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DOE OSTI2025

A chain stretch-based gradient-enhanced model for damage and fracture in elastomers

Similar to quasi-brittle materials, it has been recently shown that elastomers can exhibit a macroscopically diffuse damage zone that accompanies the fracture process. In this study, we introduce a stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials (e.g., concrete), they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening (de Borst and Verhoosel, 2016). This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. Here, we discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

Elastomers↗

DOE OSTI2025

Meso-scale modeling of UO2 nuclear fuel to high burnup

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.

fracture↗

DOE OSTI2025

Additive Manufactured Composite Phase-Change Material for Thermal Energy Storage Applications

Phase-change materials play a critical role in industrial energy storage applications to drive efficiency improvements, thermal energy management, and carbon emissions reductions. Recently, it has been shown that rapid solidification of alloys with metastable immiscibility in the liquid phase has the potential to form unique microstructures in which a low-melting phase is uniformly distributed in a high-melting matrix. This feature can be exploited using additive manufacturing to produce components with complex geometries containing such unique phase-change microstructures. Phase-field simulations utilizing high-performance computing were used to provide a detailed description of the evolution of the active phase during service in terms of their morphology and composition in different polycrystalline matrix grain morphologies that are typically produced during additive manufacturing. Phase field simulations were performed using, MEUMAPPS-SL (Microstructure Evolution Using Massively Parallel Phase-field Simulations – Solid Liquid) code that was developed in-house by the Oak Ridge National Laboratory. The simulations utilized the capabilities of the Kestrel supercomputer at the National Renewable Energy Laboratory. The simulation results were compared with experimental results generated at Siemens Energy, Inc. The results indicate that the kinetics of liquid spreading along grain boundaries is largely determined by the mobility of the triple line along the intersection of the grain boundary liquid and the grain boundary plane.

25 ENERGY STORAGE↗

DOE OSTI2025

SULI Intern Final Report: Computationally Investigating Hydrogen Thermo-Diffusion in Yttrium Hydride Using Multiscale Methods

The renaissance of nuclear energy has arrived, heralding an age of abundant inexpensive clean energy, and renewed space exploration. In nuclear-powered spacecraft and microreactors, safety and size are of utmost importance. Yttrium Hydride (YHx) is being researched for its utility as a neutron moderator in nuclear reactors; the hydrogen in YHx slows down neutrons, enabling a continuous nuclear reaction in the reactor. This has the benefit of allowing reactors to be more safe, compact, and efficient. The goal of this effort is to computationally predict the coefficient of temperature-dependent hydrogen diffusion within YHx, the Soret coefficient. This parameter is essential for determining the safe operating modes of YHx moderators. Zirconium Hydride (ZrHx) is used in the Training, Research, Isotopes, General Atomics (TRIGA) reactor, is the reference material for these calculations. In this work, nanoscale atomic modeling in the Vienna Ab initio Simulation Package (VASP) is combined with the mesoscale finite element phase-field module in the Multiphysics Object-Oriented Simulation Environment (MOOSE); this culminates in a new multiscale computational method to simulate Soret diffusion of hydrogen in YHx. This data is useful for predicting experimental outcomes. This workflow involves convergence testing followed by static, Nudged Elastic Band (NEB), Quasi-Harmonic Approximation (QHA), and Molecular Dynamics (MD) calculations - linked with phase field simulation. NEB simulates hydrogen migration, while QHA and MD predict temperature-dependent properties. The static calculations align with literature, and preliminary NEB and QHA calculations yield accurate results. Once the atomic calculations are complete, we will incorporate Electron Backscatter Diffraction (EBSD) images and VASP-generated parameters into the phase field module to simulate intra- and intergranular transport of hydrogen in ZrHx and YHx. Future research will extend our approach to fuel-moderator materials systems such as Uranium-Yttrium Hydride (U-YHx). This work contributes to the development of advanced nuclear energy solutions for space travel.

