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Overview of graphite model development. Discuss graphite in motel salt, potential degradation mechanisms, stress due to volumetric heating, and the role of different parameters. Also wear modeling, modeling salt infiltration into graphite, oxidation modeling, and the existing graphite models.
The adsorption and recombination of atomic hydrogen on a model graphite grain have been examined in a series of calculations in which a modified, iterative, extended Hueckel program was used. The hydrogen atom is found to be chemisorbed at a site with a zero-point binding energy of 0.7 eV and at an equilibrium distance of 2.25 A above the site. Despite a barrier of about 0.4 eV between adjacent sites, calculations suggest that at temperatures as low as 10 K, an H atom will tunnel through to adjacent sites in less than one nanosecond. However, a potential barrier to the recombination of two hydrogen atoms has been found which displays high sensitivity to the mutual arrangement of the two hydrogen atoms with respect to the graphite surface. Results show that at very low temperatures, recombinations can occur only by tunneling. Consistent with experiment, the region in which H2 begins to form exhibits a repulsive potential with respect to possible chemisorption of the incipient H2 entity.
Nuclear-grade graphites are extensively utilized in the core designs of various advanced nuclear reactors. Within the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, such as nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity, forecasting component performance over the reactor's lifespan, and developing design standards necessitate robust tools for predicting fracture initiation and propagation in graphite structural components within nuclear reactors. This code enables the Bayesian calibration of properties for nuclear-grade graphites. Using a hierarchical Bayesian approach, multiple experimental data sources are combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due inadequacies in the model and the inherent spread in the experimental data are quantified.
Graphite under high temperatures and irradiation is central to advanced reactors. We develop a Bayesian calibration framework for graphite property models that explicitly represents model-data mismatch via a Gaussian-process discrepancy. The approach propagates uncertainty from parameters, experimental noise, and model form, with a hierarchical variance structure to capture group and cross-group noise. Using two predictive models across five grades (IG-110, NBG-18, PCEA, NBG-17, 2114) and four properties-irradiation-induced dimension change, creep, Young’s modulus change ratio, and coefficient of thermal expansion change ratio-we obtain average predictive-error reductions of 54%, 65%, 17%, and 17% when discrepancy is included. We illustrate engineering impact with a multiphysics model of a very-high-temperature reactor prismatic reflector brick, analyzing stresses under high fluence and temperature. Accounting for model discrepancy markedly improves predictive accuracy and provides a robust basis for reliable graphite component design in advanced reactors.
Nuclear-grade structural graphite is extensively utilized in the core designs of various advanced nuclear reactors. In the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, including nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity requires accurate models of graphite's thermomechanical response. This report documents the Bayesian calibration of thermomechanical properties for nuclear-grade graphite and their application to graphite component modeling and simulation using the Grizzly code. As part of this work, uncertainty-quantified models were developed for the elastic modulus, coefficient of thermal expansion, irradiation-induced dimensional change, and irradiation-induced creep for graphite grades IG-110, NBG-18, NBG-17, PCEA, and 2114. Using a hierarchical Bayesian approach, multiple experimental data sources were combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due to inadequacies in the model and the inherent spread in the experimental data were quantified for three different models. These uncertainty-quantified models, with a model-form correction, were subsequently applied to a coupled-physics simulation of representative graphite components, revealing that the uncertainties have a large impact on the components' deformation.
