SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Purpose of this work Oxidation modeling Oxidation of full-scale components Local properties in oxidized components Graphite fracture strength Phase field fracture modeling Microstructurally informed fracture model IG-110 tensile results and comparison to experiment Work in progress and future work
Fractures that propagate off of weak slip planes are known as wing cracks and often play important roles in both tectonic deformation and fluid flow across reservoir seals. Previous numerical models have produced the basic kinematics of wing crack openings but generally have not been able to capture fracture geometries seen in nature. Here we present both a phase-field modeling approach and a physical experiment using gelatin for a wing crack formation. By treating the fracture surfaces as diffusive zones instead of as discontinuities, the phase-field model does not require consideration of unpredictable rock properties or stress inhomogeneities around crack tips. It is shown by benchmarking the models with physical experiments that the numerical assumptions in the phase-field approach do not affect the final model predictions of wing crack nucleation and growth. With this study, we demonstrate that it is feasible to implement the formation of wing cracks in large scale phase-field reservoir models.
A study was conducted to evaluate the capabilities of different numerical methods used to represent microstructure behavior at the mesoscale for irradiated material using an idealized benchmark problem. The purpose of the mesoscale benchmark problem was to provide a common basis to assess several mesoscale methods with the objective of identifying the strengths and areas of improvement in the predictive modeling of microstructure evolution. In this work, mesoscale models (phase-field, Potts, and kinetic Monte Carlo) developed by PNNL, INL, SNL, and ORNL were used to calculate the evolution kinetics of intra-granular fission gas bubbles in UO 2 fuel under post-irradiation thermal annealing conditions. The benchmark problem was constructed to include important microstructural evolution mechanisms on the kinetics of intra-granular fission gas bubble behavior such as the atomic diffusion of Xe atoms, U vacancies, and O vacancies, the effect of vacancy capture and emission from defects, and the elastic interaction of non-equilibrium gas bubbles. An idealized set of assumptions was imposed on the benchmark problem to simplify the mechanisms considered. The capability and numerical efficiency of different models are compared against selected experimental and simulation results. These comparisons find that the phase-field methods, by the nature of the free energy formulation, are able to represent a larger subset of the mechanisms influencing the intra-granular bubble growth and coarsening mechanisms in the idealized benchmark problem as compared to the Potts and kinetic Monte Carlo methods. It is recognized that the mesoscale benchmark problem as formulated does not specifically highlight the strengths of the discrete particle modeling used in the Potts and kinetic Monte Carlo methods. Future efforts are recommended to construct increasingly more complex mesoscale benchmark problems to further verify and validate the predictive capabilities of the mesoscale modeling methods used in this study.
Abstract Despite numerous experimental and theoretical investigations of the mechanical behavior of high-capacity Si and Ge Li-ion battery anodes, our basic understanding of swelling-driven fracture in these materials remains limited. Existing theoretical studies have provided insights into elasto-plastic deformations caused by large volume change phase transformations, but have not modeled fracture explicitly beyond Griffith’s criterion. Here, we use a multi-physics phase-field approach to model self-consistently anisotropic phase transformation, elasto-plastic deformation, and crack initiation and propagation during lithiation of Si nanopillars. Our computational results reveal that fracture occurs within a “vulnerable window” inside the two-dimensional parameter space of yield strength and fracture energy and highlight the importance of taking into account the surface localization of plastic deformation to accurately predict the magnitude of tensile stresses at the onset of fracture. They further demonstrate how the increased robustness of hollow nanopillars can be understood as a direct effect of anode geometry on the size of this vulnerable window. Those insights provide an improved theoretical basis for designing next-generation mechanically stable phase-transforming battery materials undergoing large volume changes.
Summary A new continuous‐discontinuous strategy for the computational modeling of crack propagation within the context of phase‐field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage band and to enhance the kinematics of the finite element approximation accordingly. The proposed approach relies on three key elements. First, we propose the use of a crack length functional to provide a trigger for initiating a continuous to discontinuous transition. Next, the crack path identification is addressed by introducing the concept of an auxiliary damage field that varies with an extension of the sharp crack surface. The sharp crack surface is extended through an optimization algorithm, in which the difference between the auxiliary field and the actual damage field stemming from the phase‐field framework is minimized. Finally, a strong discontinuity is inserted in the wake of the diffuse crack tip with the extended finite element method, completing the continuous to discontinuous transition. Several benchmark problems in two‐dimensional quasi‐static fracture mechanics are presented to demonstrate the accuracy and robustness of the method.
Results are summarized of various analyses of the exhaust plumes of the space shuttle. Specific topics discussed included: the development of the two-phase plume flow field model, including finite rate chemistry and free molecular effects; analyses of exhaust plume simulation studies; verification of the analytical two-phase plume flow field model; and complete documentation of the two-phase plume computer code.
