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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
To improve the economics of commercial nuclear power production, utilities are seeking to increase the allowable burnup limit of UO$_2$ fuel. One of the main factors that contributes to the current burnup limit of 62 GWd/MTU in commercial light water reactors (LWRs) is the risk of fine fragmentation or pulverization during a loss of coolant accident (LOCA). Pulverization primarily occurs at high burnups, especially when the high burnup structure (HBS) has formed. To allow the industry to pursue increased burnup and develop mitigation strategies, it is essential to have improved capability to predict the onset of pulverization. However, the mechanism of pulverization is not well understood, and the existing predictive capabilities implemented in the BISON fuel performance code are empirical in nature. In this report, mesoscale simulations are used to improve understanding of the formation mechanism of the HBS and how it responds during a LOCA transient, and inform development of a BISON pulverization criterion. A phase-field model was used to simulate the evolution of bubble pressure as a result of HBS formation. The simulations showed that gas atoms diffuse from grain interiors to the new grain boundaries created during HBS formation, and diffuse rapidly along these grain boundaries to reach existing bubbles. This causes an increase in bubble pressure in existing bubbles, leading to bubble growth during steady-state operation. To simulate the response of HBS bubbles to a LOCA transient, a newly developed phase-field model was used; in agreement with preliminary results from FY20, bubble size did not change significantly during the duration of the transient. A phase-field fracture model was used to study fragmentation patterns in the HBS, including using input from the phase-field model as initial conditions. Phase-field fracture simulations were used to determine a pulverization criterion for BISON. A function for the critical pressure for pulverization to occur was fit to data from the phase-field fracture simulations, and this function was implemented as a material property in BISON. For comparison, an analytical criterion for pulverization was developed and implemented within the same material property.
This study presents a novel multiphysics phase-field fracture model to analyze high-burnup uranium dioxide (UO2) fuel behavior under transient reactor conditions. Fracture is treated as a stochastic phase transition, which inherently accounts for the random microstructural effects that lead to variations in the value of fracture strength. Moreover, the model takes into consideration the effects of temperature and burnup on thermal conductivity. Therefore, the model is able to predict crack initiation, propagation, and complex morphologies in response to thermal gradients and stress distributions. Several simulations were conducted to investigate the effects of operational and transient conditions on fracture behavior and the resulting cracking patterns. High-burnup fuels exhibit reduced thermal conductivity, elevating temperature gradients and resulting in extensive radial and circumferential cracks. Transient heating rates and temperatures significantly affect fracture patterns, with higher heating rates generating steeper gradients and more irregular crack trajectories. This approach provides critical insights into fuel integrity during accident scenarios and supports the safety evaluation of extended burnup limits.
Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the effects of pressure loads on the crack faces have been developed. Further, this work investigates the performance of these models and compares them to a relatively new formulation for incorporating crack-face pressure loads. It is shown how the new formulation can be obtained either by modifying the trial space in the traditional variational principle or by postulating a new functional that is dependent on the rates of the primary variables. The key differences between the new formulation and existing models for pressurized cracks in a phase-field setting are highlighted. Model-based simulations developed with discretized versions of the new formulation and existing models are then used to illustrate the advantages and differences. In order to analyze the results, a domain form of the J-integral is developed for diffuse cracks subjected to pressure loads. Results are presented for a one-dimensional cohesive crack, steady crack growth, and crack nucleation from a pressurized enclosure.
ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.
This report summarizes the lower length scale modeling work performed in the fiscal year 2023 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to capture the microstrutural evolution and associated pulverization criteria in the high burnup regions. This year, the resolution mechanisms within the cluster dynamics code has been updated and it influence on the bubble growth in HBS regions at the mesoscale is studied. To improve the accuracy of phase-field models of fission gas bubble growth, a new Helmholtz free energy for high-density Xe gas is derived from a virial equation of state. Two previously used strategies for representing net vacancy production in phase-field models of fission gas bubble growth are compared with each other and with analytical models of bubble growth. The vacancy source only model is found to be more convenient to parameterize realistically compared with the vacancy source+sink model. Furthermore, the phase-field-fracture simulation have been performed using MD- informed failure stress values and realistic HBS structure obtained from the phase-field simulations. We also present the uncertainty bands on prediction of the critical stress to account for the effect of the lower length scale variabilities on the failure criteria at the mesoscale. It is observed that pulverization may occur in partially restructured regions with restructuring fraction as low as 17%. In light of this, an update to the BISON’s pulverization criteria is recommended.
An overview of NEAMS program activities to model fuel fragmentation and microstructual evolution to a group of industry attendees at a meeting hosted by EPRI. Topics include atomistic methods to determine grain boundary strength, phase-field fracture modeling to determine critical pressure at grain boundaries, and coupled phase-field-cluster dynamics to model microstructural evolution.
This work proposes a novel approach for coupling non-isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid-filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface-capturing phase-field fracture method and interface-tracking thermo-fluid-structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase-field approach to represent fractures and reconstruct the geometry to frame a thermo-fluid-structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase-field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid-filled fracture with the phase-field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase-field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures.