36 - MATERIALS SCIENCE↗

DOE OSTI2025

Mesoscale Modeling for Restructuring and Fragmentation in High Burnup UO 2

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.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Focused Ion Beam Tomography of Alloy 617 Corroded in Molten Chloride Salt

Materials qualification of reactor structural materials is a critical step in rapid implementation of advanced nuclear reactor technologies, particularly to assess the corrosion performance in these designs. Accelerated qualification of reactor structural materials requires incorporating powerful computational toolsets, such as phase field modelling in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, to predict the evolution of structural materials due to corrosion. Accordingly, computational toolsets will require experimental data generated at appropriate length scales to validate accuracy. Focused ion beam (FIB) provides a high degree of control over manipulation of materials for analytical purposes, including capturing data on the evolution in the microstructure and elemental composition of materials at the mesoscale, an appropriate length scale for phase field modelling of intergranular diffusion phenomena using the MOOSE framework. For instance, the FEI Helios G4 UX dual beam plasma FIB microscope at the Irradiated Materials Characterization Laboratory (IMCL) is capable of backscatter diffraction (EBSD) and energy-dispersive x-ray spectroscopy (EDS) documenting the evolution in the microstructure and elemental composition, respectively. The Helios can perform EDS and EBSD three-dimensionally (3D) using tomography, which is then combined using different software packages to visualize 3D volumes correlating elemental composition to microstructural data. The purpose of this investigation was to develop a streamlined characterization and data processing workflow for 3D tomography studies on the FEI Helios G4 plasma FIB. The investigation is segmented into three parts: 1) Optimizing the data collection workflow, 2) identifying appropriate data processing and visualization software (i.e. DREAM.3D, MIPAR, and VGStudioMax), and 3) establishing an infrastructure for public release. The optimization of the data collection workflow is in collaboration with members of the U220 department to setup formal training on the tomography operation of the G4, through ThermoFisher Scientific, and exploring DREAM.3D, MIPAR, and VGStudioMax data processing/visualization software packages. VGStudioMax currently demonstrates the most promise for future use. Optimization of the data collection and processing workflow is still ongoing. A collaboration with INL High Performance Computing (HPC) established an open-source license for expediting the public release of FIB tomography datasets through HPC. FIB tomography data generated by the G4 will provide comprehensive data for validating 3D phase field mesoscale modelling tools within the MOOSE framework for accelerated qualification of reactor structural materials.

Copeland-Johnson, Trishelle↗

DOE OSTI2025

Phase transformation kinetics model for metals

We develop a new model for phase transformation kinetics in metals by generalizing the Levitas–Preston (LP) phase field model of martensite phase transformations (see Levitas and Preston (2002a,b) and Levitas et al. (2003)) to arbitrary pressure. Furthermore, we account for and track: the interface speed of the pressure-driven phase transformation, properties of critical nuclei, as well as nucleation at grain sites and on dislocations and homogeneous nucleation. The volume fraction evolution of each phase is described by employing KJMA (Kolmogorov, 1937; Johnson and Mehl, 1939; Avrami, 1939, 1940, 1941) kinetic theory. We then test our new model for iron under ramp loading conditions and compare our predictions for the α → ϵ iron phase transition to experimental data of Smith et al. (2013). In conclusion, more than one combination of material and model parameters (such as dislocation density and interface speed) led to good agreement of our simulations to the experimental data, thus highlighting the importance of having accurate microstructure data for the sample under consideration.

