nano-layers, and they are further explained by the effect of excess volume associated with the GBs.

Mesoscale modeling of intergranular bubble percolation in nuclear fuels

Phase-field simulations are used to examine the variability of intergranular fission gas bubble growth and percolation on uranium dioxide grain boundaries on a mesoscopic length scale. Three key parameters are systematically varied in this study: the contact angle (or dihedral angle) defining the bubble shape, the initial bubble density on the grain boundary plane, and the ratio of the gas diffusivity on the grain boundary versus the grain interiors. The simulation results agree well with previous experimental data obtained for bubble densities and average bubble areas during coalescence events. Interestingly, the rate of percolation is found to be highly variable, with a large dependency on the contact angle and the initial bubble density and little-to-no dependency on the grain boundary gas diffusivity.

Thermal Properties Measurement Report

The Thermal Properties Measurement Report summarizes the research, development, installation, and initial use of significant experimental thermal property characterization capabilities at the INL in FY 2015. These new capabilities were used to characterize a U3Si2 (candidate Accident Tolerant) fuel sample fabricated at the INL. The ability to perform measurements at various length scales is important and provides additional data that is not currently in the literature. However, the real value of the data will be in accomplishing a phenomenological understanding of the thermal conductivity in fuels and the ties to predictive modeling. Thus, the MARMOT advanced modeling and simulation capability was utilized to illustrate how the microstructural data can be modeled and compared with bulk characterization data. A scientific method was established for thermal property measurement capability on irradiated nuclear fuel samples, which will be installed in the Irradiated Material Characterization Laboratory (IMCL).

Multi-scale modeling of inter-granular fracture in UO2

A hierarchical multi-scale approach is pursued in this work to investigate the influence of porosity, pore and grain size on the intergranular brittle fracture in UO2. In this approach, molecular dynamics simulations are performed to obtain the fracture properties for different grain boundary types. A phase-field model is then utilized to perform intergranular fracture simulations of representative microstructures with different porosities, pore and grain sizes. In these simulations the grain boundary fracture properties obtained from molecular dynamics simulations are used. The responses from the phase-field fracture simulations are then fitted with a stress-based brittle fracture model usable at the engineering scale. This approach encapsulates three different length and time scales, and allows the development of microstructurally informed engineering scale model from properties evaluated at the atomistic scale.

Derivation of effective fission gas diffusivities in UO2 from lower length scale simulations and implementation of fission gas diffusion models in BISON

This report summarizes the development of new fission gas diffusion models from lower length scale simulations and assessment of these models in terms of annealing experiments and fission gas release simulations using the BISON fuel performance code. Based on the mechanisms established from density functional theory (DFT) and empirical potential calculations, continuum models for diffusion of xenon (Xe) in UO2 were derived for both intrinsic conditions and under irradiation. The importance of the large XeU3O cluster (a Xe atom in a uranium + oxygen vacancy trap site with two bound uranium vacancies) is emphasized, which is a consequence of its high mobility and stability. These models were implemented in the MARMOT phase field code, which is used to calculate effective Xe diffusivities for various irradiation conditions. The effective diffusivities were used in BISON to calculate fission gas release for a number of test cases. The results are assessed against experimental data and future directions for research are outlined based on the conclusions.