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DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Modeling and simulation of oxygen transport in high burnup LWR fuel

We have developed a formulation for oxygen transport in uranium dioxide nuclear fuel that accounts for the effects of irradiation. The overall simulation combines the evolving isotopic composition, thermochemistry, and oxygen transport in irradiated fuel. The driving forces for oxygen transport are computed from local thermodynamic equilibrium calculations and account for the effects of temperature gradients and composition, including fission products. The proposed method provides a mechanism for including complex thermodynamic models of nuclear fuel in modeling of mass redistribution, and alleviates difficulties associated with the common thermodiffusion formulation. Here, the transport model has been implemented within the nuclear fuel performance code BISON utilizing the thermochemistry code Thermochimica, with burnup calculations provided by the ORIGEN isotopic transmutation code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Point defect evolution under irradiation: Finite size effects and spatio-temporal correlations

The evolution of point defect concentrations under irradiation is controlled by their diffusion properties, and by their formation and elimination mechanisms. The latter includes the mutual recombination of vacancies and interstitials, and the elimination of point defects at sinks. Two models are traditionally used to predict the defect concentration evolution, the standard rate theory (SRT) and the atomistic kinetic Monte Carlo (AKMC). We show in this work a large discrepancy in the defect concentrations between both methods when the average number of defects in the AKMC simulation box is close or lower than one. The reason is that AKMC naturally captures strong space and time correlations between vacancies and interstitials generated by the finite size of the periodic simulation box. These correlations strongly affect the recombination rate and the point defect concentrations. SRT fails to predict such correlations, and the corresponding solution deviates from the more accurate solution given by the AKMC simulation under similar conditions. These finite size correlation effects are strong when the elimination of point defects occurs by recombination only, but can still be significant in the presence of sinks. In order to account for the spacio-temporal correlation in a continuum framework, we introduce a Correlated Pair Theory (CPT). This theory fully takes into account the correlations between vacancy and interstitial pairs and predicts point defect concentrations in good agreement with AKMC simulations. Inversely, if the goal is for the AKMC to reproduce defect concentrations in bulk using small simulation boxes, the naturally occurring correlations need to be corrected. We show here that the CPT can be used to modify the elimination rates in the AKMC simulations, so as to yield point defect concentrations in agreement with SRT.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Mechanistic verification of empirical UO 2 fuel fracture models

Standard UO 2 fuel pellets used in light-water reactors fracture during irradiation due to the large thermal gradient in the radial direction. Over the decades, numerous researchers have explored fuel cracking from experimental and modeling points of view. To date, there have been both empirical and mechanistic approaches to predict the number of fragments that form in UO 2 . The empirical models only consider maximum power and burnup as inputs. Existing mechanistic approaches for normal operation have not accounted for irradiation effects. Here, this work employs a mechanistic fuel cracking model using the extended finite element method to explore radial crack formation while including a sensitivity analysis that accounts for the randomization of tensile strength within the fuel, the strength randomization criteria (uniform or volume-weighted Weibull), power ramping rates, computational mesh density, maximum power level, and irradiation (burnup) effects. The results indicate that the uncertainty in this mechanistic modeling approach envelopes the predicted values from three different empirical correlations in almost all cases. This means that, for computationally intensive analyses involving UO 2 fragmentation, the empirical correlations can be used. However, since the mechanistic calculations bound those of the empirical correlations, there is confidence in the applicability of the mechanistic approach developed in this work to generate a correlation for fuel types where limited data exists (e.g., doped-UO 2 , U 3 Si 2 ).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Efficient high-fidelity TRISO statistical failure analysis using Bison: Applications to AGR-2 irradiation testing