36 MATERIALS SCIENCE↗

DOE OSTI2025

HPC for Optimizing Process Parameters to Control Material Evolution in Seamless Induction Hardening of Wind Turbine Main Shaft Bearings

Work proposed in this project focused on understanding the effect of martensitic transformation in the steel on the potential for cracking during seamless induction hardening (SIH) as a function of process conditions to allow the process to optimally scale up. Large-scale, three-dimensional phase-field simulations of martensitic transformation were performed using MEUMAPPS-SS (Microstructure Evolution Using Massively Parallel Phase-field Simulations – Solid State) code developed at Oak Ridge National Laboratory. The simulations were guided by location-specific thermal history generated by experimental measurements of time-temperature history generated at The Timken Company. The simulations were able to capture the morphological evolution of the martensite variants in an Fe-1.0C-1.5Cr steel based on the Nishiyama-Wasserman (NW) orientation relationship. The simulations were also able to quantify the stress-state at the interface between impinging martensite variants. The simulations indicated that the magnitude of the various stress and strain components were dependent on the sizes of the impinging plates with a reduction in these quantities with reduced plate size in agreement with experimental findings. The results obtained from the simulations will be used to guide the optimization of the alloy thermal conditions to eliminate quench cracking during SIH of bearing steels.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2025

Holistic Microstructure Control Strategies in Photopolymerization‐Induced Phase Separation of Acrylate Systems

Open porous materials, known for their large surface area and interconnected structures, are essential in various applications, including batteries, ion exchange, catalysis, filtration, and electronic waste recycling. A critical aspect of the functionality of porous membranes is the precise control of pore size and morphology. Photopolymerization-induced phase separation (photo-PIPS) offers a convenient and versatile methods for creating porous structures. However, controlling the porous morphology remains challenging due to the complex interplay between thermodynamics, polymerization kinetics, and monomer structures, which makes it difficult to establish the relationship between processing conditions and resulting morphology in photo-PIPS. Herein, a physics-based phase-field model capable of generating and characterizing the microstructures of porous materials based on both average and localized features is developed. Using the phase-field simulations as test bed, the effects of polarity, light intensity, and curing temperature, as well as the previously unexplored roles of chain transfer agents and substrates, on the morphology of the resulting porous microstructure are investigated. Experiments are performed to verify the results predicted by the simulations. This work lays out a comprehensive guide for designing PIPS-derived porous microstructures and offers practical engineering strategies for tailoring microstructure-level topology and size of pores for application-specific needs.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Lower length scale model for palladium attack of silicon carbide in TRISO fuel

TRistructural ISOtropic (TRISO) particle fuels rely on silicon carbide (SiC) as the primary barrier for metallic fission product (FP) release. Palladium (Pd) generated by fission degrades the SiC layer, resulting in the formation of lamellar layers of palladium silicides (PdxSi) and carbon (C) perpendicular to the direction of attack. The Pd attack has been hypothesized to be responsible for failure of the SiC layer and enhance FP release. To better understand and quantify Pd attack of SiC in TRISO particles, a multiscale, mechanistic model of Pd transport is being developed by the NEAMS program. Previous work provided an initial hypothesis for modeling lamellar microstructure formation in SiC due to Pd attack using a phase-field model. The work described in this report builds on the previous model by using molecular dynamics (MD) simulations to parameterize the phase-field model kinetics, and build a reduced order model in BISON using the improved mesoscale Pd penetration model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

High-field magnetic phase diagrams of the 𝑅⁢Mn 6 ⁢Sn 6 (𝑅=Gd–Tm) kagome metals

𝑅⁢Mn 6 ⁢Sn 6 (𝑅=Y, Gd–Lu) kagome metals are promising materials hosting flat electronic bands and Dirac points that interact with magnetism. The coupling between the two magnetic 𝑅 and Mn sublattices can drive complex magnetic states with potential consequences for spin and charge transport and other topological properties. Here, in this work, we use a detailed magnetic Hamiltonian to calculate and predict the magnetic phase diagrams for 𝑅⁢Mn 6 ⁢Sn 6 kagome metals within the mean-field approximation. These calculations reveal a variety of collinear, noncollinear, and noncoplanar phases that arise from competition between various interlayer magnetic exchange interactions and magnetic anisotropies of the 𝑅 and Mn ions. We enumerate these phases and their magnetic space groups for future analysis of their impact on topological and trivial bands near the Fermi surface.