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.
A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative where plasticity and fracture are strongly coupled. Several representative numerical examples motivate specific modeling choices. In particular, a linear crack geometric function provides an “unperturbed” ductile response prior to crack initiation, and Lorentz-type degradation functions ensure that the critical fracture strength remains independent of the phase-field regularization length. In addition, the response of the model is demonstrated to converge with a vanishing phase-field regularization length. Additionally, the model is then applied to calibrate and simulate a three-point bending experiment of an aluminum alloy specimen with a complex geometry. The effect of the proposed coalescence dissipation coupling on simulations of the experiment is first investigated in a two-dimensional plane strain setting. The calibrated model is then applied to a three-dimensional calculation, where the calculated load-deflection curves and the crack trajectory show excellent agreement with experimental observations. Finally, the model is applied to simulate crack nucleation and growth in a specimen from a recent Sandia Fracture Challenge.
To study the mechanical behavior of mock high explosives, an experimental and simulation program was developed to calibrate, with quantified uncertainty, a material model of the bonded granular material Idoxuridine and nitroplasticized Estane-5703. This paper reports on the efficacy of such a framework as a generalizable methodology for calibrating material models against experimental data with uncertainty quantification. Additionally, this paper studies the effect of two manufacturing temperatures and three initial granular configurations on the unconfined compressive behavior of the resulting bonded granular materials. In each of these cases, the same calibration framework was used; in that, hundreds of high-fidelity direct numerical simulations using a new, graphics processing unit-enabled, high-performance finite element method software, Ratel, were run to calibrate a finite-strain phase-field fracture model against experimental data. It was found that manufacturing temperature influenced the elastic response of the mock high explosives, with higher temperatures yielding a stiffer response. By contrast, it was found that the initial configuration of the grains had a negligible impact on the overall behavior of the mock high explosives though it remains possible that local damage accumulation within the specimens could be altered by the initial configurations. Overall, the calibration framework was successful at creating well-calibrated models, showing its usefulness as an engineering and scientific tool.
Phase field models for ductile fracture have gained significant attention in the last two decades due to their ability in implicitly tracking the nucleation and propagation of cracks. However, most crack phase field formulations for elastoplastic solids focus only on the effects of plastic deformation, and do not consider the different multi-axial stress states that may arise in practical designs. In this work, a thermodynamically consistent phase field approach coupled with finite strain plasticity, considering multi-axial stress states is presented. In order to account for the coupling between plasticity and stress states, the Stress-Weighted Ductile Fracture Model (SWDFM) is utilized. The SWDFM represents a criterion for predicting ductile crack initiation under both monotonic and cyclic loadings based on histories of an internal plastic variable, stress triaxiality, and the Lode angle parameter. The excellent performance of the SWDFM for predicting ductile crack initiation motivates for its incorporation into a phase field approach for predicting both crack initiation and propagation through degradation of the fracture toughness. Moreover, based on the second law of thermodynamics, exact requirements are imposed on the rate at which the fracture toughness can evolve. Here, a novel function for degrading the plastic yield surface during the evolution of damage is introduced. This function, in line with experimental observations, leads to an accumulation of plastic deformation in damaged regions of a solid, and avoids numerical instabilities arising from concentrations of large plastic deformations in severely damaged regions. For validating the proposed model, results of computational simulations are compared to data from selected tests considering different multi-axial stress states. Comparisons of the numerical results with data from laboratory experiments demonstrate the capabilities of the proposed framework.
To improve the economics of light water reactors for commercial nuclear energy generation, utility operators are seeking to obtain regulatory approval to run UO2 fuel to higher levels of burnup. One potential impediment to obtaining this approval is the phenomenon of fuel fragmentation, relocation, and dispersal (FFRD). FFRD can result when fuel experiences a rapid temperature transient, such as that occurring during a Loss Of Coolant Accident (LOCA). FFRD has historically been most associated with the rim region in UO2 fuel pellets, where the phenomenon of fragmentation is also referred to as pulverization due to the small size of the fragments. More recent evidence suggests that the so-called “dark zone” (due to its appearance in micrographs) that can be observed in the mid-radial regions of high burnup fuel is also susceptible to FFRD. Although empirical fuel performance models have been developed that can adequately predict pulverization in the rim region under typical LWR conditions, a scientific understanding of what underlies fuel restructuring and subsequent FFRD is lacking even in the rim region, and no models are currently available for the behavior the dark zone. To address these challenges, the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has employed a multi-scale modeling approach to improve scientific understanding and develop new fuel performance models. In this talk, I will focus on meso-scale efforts, which form a crucial link between atomic-scale and engineering-scale models. Phase-field modeling combined with cluster dynamics is used to predict the restructuring process in the rim region. Phase-field fracture modeling, informed by atomistic simulations, is used to predict the onset of pulverization in the rim region. Combining these techniques together allows the extent of rim pulverization to be predicted. The formation and evolution of the dark zone has also been simulated with the phase-field method, using an improved approach to vacancy source term parameterization. The work shows the important impact of microstructure on fuel performance.