Molten-salt reactors (MSRs) represent a promising next-generation reactor design, with graphite serving as a moderator and/or reflector in several designs. However, due to limited experimental data and operational experience, a technical understanding of the structural integrity of graphite in molten salt environments remains incomplete. This report presents a modeling-based evaluation of graphite degradation in MSR environments, focusing on the effects of salt infiltration in fuel salt-based designs and surface wear in pebble bed reactor designs. The objective of this study is to enhance understanding of the structural integrity challenges posed by these degradation mechanisms and to provide a framework for assessing graphite behavior in MSRs. The first part of the report investigates the phenomenon of molten salt infiltration into graphite. This infiltration occurs when molten salt permeates the interconnected pore structure of the graphite moderator, driven by factors such as pressure differentials and the physical properties of both the salt and graphite. The infiltration process is influenced by characteristics of the pore structure, viscosity of the molten salt, and the interfacial energies between the graphite, salt, and the atmosphere within the graphite pore. Utilizing a coupled multiphysics modeling approach with Grizzly software, the study evaluates the stress induced by internal heat sources due to infiltration, which can lead to structural concerns. This evaluation is crucial for understanding how infiltration affects the mechanical integrity of graphite components in MSRs. The study considers the Molten-Salt Reactor Experiment (MSRE) graphite stringer geometry due to the availability of relevant data. Through detailed finite element analysis, the study examines stress distributions at varying infiltration percentages, revealing that stress levels increase with higher amounts of infiltration. Rare-event simulations, using the parallel subset simulation (PSS) framework, further quantify the failure probabilities under input uncertainties, with a user-specified failure metric. The PSS framework also identifies critical input parameters that significantly affect the stress values, including infiltration amount, thermal conductivity, and power density. Additionally, considering realistic reactor scenarios, the analysis was performed to account for the combined effects of radiation and infiltration, and modeling strategies on how to analyze new reactor designs or new graphite grades are discussed. The second part of the report focuses on wear mechanisms in pebble bed-based MSRs. As graphite fuel pebbles interact with the graphite reflector block, wear can result in material loss and the formation of surface defects, which may act as stress concentrators. A similar multiphysics modeling framework is employed to assess the impact of wear on the structural integrity of graphite components. This study considers a generic fluoride-cooled high-temperature reactor (gFHR) design due to the availability of comprehensive data. Worst-case scenario dimensions of the reflector blocks were analyzed under thermal and radiation conditions. Subsequently, wear in the form of idealized pits and grooves is modeled on the inner surface of the graphite block, with the maximum stress from previous simulations. The simulations show that groove-type defects are more detrimental than pits, leading to higher stress concentrations. Considering worst-case simulation scenarios and experimental wear rates, it was determined that the formation of a surface defect critical enough to affect the stress may not be possible in a gFHR design. Overall, the findings of this research contribute to the development of robust modeling tools for predicting graphite behavior under various operational conditions in MSRs.
Instrumented ATJ-S graphite shell nosetip models were tested in the AFFDL 50 MW RENT Facility. The inside surface of the models were instrumented with seven thermocouples and three clip-on extensometers. One thermocouple was located at the inside stagnation point and three thermocouples were located at 120 degree intervals on the aft portion of the skirt of the model. In addition, three thermocouples at 120 degree intervals plus three clip-on extensometers at 120 degree intervals offset 60 degrees from the thermocouples were located in the critical region. The outside surface temperature of the models was monitored in two locations by optical pyrometers. Finally, the tests were recorded by three high speed motion picture cameras. Pressure models and calorimeters were also tested in order to help define the flow field condition and heating distribution around the models.
Molten salt reactors (MSRs) often employ graphite as a moderator and reflector. An important challenge for deploying graphite in these reactors is that, due to limited experimental data, our understanding of graphite’s structural integrity in molten salt environments remains incomplete. Here, this study addresses heat generation from fuel-bearing salt that has infiltrated open pores in the graphite, driven primarily by pressure differentials. This is one of multiple identified physical and chemical mechanisms through which molten salt could potentially degrade graphite. Thermally driven stresses are quantified using the Molten-Salt Reactor Experiment (MSRE) graphite moderator elements as a case study. Finite element simulations predict stress distributions at varying infiltration levels, indicating that thermal stresses increase with higher infiltration. Rare-event simulations using the parallel subset simulation framework identify the combinations and corresponding ranges of input parameters that lead to stresses above a specified threshold. In particular, combinations involving high infiltration amounts, high power density, and low thermal conductivity tend to induce the highest stresses. Under the inputs and assumptions considered in this work, the magnitudes of the thermally driven stresses are quite low, with a very low likelihood of causing failure due to exceeding the graphite’s tensile strength. Additionally, rare-event simulations were performed for two more scenarios: a scaled-up moderator geometry and a localized hotspot in the original geometry. Both cases resulted in increased susceptibility to failure, though not to a detrimental extent. Furthermore, the combined effects of irradiation and infiltration-induced thermal stresses were evaluated. The results showed that thermal stresses from infiltration were negligible compared to those caused by irradiation. The findings of such a study are inherently component-specific, but the methodology presented here could be used for similar assessments of salt-infiltration effects in other graphite components.