kagome metal↗

DOE OSTI2025

The influence of cooling rates on strain phase diagrams and domain structures of ferroelectric thin films: A case study of PbTiO 3

Strain engineering has been established as an effective approach to control phase equilibria, domain configurations, and functional properties of ferroelectric thin films. Temperature-strain phase diagrams have been used as powerful tools for providing insights into strain engineering. However, almost all existing phase diagrams established using the phase-field approach assume quenching conditions without considering actual cooling rates during the post-deposition annealing process of ferroelectric thin films. Within this work, we systematically investigate the influence of cooling rates on domain structures and the strain-phase diagram of ferroelectric thin films using phase-field simulations, taking PbTiO 3 thin films as a model system. We found that both the position of phase boundaries in the strain phase diagrams and the domain morphology are significantly influenced by the cooling rates. It is revealed that while the paraelectric-ferroelectric phase boundary remains invariant, the phase boundaries between single-phase and multi-phase regions tend to shift toward the corresponding multi-phase region as the cool rate reduces. Slow cooling generally leads to more ordered domain structures with increased domain size. Using the obtained equilibrium domain structures, we calculated effective thermal conductivities and found significant variations that can be tuned by the cooling rates. In conclusion, this work reveals an underexplored yet critical impact of cooling rates on phase equilibria and domain structures in ferroelectric thin films, which may inspire further fine-tuning of domains and domain walls in low-dimensional ferroelectrics for multifunctional applications.

Domain structures↗

DOE OSTI2026

PyJMAK: An Open-Source Python Toolkit for Modeling Solid-State Metallurgical Phase Transformations

Accurate prediction of metallurgical phase transformations is an essential basis for autonomous optimization and rapid part qualification. Several methods can be used to estimate the evolution of phase fractions such as JMAK kinetics-based models, phase-field models, thermodynamic models, and data-driven machine learning models. Thermodynamic and phase-field-based methodologies solve multiphysics equations requiring numerous calibration parameters and significant computational resources. As a result, the computation domain is limited to a point or on order of micron-meters. The data-driven models rely on large datasets from experiments and simulations. While the JMAK model only provides information about phase fraction evolution, it can predict this evolution in near real-time using thermal history and thermodynamic data without restriction on the domain. JMAK models have been popularly used by researchers to model phase transformations occuring during additive manufacturing or over arbitrary temperature profiles. Commercial proprietary software such as Abaqus and Ansys or closed-source in-house implementations offer the ability to model JMAK based kinetics to predict phase transformation. However, these software packages are not open-source or freely available for use and development in conjunction with manufacturing machines, sensors, and machine learning algorithms. In addition, the use of the model is restricted by a license token. In contrast, given temperature profiles at multiple points in the domain, this Python-based PyJMAK model can compute phase evolution in parallel due to its stand-alone modular, voxel-based structure, and it can be executed on high-performance computing resources without any license restrictions.

Prabhune, Bhagya [Oak Ridge National Laboratory (O↗

DOE OSTI2025

Unraveling the Determinant Mechanisms in Flow-Mediated Crystal Growth and Phase Behaviors

To uncover the critical mechanisms responsible for mesoscopic level development during flow-mediated crystal growth, we develop a semi-two-way hydrodynamic coupled structural phase-field crystal formalism (HXPFC-s2). The new formalism, inspired by previous attempts at coupling hydrodynamic and phase-field crystal (PFC) equations, allows for studying mesoscopic flow-mediated crystallization at diffusive timescales pertinent to industrial applications. Unlike previous efforts, the devised coupling to the structural PFC (XPFC) equations allows generalization to more complex crystal structures through explicit parameterization of the direct correlation function (DCF). Utilizing the HXPFC-s2 formalism, we seek to uncover the determinant physical mechanisms in crystallization under simple shear flows by comparing temperature-driven crystallization to flow-mediated crystallization under varying flow-strengths. Parallels and deviations of under-cooling and flow-strength effects on crystal growth are drawn using the crystal cluster-size and system ordering time evolutions. In doing so, we identify scaling behaviors with a Peclet-like number, Pe∼, a critical Peclet-like number, Pe∼*, and flow-field-crystal plane-dependent interactions. Our findings may be relevant for controlling crystal growth and phase behaviors in flow applications.