Here, this work investigated brittle fracture of polycrystalline materials due to thermal stresses arising from anisotropic thermal expansion. We used phase-field fracture simulations with the properties of alpha-uranium (α-U) and assumed a linear elastic mechanical response. Three-dimensional simulations were used to predict fracture for various conditions and crystallographic textures. We found that fracture was more pronounced during cooling than during heating because the anisotropy increased with temperature. We also found that the total crack surface area increased with increasing average misorientation, while the net shape change of the material decreased with increasing misorientation. Two-dimensional simulations in which one crystallographic coefficient of thermal expansion (CTE) was set to zero indicated that the expansion behavior in the crystallographic direction with the smallest CTE was the primary cause of fracture.
This report summarizes lower length scale computational research conducted to improve the pulverization criterion for high-burnup UO 2 fuel in the BISON fuel performance code. This research was sponsored by the NEAMS program during FY22. Efforts to improve the model primarily focus on calculating the current pressure of bubbles in the high-burnup structure (HBS) region, as well as the critical bubble pressure at which pulverization occurs in the HBS. The phase-field model for predicting initial bubble pressure in the HBS was improved by implementing a more realistic model for defect production, and by coupling the phase-field model for inter-granular bubble evolution with the spatially-resolved cluster dynamics code Xolotl to simulate intra-granular fission gas evolution. An evolution equation for current bubble pressure was added to BISON, an improvement over the previous model that assumed that bubble pressure was static following HBS formation. To improve calculations of critical bubble pressure for pulverization, 3-D phase-field fracture simulations were performed, and a function for critical bubble pressure was fit—based on the simulation results—to replace the previous function, which had been determined using 2-D simulations. The impacts of these modifications to the existing pulverization assessment cases will be reported in the forthcoming engineering scale milestone on high-burnup UO 2 pulverization. A poromechanics-based approach was used to include the effect of bubble over pressurization on the stress state of the pellet at the engineering scale, and the initial strategy for integration of the pulverization criterion with pellet-scale mechanical degradation using a smeared cracking model was developed. This report also describes the initial research that was conducted to inform a forthcoming transient fission gas release (tFGR) model in BISON. Focusing on the fission gas release caused by pulverization of the outer pellet rim, a model for the amount of fission gas release was developed as a function of fuel porosity, bubble size, and fragment size. Implementation of this model in BISON and its impact of engineering-scale predictions will also be described in the aforementioned engineering-scale milestone on high-burnup UO 2 pulverization.
The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry poses a significant challenge in calculating the crack opening (aperture) of phase-field fracture, which governs the fracture permeability and hence the overall hydromechanical behavior. Although several approaches have been devised to compute the crack opening of phase-field fracture, they require a sophisticated algorithm for post-processing the phase-field values or an additional parameter sensitive to the element size and alignment. Here, we develop a novel method for calculating the crack opening of fluid-filled phase-field fracture, which enables one to obtain the crack opening without additional algorithms or parameters. Here we transform the displacement-jump-based kinematics of a fracture into a continuous strain-based version, insert it into a force balance equation on the fracture, and apply the phase-field approximation. Through this procedure, we obtain a simple equation for the crack opening which can be calculated with quantities at individual material points. We verify the proposed method with analytical and numerical solutions obtained based on discrete representations of fractures, demonstrating its capability to calculate the crack opening regardless of the element size or alignment.
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This report summarizes the mesoscale modeling conducted in fiscal year 2025 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, focusing on the microstructural evolution and restructuring in high burnup UO 2 nuclear fuel and its impact on fuel fragmentation. We developed a pioneering phase-field model to simulate restructuring behavior across different regions of high burnup fuel, including the dark zone and rim region. A grand-potential-based phase-field model is employed to concurrently evaluate subgrain formation and the growth of fission gas bubbles within the fuel. An energy-based subgrain formation criterion was introduced to simulate the restructuring process. The effects of temperature and burnup rate were studied to capture how each of these parameters influences the characteristics of the restructured fuel. Subgrain formation was observed to initiate around existing fission gas bubbles and proceed toward triple junctions, grain boundaries, and grain interiors. Under a given subgrain formation rate, the rate of restructuring increases with rising fuel temperature. The restructuring occurs faster with higher burnup rate. A restructuring bias was observed within the microstructure, due to the variation in defect accumulation when comparing different grains. Microstructures corresponding to the dark zone and rim region can be obtained by parameterizing the model with the appropriate defect production rate, as determined based on the burnup rate and temperature. The predicted microstructures are consistent with experimental observations of the restructured regions. Based on the mesoscale simulations, a mechanistic model for restructuring and grain size evolution was implemented in BISON. Thus, this work provides a first-of-its-kind restructuring model for different regions of high-burnup fuel to BISON. It was shown that the model predicts appropriate grain size evolution along fuel radius as those observed in experiments. This model enables BISON to predict the effect of restructuring on the fission gas release. Finally, the phase-field fracture simulation with dark zone specific microstructures were presented to provide the fragmentation criteria for the dark zone. This work introduces a first-of-its-kind restructuring model for high burnup fuel, significantly enhancing BISON's predictive capabilities.