IR radiation of NML Cygnus with O/C ratio close to unity ascribed to circumstellar shell of graphite particles
Scale models of the Galileo Probe made of polycarbonate, AXF5Q graphite, carbon-carbon composite, and carbon-phenolic were flown in a free flight range in an ambient gas of air, krypton, or xenon. Mach numbers varied between 14 and 24, Reynolds numbers between 300,000 and 1,000,000, stagnation pressures between 31 and 200 atm, and stagnation point heat transfer rates between 10 and 1,000 kW/sq cm. Shadowgraphs indicate gouging ablation of the aft portion of the frustum; the gouging was moderate in air and severe in the noble gases. The graphite models break in the same region. An explanation of the phenomena is offered in terms of the strong compression and shear caused by the reattachment of a turbulent separated flow. Conditions are calculated for similar tests appropriate for Von Karman Facility of the Arnold Engineering Development Center in which a larger model can be flown in argon.
The NEAMS Multiphysics Applications team continues to assess code usability and functionality for microreactor design and safety analyses, while demonstrating that NEAMS tools capture both steady-state and transient behavior across distinct microreactor concepts. In FY2025, the team advanced full-core, high-fidelity, multiphysics models that solve more complex problems and strengthen verification/validation for several microreactor systems: heat-pipe microreactor (HPMR), gas-cooled microreactor (GCMR), and the KRUSTY experiment. These models employ the MOOSE MultiApp/Transfers architecture with Griffin for neutronics, BISON for heat conduction/thermomechanics, Sockeye for heat pipes, SAM/THM for coolant channels and loops, and SWIFT for hydride behavior, with meshes generated via the MOOSE Reactor Module. The graphite models available in the Grizzly code were also investigated for future analyses. For the HPMR, a Na-HPMR variant was constructed to align with recently validated heat-pipe experiments and Sockeye’s LCVF capability, enabling mechanistic heat-pipe transients and startup modeling. The Na-HPMR will serve as the primary model for HPMR investigations in upcoming tasks. The load-following and single heat-pipe failure scenarios (Griffin/BISON/Sockeye), which were previously modeled for the K-HPMR, were replicated for the Na-HPMR, showing strong negative temperature feedback and highly localized thermal effects, respectively, while the startup case captured vapor-front progression and heat-removal activation. Solid mechanics was added to the previously built K-HPMR full-core model in BISON, showing minimal impact on steady-state reactivity yet enabling stress-field predictions that prepare the path for full-core TRISO performance analyses. For the GCMR, automated steady-state and four transient scenarios were executed using Griffin/BISON/SAM/SWIFT. Results confirm robust inherent safety: power collapses promptly in loss-of-cooling events, the inlet-temperature drop settles to a new equilibrium, and a single-channel blockage yields only a ~30 K local fuel-temperature rise with <0.4% power decrease. SWIFT-predicted hydrogen redistribution affects reactivity during both steady-state and transient conditions, underscoring its importance. A Brayton-cycle balance of plant (BOP) model in SAM/THM demonstrated stable startup behavior, and xenon-driven reactivity during load following was analyzed. To improve TRISO-compact temperature fidelity, a fast multiscale Heat Source Decomposition (HSD) treatment was implemented. Against heterogeneous benchmarks, HSD reduces underprediction of kernel temperatures and lowers predicted peak powers in reactivity-insertion transients compared to previous homogenized models. KRUSTY warm-critical validation progressed from FY2024 baselines: the 15Ȼ insertion shows excellent agreement in peak power (~2% high) and temperature trends, and the 30Ȼ case was automated via a feedback controller that maintained power near 3 kW for ~150 s with close agreement to data. The successful modeling of the warm critical tests has laid a strong foundation for simulating more complex nuclear system tests in the years ahead. Throughout FY2025, developer feedback was provided (e.g., MOOSE batch mesh generation, distributed pre-split meshes, Griffin sweeper on displaced meshes), several new models were contributed to the Virtual Test Bed, and an OECD-NEA WPRS multiphysics benchmark based on the HPMR was initiated to enable broader cross-comparison and best-practice development with the nuclear community at large.
