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DOE OSTI2025

Evaluating design safety margins in the American Society of Mechanical Engineers graphite core components design-by-analysis assessments

Graphite is an important material being used for core components in next-generation high-temperature gas-cooled nuclear reactors. The selection of graphite grade for a specific Designer is a complex task, dependent on reactor conditions, component functionality, and required reliability. The American Society of Mechanical Engineers (ASME) provides two semi-probabilistic design-by-analysis assessments to evaluate graphite core components against design reliability targets. The simplified assessment uses a 2-parameter Weibull distribution to describe the graphite grade’s tensile-strength distribution to establish component stress limits. The full assessment uses the 3-parameter Weibull distribution and a modified Weakest-Link Theory approach to calculate a component design probability of failure. The paper defines recommended assessment rules, which are the as-written simplified assessment and the full assessment with parameter lower bounds, the modulus update with threshold reduction, and the 2027 grouping rules. Code rules are applied to three grades: 2114, IG-110, and NBG-18. The baseline margin calculation is developed using the experimental tensile dogbone specimen. Percent margin is defined as the percent reduction in the median experimental load to obtain the allowable load per ASME assessments. Under the recommended rules, the SRC–1 margin in the simplified assessment ranged from 40.2 % to 52.7 % among the grades in this study and from 36.1 % to 49.8 % in the full assessment. The full assessment only decreases the margins by 2.5–4.5 % for the SRC-1 components and 0–1.5 % for the SRC-2 components for this baseline case. Margin is inversely related to material median strength (i.e., the strongest grade, 2114, has the lowest margin).

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Evaluating Fracture Behavior of Bioinspired Alumina-YSZ Composites through Static and Dynamic Mechanical Testing

Ceramic materials are known for their high hardness and strength but are limited by low toughness and sudden failure. Inspired by the microstructure of dental enamel, which features undulating rods that promote crack deflection and energy absorption, architected specimens were designed and manufactured. A bespoke ball-on-ring (BoR) testing apparatus measured the static biaxial rupture strength of these bioinspired materials. Additionally, impact testing with spherical steel projectiles assessed their behavior under dynamic conditions. Monolithic alumina specimens were compared to architected alumina reinforced with yttria-stabilized zirconia (YSZ) rods produced via direct ink write 3D printing. BoR tests revealed that monolithic alumina had a Weibull modulus of 10.53 and a characteristic strength of 372.3 MPa, while the composite specimens showed a Weibull modulus of 5.46 and a characteristic strength of 213.3 MPa. Although the composite failed at lower stresses and projectile velocities, it exhibited notable crack deflection and fracture resistance, with cracks being effectively interrupted by the rod inclusions. The composite specimens also resulted in fewer and larger fragments upon impact. Finite element simulations confirmed the effectiveness of the rod structures in enhancing fracture resistance.

Bioinspired materials↗

DOE OSTI2023

FINITE ELEMENT MODEL MESH REFINEMENT EFFECTS ON QUALIFICATION OF NUCLEAR GRADE GRAPHITE COMPONENTS

The American Society of Mechanical Engineers (ASME) provides the full and simplified design-by-analysis probabilistic assessments for determining acceptance of nuclear grade graphite core components. The assessments can be characterized by three parts: (1) a component stress distribution, often determined by a finite element (FE) model; (2) a Weibull probability density function (pdf) that characterizes the experimental tensile strength distribution; and (3) the post-processor, which combines the FE model and the Weibull strength distribution in accordance with the full and simplified assessments to determine component acceptance. It is known that the level of mesh refinement in FE models can affect the modeled component’s calculated stress distribution. Depending on the component geometry, the stress distribution may converge with sufficient refinement. It was previously unknown whether the acceptance decision resulting from the full and simplified assessments might change even with sufficient mesh refinement. This study explores that question using experimental strength results for a dog-bone geometry for two graphite grades, IG-110 and PCEA. The simplified assessment has two criteria that must be met, the first limits the combined membrane stress by the allowable stress and the second limits the peak equivalent stress by the allowable stress scaled by the ratio of flexural to tensile strength. In the application of the simplified assessment, convergence of the peak equivalent stress required extreme mesh refinement, however, the acceptance decision was not affected. It is hypothesized that more complex geometries with stress concentrations may present mesh refinement effects on the simplified assessment acceptance decision. Mesh refinement did affect the acceptance decision in the full assessment for the applied pressure loadings in this study. This work suggests component stress distribution convergence is not a sufficient criteria for POF convergence in the full assessment and that mesh refinement should continue until the POF has converged, especially where the resulting POF is bordering the SRC acceptable POF limit.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Additive manufacturing of mullite ceramic by digital light processing