Willis, L. Connor (ORCID:0009000961321848)↗

DOE OSTI2025

HPC for optimizing process parameters to control material evolution in seamless induction hardening of wind turbine main shaft bearings

17 WIND ENERGY↗

DOE OSTI2026

Computational simulation of asymmetric phase transformation in cracked Li₇La₃Zr₂O₁₂: Variant selection and chemo-mechanical implications

Coupling between microcracks and phase transformation in ion-conducting ceramics can jointly affect mechanical responses and ion transport. In this work we investigate the cubic-to-tetragonal phase transformation in Li₇La₃Zr₂O₁₂ in the presence of a microcrack under hydrostatic loading and quantify its implications for crack-tip stress concentration and Li-ion transport using phase-field and molecular dynamics simulations. The phase transformation exhibits a strong asymmetry between hydrostatic tension and compression. Under tension, the crack edge nucleates one tetragonal variant that amplifies the crack-tip stress intensity and promotes crack opening. Under compression, the crack tip nucleates a different tetragonal variant that enhances the stress-induced crack-closure tendency. Effective Li diffusivity analysis shows faster transport degradation under compression due to accelerated transformation kinetics, exposing a trade-off between mechanical stability and ionic conductivity. These results highlight the intertwined nature of cracking, phase transformation, and ionic transport in ion-conducting oxides and provide mechanistic insights into chemo-mechanical degradation of solid electrolytes.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Material Fracturing and Failure Simulation Datasets

Fracturing is a fundamental physics phenomena with broad relevance across multiple domains, ranging from infrastructure integrity, aerospace durability, reservoir production, and seismic events. We present a diverse dataset of simulated fracture evolution and material failure generated from two numerical solvers: the phase-field method and the combined finite-discrete element method (FDEM). These solvers differ in formulation, physical fidelity, and computational efficiency. The dataset includes five materials: PBX, anisotropic shale, tungsten, aluminum, and steel. For each, phase-field simulations span 400,000 cases: 200,000 under uniaxial tension and 200,000 under biaxial tension. The computationally expensive FDEM simulations include 90,000 split evenly among PBX, shale, and tungsten under uniaxial loading. All simulations begin with randomized initial fracture patterns. Each entry includes temporal data capturing fracture propagation dynamics. This comprehensive dataset is designed to support the development of foundational or surrogate machine learning approaches for predicting material failure. While no such models are introduced here, the dataset lays a robust foundation for advancing future research and innovation in these areas.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Quantification and prediction of solidification textures under additive manufacturing conditions

Crystallographic textures are a major determinant of the macroscale anisotropic properties of polycrystalline metallic alloys produced in a wide range of additive manufacturing (AM) processes. Here, we introduce a statistical method that can accurately quantify the degree of orientational order of textures despite the large random fluctuations in the orientation of individual grains inherent in AM processes. The method, demonstrated for laser and resolidification of AlSi thin films, extends Z-scoring to a dynamical regime to assess the statistical significance of observed textures compared to randomly generated ones at different stages of solidification. We further show that, combined with phase-field modeling, this method can be used to infer fundamental anisotropic properties of the solid-liquid interface that are essential for texture prediction, and are compared here to the results of atomistic simulations. In addition, phase-field modeling reveals that, even at rapid AM solidification rates, the observed 〈110〉-dominated textures in the AlSi thin films are controlled predominantly by the anisotropy of the interface free-energy and sheds light on the physical mechanism of grain competition. These results significantly enhance both the existing tools for the quantification and prediction of AM crystallographic textures and our basic understanding of their formation.

36 MATERIALS SCIENCE↗