The ability of tri-structural isotropic (TRISO) fuel to contain fission products is largely dictated by the quality of the manufacturing process, since most of the fission product release is expected to occur due to coating layer failure in a small number of particles containing defects. The Bison fuel performance code has capabilities to predict failure in individual particles, accounting for the presence of defects, and to apply statistical analysis methods to compute the probability of failure in a set of fuel particles. Bison has recently undergone significant development both to improve its physical representations of fuel particle behavior and to improve the efficiency of its statistical failure calculations. Physical model improvements include new capabilities to account for the pressure generated by fission gases on inner pyrolytic carbon (IPyC) crack surfaces and to use local material coordinate orientation to accurately incorporate the anisotropy in the material properties in aspherical particles. To improve statistical modeling efficiency, a direct integration approach which involves directly integrating the failure probability function associated with statistically varying parameters has been developed. The direct integration approach is much more efficient than the Monte Carlo (MC) schemes commonly employed, and allows Bison to directly run high-dimensional fuel performance models, which improves the accuracy of failure probability calculations. Finally, a set of benchmark problems is considered here to compare the MC and direct integration approaches, and a statistical failure analysis of compacts in the Advanced Gas Reactor (AGR)-2 experiments is performed using the direct integration approach.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Development of hydrothermal corrosion model and BWR metal coating for CVD SiC in light water reactors

SiC/SiC fiber composites with CVD SiC overcoats are potential candidates for light water reactor advanced accident tolerant cladding materials. Understanding its corrosion kinetics in Light Water Reactor (LWR) conditions is essential to evaluate the concept's viability. Existing models only account for the temperature and oxygen concentration effect on the hydrothermal corrosion behavior applicable to LWR operating conditions. However, the development of a general corrosion rate for CVD SiC that accounts for the impact of irradiated microstructure, flow rate, electrical resistivity, pH, and surface roughness is critical for the practical realization of SiC/SiC-based cladding concepts. After a rigorous experimental campaign, this work updates the existing hydrothermal corrosion model to predict hydrothermal corrosion in LWRs. Numerical radiation and coolant chemistry analysis for LWRs conducted based on the updated corrosion kinetic models suggests that CVD SiC is likely a viable environmental barrier coating for Pressurized Water Reactors while questionable for Boiling Water Reactors (BWR) when the effect of irradiation damage on SiC corrosion is considered. An effective mitigation strategy for the double-layer metal coating is proposed for BWR applications. The double-layer metal coating comprising a FeCrAl overcoat with an intermediate Cr bond coating was observed to provide a stable protective barrier against SiC dissolution in BWR conditions. Finally, the proposed metal coating was also fully adherent following quench and burst tests.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Co-ion specific effect on sodium halides sorption and transport in a cross-linked poly(p-styrene sulfonate-co-divinylbenzene) for membrane applications

Here, sodium halide sorption and transport in a cation exchange membrane based on cross-linked poly(p-styrene sulfonate-co-divinylbenzene) (CR61) were investigated experimentally and theoretically. At fixed co-ion valence, sodium halide partitioning between aqueous electrolyte solutions and ion exchange polymers is only minimally sensitive to co-ion chemical identity. NaCl, NaF and NaI exhibit similar solubility coefficients in CR61, which agrees reasonably well with predictions of the Donnan-Manning model, especially at high external salt concentrations. Ion activity coefficients in the membrane were evaluated and ion sorption thermodynamics were investigated. Ion diffusion coefficients in CR61 were predicted using a recently developed framework based on the Manning diffusion model, which accounts for electrostatic effects on ion diffusion, and the Mackie-Meares model, which accounts for tortuosity/area effects on ion diffusion in swollen polymers. Model predictions agree reasonably well with the experimental data, especially at high external salt concentrations. The observed decrease in salt diffusion coefficients in CR61 relative to values in aqueous solutions is due primarily to tortuosity/area effects. Salt diffusion coefficients correlate with co-ion hydrated radius and membrane water content. Finally, salt permeability coefficients predicted using the solution-diffusion model exhibit good agreement with experimental data, especially at external salt concentration greater than 0.1 mol/L.

42 ENGINEERING↗

DOE OSTI2022

twoaxistracking – a python package for simulating self-shading of two-axis tracking solar collectors

Self-shading in fields of two-axis tracking collectors typically ranges from 1% to 6% of the annual incident irradiation. It is thus essential to account for shading in order to obtain accurate yield estimates and financing for such solar projects. The present study presents the free and open-source Python package twoaxistracking for simulating self-shading in fields of two-axis tracking collectors. The package is freely available at: https://github.com/pvlib/twoaxistracking. The main steps of the method and mathematical formulation are described. Additionally, a demonstration of how to use the package is presented. The shading calculation method excels over previous methods found in the literature in that it can: handle arbitrary aperture geometries and distinguish between the total and active areas; account for sloped ground and collectors with different heights within the same field; reduce computation time by skipping calculations at high solar elevation angles.