The purpose of this project was to utilize computational tools to understand the relationships between processing, microstructure, and properties for additively manufactured (AM) aluminum alloys for automotive applications, and to provide an engineering solution for helping to optimize process conditions. The project leverages ORNL developments in computational modeling, including AM process modeling, phase-field based microstructure evolution predictions, and data analytics techniques for mapping process conditions to material outcomes. The project utilized an Al-Cu-Mn-Zr alloy as a model material for studying formation of defects and microstructural features in response to variations in process conditions. Based on both pre-existing experimental data and simulation results, statistical process maps were constructed to identify regions of process space with minimal defect formation and advantageous microstructures and properties. The software tools used for this purpose were successful disseminated to GM, who were able to successful compile the relevant HPC codes within their own computing ecosystem and perform initial calculations to reproduce ORNL results.
Scientific Successes • The first phonon density of states (PDOS) measurements for UO2 to include anharmonicity were obtained using time-of-flight inelastic neutron scattering at the Spallation Neutron Source (SNS), and an innovative, experimental-based anharmonic smoothing technique has enabled quantitative benchmarking of ab initio PDOS simulations. • Direct comparison between anharmonicity-smoothed ab initio PDOS simulations for UO2 and experimental measurements has demonstrated the need for improved understanding of UO2 at the level of phonon dispersion, and, further, that advanced lattice dynamics simulations including finite temperatures approaches will be required for handling this strongly correlated nuclear fuel. • PDOS measurements performed on polycrystalline samples have identified the phonon branches and energy ranges most highly impacted by fission-product and hyper-stoichiometry lattice defects in UO2. These measurements have revealed the broad-spectrum impact of oxygen hyper-stoichiometry on thermal transport. The reduction in thermal conductivity caused by hyper-stoichiometry is many times stronger than that caused by substitutional fission-product impurities. • Laser-based thermo-reflectance measurements on UO2 samples irradiated with light (i.e. He) ions to introduce point defects have been coupled with MD simulations and lattice parameter measurements to determine the role of uranium and oxygen point defects in reducing thermal conductivity. • A rigorous perturbation theory treatment of phonon lifetimes in UO2 based on a 3D discretization of the Brillouin zone coupled with experimentally measured phonon dispersion has been implemented that produces improved predictions of the temperature dependent thermal conductivity. • Atom probe investigations of the influence of grain boundary structure on the segregation behavior of Kr in UO2 have shown that smaller amounts of Kr are present at low angle grain boundaries than at large angle grain boundaries due to the more dense dislocation arrays associated with large angle boundaries; this observation has potentially important ramifications for thermal transport in the high burn-up rim region of light water reactor fuel. • A variable charge interatomic potential has been developed that not only provides an accurate representation of the fluorite UO2 phase, it is further capable of describing continuous stoichiometry changes from UO2 to hyper-stoichiometric UO2+x, to U4O9 and U3O7, and possibly to orthorhombic U3O8. This is the first potential that features many-body effects in all possible interactions (U-U, U-O and O-O) combined with the variable charge. • A theoretical proof has been formulated showing that it is necessary to use the so-called model C phase field approach, consisting of Cahn-Hilliard and Allen-Cahn equations, to describe void evolution in irradiated materials. This work resolved a longstanding literature controversy regarding how to model voids at the mesoscale. • A novel cluster dynamics model has been developed for the nucleation of voids and loops in UO2 under irradiation. This model is important in understanding the defect state of UO2 after irradiation and, more importantly, reveals off-stoichiometric states of irradiated UO2 that are critical for understanding the impact of irradiation on thermal transport. Personnel Successes
We study microstructure selection during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Lambda and tip radius rho. While rho shows a good agreement between experimental measurements and dendrite growth theory, with rho similar to V-1/2, Lambda is observed to increase with V (partial derivative Lambda/partial derivative V > 0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that partial derivative Lambda/partial derivative V <0. We show through simulations that this trend inversion for Lambda(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. We explain the observed inversion of partial derivative Lambda/partial derivative V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.
Cobalt-based superalloys with two phase $\gamma$/$\gamma '$ microstructures offer great promise as candidates for next-generation high-temperature alloys for applications, such as turbine blades. It is essential to understand the thermodynamic and kinetic factors that influence the microstructural evolution of these alloys in order to optimize the alloy compositions and processing steps with a goal to improve their coarsening, creep and rafting behavior. We are using a continuum phase field approach to study the diffusion process and to predict the equilibrium shapes of Co-Al-W $\gamma '$ precipitates. In order to obtain quantitatively predictive capabilities, we extract chemical free energies for the $\gamma$/$\gamma '$ phases based on CALculation of PHAse Diagrams (CALPHAD) thermodynamic data and diffusion mobilities for Co alloys based on CALPHAD kinetic data. We also use experimental or first-principles data for other quantities, such as misfit strain and interface information, for the parameterization of our model. A particular focus of our study is to understand how different energy balances, misfit strain and kinetics affect the coarsening and rafting behavior of $\gamma '$ precipitates, and the sensitivity of the final precipitate shape to materials parameters. Here, we find that the equilibrium shape of the precipitate results from a delicate competition between chemical, interfacial, and elastic energies, and it is very sensitive to changes in model parameters. Here, we examine how modeling input parameters affect the equilibrium shape of precipitates and relate these parameters to experimentally available values.