Introduction of ART Graphite R&D to include oxidation activities, oxidation resistant graphite, model development, ASME component failure, ASME code development (design rules), ceramic composites, AGC update, molten salt intrusion, split-disk studies, wear testing, and concluding remarks.
Utilizing a series of existing computer codes, ablation experiments in the Giant Planet Facility are numerically simulated. Of primary importance is the simulation of the low Mach number shock layer that envelops the test model. The RASLE shock-layer code, used in the Jupiter entry probe heat-shield design, is adapted to the experimental conditions. RASLE predictions for radiative and convective heat fluxes are in good agreement with calorimeter measurements. In simulating carbonaceous ablation experiments, the RASLE code is coupled directly with the CMA material response code. For the graphite models, predicted and measured recessions agree very well. Predicted recession for the carbon phenolic models is 50% higher than that measured. This is the first time codes used for the Jupiter probe design have been compared with experiments.
A micromechanical modeling procedure is developed to predict the viscoelastic properties of a graphite nanoplatelet/epoxy composite as a function of volume fraction and nanoplatelet diameter. The predicted storage and loss moduli from the model are compared to measured values from the same material using Dynamical Mechanical Analysis, nanoindentation, and tensile tests. In most cases, the model and experiments indicate that for increasing volume fractions of nanoplatelets, both the storage and loss moduli increase. Also, in most cases, the model and experiments indicate that as the nanoplatelet diameter is increased, the storage and loss moduli decrease and increase, respectively.
Scale model graphite-epoxy composite specimens were fabricated using the 'sub-ply level' approach and tested as beam-columns under an eccentric axial load to determine the effect of specimen size on flexural response and failure. In the current research project, although the fiber diameters are not scaled, the thickness of the pre-preg material itself has been scaled by adjusting the number of fibers through the thickness of a single ply. Three different grades of graphite-epoxy composite material (AS4/3502) were obtained from Hercules, Inc., in which the number of fibers through the thickness of a single ply was reduced (Grade 190 with 12 to 16 fibers, Grade 95 with 6 to 8 fibers, and Grade 48 with 3 to 4 fibers). Thus, using the sub-ply level approach, a baseline eight ply quasi-isotropic laminate could be fabricated using either the Grade 48 or Grade 95 material and the corresponding full-scale laminate would be constructed from Grade 95 or standard Grade 190 material, respectively. Note that in the sub-ply level approach, the number of ply interfaces is constant for the baseline and full-scale laminates. This is not true for the ply level and sublaminate level scaled specimens. The three grades of graphite-epoxy composite material were used to fabricate scale model beam-column specimens with in-plane dimensions of 0.5*n x 5.75*n, where n=1,2,4 corresponsing to 1/4, 1/2, and full-scale factors. Angle ply, cross ply, and quasi-isotropic laminate stacking sequences were chosen for the investigation and the test matrices for each laminate type are given. Specimens in each laminate family with the same in-plane dimensions but different thicknesses were tested to isolate the influence of the thickness dimension on the flexural response and failure. Also, specific lay-ups were chosen with blocked plies and dispersed plies for each laminate type. Specimens were subjected to an eccentric axial load until failure. The load offset was introduced through a set of hinges which were attached to the platens of a standard load test machine. Three sets of geometrically scaled hinges were used to ensure that scaled loading conditions were applied. This loading condition was chosen because it promotes large flexural deformations and specimens fail at the center of the beam, away from the grip supports. Five channels of data including applied vertical load, end shortening