14 SOLAR ENERGY↗

DOE OSTI2023

Dislocation-density evolution and pileups in bicrystalline systems

Here, a dislocation-density crystalline plasticity (DCP) framework based on total and partial dislocation densities interactions was used to investigate the behavior of Cu/Pb bicrystals with a focus on GB effects. The modeling predictions were validated with bicrystal compression micropillar experiments. A key new aspect of the modeling approach is to account for partial dislocation-densities. A GB formulation that is directly linked to GB energies was used to monitor GB transmission and blockages, such that pileups can be monitored and predicted at the GB interfaces for misorientations. The predictions indicate that pileups can form due to fully and partially blocked slip-rates and perfect and partial dislocation-densities. As the nominal strain increases from five to fifteen percent, dislocation-densities and pileups significantly increase by almost an order of magnitude. The proposed validated approach provides a microstructural scale predictive framework that accounts for a myriad of defects related to the interactions of partial and perfect dislocation densities that interact at highly misoriented GBs; it is these interactions that are critical to the formation and evolution of dislocation-density pileups that can lead to physically limiting stress accumulations in bicrystals.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Synchrotron X-ray diffraction analysis of constituent phases in transition joint between nickel alloy 738LC and a MnFeCoNiCu alloy

Synchrotron x-ray diffraction (XRD) analysis was performed on transition joints between a single-phase MnFeCoNiCu alloy and Ni-base Alloy 738LC to efficiently identify the constituent phases across the interface, with different levels of material intermixing generated by laser-welding with variable power. Here, the intermixing extent was quantified by postmortem energy dispersive x-ray spectroscopy mapping. Diffraction-based analyses on complex composition spaces with limited prior data present significant challenges because elemental substitution in both disordered and ordered phases is more extensive than in conventional alloy spaces, which may effectuate relatively large shifts in the observed lattice parameters that convolute the analysis. Therefore, thermodynamic simulations and crystallographic literature data were employed to construct a system-specific diffraction library of twelve prospective phases for the composition space investigated. Subsequently, for predicted disordered cubic phases, statistical hard-sphere models were established to estimate the lattice parameters and predict diffraction peak positions for inclusion in the library. The library was then employed to analyze diffraction profiles measured from the variably intermixed transition joints, with focus on accounting for both high and low-intensity peaks. 99.0 % of diffraction peaks with relative intensity greater than 0.001 were assigned to phases from the system-specific library, exemplifying rigorous peak accounting and indicating that no unexpected phases were present. Up to six of the twelve library phases were experimentally found in the transition joints. The lattice parameters predicted by the statistical hard-sphere model based upon thermodynamic simulations agree reasonably well with the measured values for the disordered FCC matrix phase.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Improved plutonium and americium photon branching ratios from microcalorimeter gamma spectroscopy

Photon branching ratios are critical input data for activities such as nuclear materials protection and accounting because they allow material compositions to be extracted from measurements of gamma-ray intensities. Uncertainties in these branching ratios are often a limiting source of uncertainty in composition determination. Here, we use high statistics, high resolution - (60–70 eV full-width-at-half-maximum at 100 keV) gamma-ray spectra acquired using microcalorimeter sensors to substantially reduce the uncertainties for 11 plutonium ( 238 Pu, 239 Pu, 241 Pu) and 241 Am branching ratios important for material control and accountability and nuclear forensics in the energy range of 125 keV to 208 keV. Lastly, we show a reduction in uncertainty of over a factor of three for one branching ratio and a factor of 2–3 for four branching ratios.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

The Dynamics of Ions on Phased Radio-frequency Carpets in High Pressure Gases and Application for Barium Tagging in Xenon Gas Time Projection Chambers