In this work, a phase field grain growth model coupled with a spectral stress calculation method is used to investigate the effect of applied elastic deformation on grain growth in 2D copper polycrystals with isotropic grain boundary properties. The applied deformation accelerates the grain growth compared to a relaxed polycrystal, though the effect of the deformation decreases rapidly with time. The softest grain orientations with respect to the applied deformation grow at the expense of other orientations, though they have higher elastic energy density. Due to a rapid decrease in the elastic energy stored in the system, the GB energy eventually dominates the growth leading to a linear change in the average grain area with time. Increasing the magnitude of the applied deformation accelerates the growth, while increasing the temperature accelerates the growth but decreases the effect of the applied deformation.
TRistructural ISOtropic (TRISO) particles use silicon carbide (SiC) as the primary structural member and barrier against metallic fission product (FP) release. palladiums (PDs), produced by fission in the fuel kernel, can diffuse to and chemically interact with the SiC layer, degrading its structural integrity and ability to contain radioactive FPs. Existing temperature-dependent correlations for predicting Pd penetration rely on experimental data with significant scatter due to varying conditions, potentially complicating ongoing fuel qualification and licensing efforts for advanced reactors that would subject TRISO fuels to operating conditions outside of those examined in the experiments. A mechanistic model of Pd production, transport, and reaction is developed in this work to better understand and predict PD attack of SiC in TRISO particles. molecular dynamicss (MDs) simulations are utilized to calculate the Pd diffusivity in SiC grain bulk and grain boundaries. A mesoscale phase-field diffusion model, informed by the MD diffusivities, is used to develop a reduced order model (ROM) for the effect of SiC microstructure on the Pd penetration rate. The engineering scale BISON model calculates Pd production and transport, utilizing the ROM to predict penetration rates consistent with experimental data. This novel mechanistic ROM captures the effect of temperature, microstructure, and irradiation history on Pd penetration. In conclusion, these new capabilities are expected to support ongoing qualification and licensing efforts associated with near-term TRISO-fueled reactor applications.
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.
Two-phase nanolaminates are well-renowned for achieving extraordinarily high strengths but at the sacrifice of reduced toughness and strain to failure. Recently ”thick” interfaces, or so called 3D interfaces, in Cu/Nb nanolaminates were experimentally shown to improve both of these mechanical properties. Here, in this work, we study the effect of 3D interfaces in the hexagonal close packed (HCP)/body centered cubic (BCC) Ti/Nb nanolaminate system. Nanoindentation hardness testing suggests increased strength with the introduction of a 3D Ti–Nb interface and a positive size effect with increases in 3D interface thickness from 5 nm to 20 nm. To understand this effect from a single dislocation perspective, we present a phase-field dislocation dynamics (PFDD) model for multi-phase HCP/BCC systems. We employ the model to simulate stress-driven transfer of single dislocations across 3D Ti/Nb interfaces of various thicknesses. Our results show that the critical stress for slip transfer increases with the thickness of the interface. This positive size effect is stronger for transfer from basal or prismatic dislocations in the Ti layer to 110$\langle$111$\rangle$ dislocations in the Nb layer than the reverse. For this Ti/Nb system, a critical thickness of 2 nm is identified at which the asymmetry in slip transfer is minimized. This work showcases 3D interfaces as a beneficial microstructure modification to strengthen as well as reduce anisotropy in nanocrystalline materials containing HCP phases.
Here, coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to t 1/4 for surface diffusion and t 1/3 for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.
Uranium Dioxide (UO 2 ) fuel powers almost all commercial Nuclear Power Plants (NPPs) worldwide, generating carbon-free energy and contributing to the fight against climate change. UO 2 fuel incurs damage and fractures due to large thermal gradients that develop across the fuel pellet during normal and transient operating conditions. A comprehensive understanding of the underlying mechanisms by which these processes take place is still lacking. A combined experimental and computational approach is utilized here to quantify the behavior of UO 2 fuel fracture induced by thermal shock. Here, this work introduces both (1) an experimental study to understand the fuel fracturing behavior of sintered UO 2 pellets when exposed to thermal shock, and (2) a Multiphysics phase-field fracture model capable of simulating this process. Parametric studies were conducted to evaluate the effects of uncertainties in fracture properties on the fracture behavior of UO 2 due to thermal shocking. A set of energy release rate (or equivalently fracture toughness) and contract area (the part of the fuel pellet in direct contact with the cold bath) were able to capture the overall fracture trends of the corresponding experimental data. Our combined approach presents a new method for accounting for the effects of microstructure and sample size on the energy release rate/fracture toughness. The experimental data were collected from multiple experiments that exposed UO 2 pellets to high-temperature conditions (589–676 °C) followed by a quench in sub-zero water. This work demonstrates that joint experimental and computational efforts are able to advance the understanding of thermal fracture in the primary fuel source for existing and future NPPs.
Grain boundaries (GBs) are driven to migrate up a temperature gradient. In this work, we use a phase field (PF) model to investigate the impact of temperature gradients on normal 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 change in the GB mobility due to the temperature gradient results in larger grains in the hot portion of the polycrystal.
This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.