displacement, strain from gages applied back-to-back at the midspan of the beam, and rotation of the hinge from a bubble inclinometer were recorded for each specimen. The beam-column test configuration was used previously to study size effects in ply level scaled composite specimens of the same material system, sizes, and stacking sequences. Thus, a direct comparison between the two scaling approaches is possible. Ply level scaled beam-columns with angle ply, cross ply, and quasi-isotropic lay-ups exhibited no size dependencies in the flexural response, but significant size effects in strength. The reduction in strength with increasing specimen size was not predicted successfully by analysis techniques. It is anticipated that results from this investigation will lead to a better understanding of the strength scale effect in composite structures.
Defining the electromagnetic environment inside a graphite composite fairing due to lightning is of interest to spacecraft developers. This paper is the first in a two part series and studies the shielding effectiveness of a graphite composite model fairing using derived equivalent properties. A frequency domain Method of Moments (MoM) model is developed and comparisons are made with shielding test results obtained using a vehicle-like composite fairing. The comparison results show that the analytical models can adequately predict the test results. Both measured and model data indicate that graphite composite fairings provide significant attenuation to magnetic fields as frequency increases. Diffusion effects are also discussed. Part 2 examines the time domain based effects through the development of a loop based induced field testing and a Transmission-Line-Matrix (TLM) model is developed in the time domain to study how the composite fairing affects lightning induced magnetic fields. Comparisons are made with shielding test results obtained using a vehicle-like composite fairing in the time domain. The comparison results show that the analytical models can adequately predict the test and industry results.
This paper describes the development of input properties for a continuum damage mechanics based material model, Mat 58, within LS-DYNA(Registered Trademark) to simulate the response of a graphite-Kevlar(Registered Trademark) hybrid plain weave fabric. A limited set of material characterization tests were performed on the hybrid graphite-Kevlar(Registered Trademark) fabric. Simple finite element models were executed in LS-DYNA(Registered Trademark) to simulate the material characterization tests and to verify the Mat 58 material model. Once verified, the Mat 58 model was used in finite element models of two composite energy absorbers: a conical-shaped design, designated the "conusoid," fabricated of four layers of hybrid graphite-Kevlar(Registered Trademark) fabric; and, a sinusoidal-shaped foam sandwich design, designated the "sinusoid," fabricated of the same hybrid fabric face sheets with a foam core. Dynamic crush tests were performed on components of the two energy absorbers, which were designed to limit average vertical accelerations to 25- to 40-g, to minimize peak crush loads, and to generate relatively long crush stroke values under dynamic loading conditions. Finite element models of the two energy absorbers utilized the Mat 58 model that had been verified through material characterization testing. Excellent predictions of the dynamic crushing response were obtained.
A multi-scale method is utilized to determine some of the constitutive properties of a three component graphite-epoxy-nanotube system. This system is of interest because carbon nanotubes have been proposed as stiffening and toughening agents in the interlaminar regions of carbon fiber/epoxy laminates. The multi-scale method uses molecular dynamics simulation and equivalent-continuum modeling to compute three of the elastic constants of the graphite-epoxy-nanotube system: C11, C22, and C33. The 1-direction is along the nanotube axis, and the graphene sheets lie in the 1-2 plane. It was found that the C11 is only 4% larger than the C22. The nanotube therefore does have a small, but positive effect on the constitutive properties in the interlaminar region.