Radio-frequency (RF) carpets with ultra-fine pitches are examined for ion transport in gases at atmospheric pressures and above. We develop new analytic and computational methods for modeling RF ion transport at densities where dynamics are strongly influenced by buffer gas collisions. An analytic description of levitating and sweeping forces from phased arrays is obtained, then thermodynamic and kinetic principles are used to calculate ion loss rates in the presence of collisions. This methodology is validated against detailed microscopic SIMION simulations. We then explore a parameter space of special interest for neutrinoless double beta decay experiments: transport of barium ions in xenon at pressures from 1 to 10 bar. Our computations account for molecular ion formation and pressure dependent mobility as well as finite temperature effects. We discuss the challenges associated with achieving suitable operating conditions, which lie beyond the capabilities of existing devices, using presently available or near-future manufacturing techniques.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Average charge states of heavy ions in rarefied hydrogen

In this work, we present the results of experiments on measuring the charges of heavy ions from Rn (Z=86) to Og (Z=118) in rarefied hydrogen performed at the DGFRS and DGFRS-2 separators. Two formulae are proposed that can be used to calculate the charges of ions in H 2 and which take into account the influence of the shell structure of atoms on the charge value. The accuracy of estimating the charge of ions of superheavy atoms was measured to be 2%. The charges of Ra, Th, and No ions were measured at a hydrogen pressure from 0.5 to 3.3 mbar, which allowed us to evaluate the effect of H 2 density on the charge value. A formula is proposed to account for the effect of gas density when performing experiments at different gas pressures. It is shown that the results of experiments performed at different separators DGFRS and DGFRS-2 are in good agreement with each other.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Characterization of a platform for the gas transport, collection, and identification of fission products in the high-intensity laser environment

Recent progress in the production of laser accelerated high flux proton beams opens new possibilities for the study of fission in unique environments. To this end, we are currently pursuing the development of a platform for the swift gas transport, collection, and identification of fission products. Fission is induced in targets fixed inside a sealed chamber through which a carrier gas flows, transporting fission products to a carbon filter for collection and online spectroscopy. This has been recently demonstrated using target normal sheath accelerated protons at the PHELIX laser facility. There were large discrepancies between measured rates and those expected based on established fission yields and measured beam parameters. These discrepancies prompted a large number of tests at the Idaho Accelerator Center (IAC), where fission in uranium is induced by bremsstrahlung photons generated by 21 MeV electrons from a linear electron accelerator. Here, the results are compared to a series of models that account for the slowing of energetic fission fragments in the carrier gas and the fluid dynamics of the gas flow that transports fission products to the collection filter. Characterization of the apparatus reveals a few mechanisms that together account for a portion of the previously observed discrepancies at the PHELIX laser facility. However, additional research is necessary before high-accuracy experiments can be performed with the apparatus. Work performed under the auspices of the U.S. Department of Energy by LLNL under contract DE-AC52-07NA27344.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Object detection with deep learning for rare event search in the GADGET II TPC

In the pursuit of identifying rare two-particle events within the GADGET II Time Projection Chamber (TPC), this paper presents a comprehensive approach for leveraging Convolutional Neural Networks (CNNs) and various data processing methods. To address the inherent complexities of 3D TPC track reconstructions, the data is expressed in 2D projections and 1D quantities. This approach capitalizes on the diverse data modalities of the TPC, allowing for the efficient representation of the distinct features of the 3D events, with no loss in topology uniqueness. Additionally, it leverages the computational efficiency of 2D CNNs and benefits from the extensive availability of pre-trained models. Given the scarcity of real training data for the rare events of interest, simulated events are used to train the models to detect real events. To account for potential distribution shifts when predominantly depending on simulations, significant perturbations are embedded within the simulations. This produces a broad parameter space that works to account for potential physics parameter and detector response variations and uncertainties. These parameter-varied simulations are used to train sensitive 2D CNN object detectors. When combined with 1D histogram peak detection algorithms, this multi-modal detection framework is highly adept at identifying rare, two-particle events in data taken during experiment 21072 at the Facility for Rare Isotope Beams (FRIB), demonstrating a 100% recall for events of interest. Here, we present the methods and outcomes of our investigation and discuss the potential future applications of these techniques.

Convolutional neural network↗

DOE OSTI2022

BISON fuel performance modeling optimization for experiment X447 and X447A using axial swelling and cladding strain measurements

With the recent need to qualify new reactor designs such as the Versatile Test Reactor (VTR), fuel performance calculations need to be performed to determine safety criteria of the proposed designs. In order to validate the fuel performance results obtained by a fuel performance code, BISON, for new reactor designs, legacy fuel from EBR-II and FFTF MFF with Post -Irradiation Examination (PIE) data need to be used as validation cases to benchmark models. Here in this work, BISON has been paired with the Fuels Irradiation & Physics Database (FIPD) and IFR Materials Information System (IMIS) to supply PIE data for comparison with simulations of EBR-II experiments X447/X447A. X447/X447A were assessed by implementing models for Fuel Cladding Chemical Interaction (FCCI) within BISON and optimizing the friction coefficient between the fuel surface and the cladding, the anisotropic swelling factor, and the HT9 first thermal creep scalar (which scales the first term in the HT9 creep equation) to best match the PIE axial fuel swelling height and cladding profilometry for all pins in X447/X447A. The optimal values were found using a generic algorithm developed to select different values for the three parameters until end criteria was met and error couldn’t be reduced further. The BISON-simulated cladding profilometry was evaluated using Standard Error of the Estimate (SEE) to account for the profile shape of the cladding profilometry. Optimal values for the friction coefficient, anisotropic fuel swelling factor, and HT9 first thermal creep scalar were found to best fit the BISON simulation results to the PIE measurements found in IMIS and FIPD. Improvements to current models are suggested to account for the underprediction of fuel swelling at low burnups and the overprediction of fuel swelling at higher burnups observed for the axial fuel swelling height. Although two pins in EBR-II X447/X447A (DP70 and DP75) were known to fail due to FCCI, none of the pins simulated in BISON reached a cumulative damage fraction (CDF) above 0.008 with FCCI correlations coupled in the BISON simulations. The error estimate generated for all pins in X447/X447A using optimal values was 209 µm, which is deemed acceptable.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

3D probabilistic fracture mechanics / computational fluid dynamics simulation of a reactor pressure vessel under transient conditions

Reactor pressure vessels (RPVs) are safety-critical light-water-reactor components that, under irradiation, experience long-term material degradation in the form of embrittlement. This can increase their susceptibility to fracture under thermal-shock conditions, which could occur during off-normal transients such as loss-of-coolant accidents (LOCAs). During a LOCA, the most severe conditions for the RPV occur when emergency core cooling water is injected through the cold legs into the water-and-steam-filled RPV. The rapid cooling of the downcomer and internal RPV surface causes decreased temperature and elevated thermally driven tensile stresses in the RPV wall. This, combined with long-term material embrittlement, may cause fracture initiation at pre-existing flaws, challenging the integrity of the RPV. Assessing RPV integrity during transients with a large spatial variation in the coolant temperature requires a modeling approach that considers the effects of spatially varying coolant temperature on the fracture probability of a population of flaws distributed throughout the RPV, accounting for spatially varying embrittlement. Here, the present study addresses this need by demonstrating first-of-its-kind coupling of a high-fidelity 3D computational fluid dynamics code with 3D probabilistic fracture mechanics This was accomplished using representative models of a pressurized-water reactor subjected to small- and medium-break LOCA conditions, both of which can result in large spatial temperature variations. While the observed impact of accounting for 3D effects was minimal under the small-break LOCA this study indicates a significant increase in the probability of fracture initiation under the medium-break LOCA when 3D effects are considered, relative to a spatially uniform cooling scenario.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Trace impurity transport in multi-species plasmas with large particle fluxes

A burning fusion plasma has a large inwards flux of fuel and outwards flux of ash. Existing impurity transport theories do not account for a steady-state environment of such large fluxes. In this paper, we extend classical transport theory to account for a background of such fluxes. In a mainly two-ion species magnetized plasma, with oppositely directed density gradients maintained by oppositely directed sources of the two species, trace impurity ions are shown to align with the larger mass ions. This unexpected behavior is derived analytically and simulated numerically using the MITNS (Multiple-Ion Transport Numerical Solver) code. Overall, the result suggests a potential advantage of edge-fueled p-B11 fusion in extracting high-Z impurities, and possible applications in plasma-based separation methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