Mullite material was successfully additively manufactured using digital light processing (DLP). The printed geometry involves a one-step process of pyrolysis, de-binding, and sintering under a plain atmosphere to achieve an average of 76 % ceramic yield and linear shrinkage of 12 %. Furthermore, the thermal profile was carefully controlled to obtain consistent phases in which the XRD shows a mullite phase. Here, in addition, the Weibull analysis was conducted on the sintered flexural specimens, showing a Weibull modulus (m) of 13.05 with a characteristic strength (σ 0 ) of 94.96 MPa. Synchrotron microtomography was performed on the sintered specimens, which showed two distinct porosity distributions (small and large). Large porosity (non-spherical elongated) is the primary cause of decreased material strength, while small porosity (spherical) is the sintering product. The measured thermal conductivity of the specimens was in the range of 2.7–3.1 W/m∙k and decreased with an increase in temperature. Lastly, large-scale prototypes were printed concurrently with a fine resolution of 25 μm without any compromise on the predetermined design and structure.

Additive manufacturing↗

DOE OSTI2021

Processing and mechanical characterization of short carbon fiber-reinforced epoxy composites for material extrusion additive manufacturing

Fiber-reinforced polymer composites have been extensively utilized in recent years as feedstock materials for material extrusion additive manufacturing (AM) processes to improve strength, stiffness, and functionality of printed parts over unfilled printed polymers. However, the widespread adoption of AM of fiber-reinforced polymer composites requires a deeper understanding of the process-structure-property relationships in printed components, and such relationships are not well understood yet. Fiber length is critically important to the mechanical performance of short fiber composites, but very few studies to-date have focused on how the fiber length distribution (FLD) evolves during processing of composite feedstocks and how this evolution affects printing behavior and mechanical properties in 3D-printed composites. Here, FLD is measured for carbon fiber reinforced epoxy composites over a wide range of ink compositions and shear mixing times, and the distributions are fit with a Weibull-type distribution function. The effects of FLD on the tradeoff between ink processability, ink rheology, printing behavior and mechanical properties are investigated. Furthermore, the effects of printing parameters (nozzle size and print speed) on mechanical anisotropy and fiber orientation distribution (FOD) in printed composites are explored. Mechanical properties of printed composites are characterized via 3 pt-flexural testing, and microstructure is investigated using optical and scanning electron microscopy (SEM), and x-ray computed tomography. Finally, the fitted Weibull parameters are fed into a composite model that incorporates FLD and FOD, and model predictions are found to be in excellent agreement with experimental observations.

3D printing↗

DOE OSTI2019

Modeling reactivity insertion experiments of TRISO particles in NSRR using BISON

This research presents BISON simulations of stress, temperature, and failure probability of tristructural isotropic (TRISO) fuel particles subjected to transient power pulse conditions in the Nuclear Safety Research Reactor (NSRR). We report that by modifying the default elastic properties of the PyC and the UO 2 coefficient of thermal expansion correlation, BISON was found to produce suitable agreement with the observed and independently simulated results when appropriate shape and scale Weibull parameters for SiC failure were chosen. The Weibull parameter effects were also explored within the range of SiC failure and were applied using experimental data from hemispherical crush testing.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Failure evaluation of neutron-irradiated SiC/SiC composites by underwater acoustic emission

Here, understanding the statistical properties of mechanical properties of non-irradiated and neutron-irradiated SiC/SiC composites is essential for component design. This study aims to evaluate the detailed damage accumulation behavior of composites focusing on two fracture parameters: proportional limit stress (PLS) and acoustic emission (AE) onset stress. The developmental underwater AE technique, which is benefit in non-contact in-situ failure monitoring method during mechanical testing and in handle of the irradiated material, was first applied to evaluate damage accumulation behavior. Two types of chemical vapor infiltration SiC/SiC composites were used: one reinforced with Hi-Nicalon Type-S SiC fiber and one reinforced with Tyranno-SA3 SiC fiber in the form of satin-woven 2D fabrics with pyrolytic carbon interface. Neutron irradiation in the High Flux Isotope Reactor at Oak Ridge National Laboratory reached a fluence of 30 dpa at a temperature of 620–670°C. Four-point flexural tests were conducted to evaluate post-irradiation strength. Weibull statistics did not suggest marked degradation of composite strength. Detailed failure behavior evaluated by AE demonstrated no irradiation-induced change of the AE onset stress (i.e., crack initiation equivalent stress). Failure probability analysis suggests that increasing the reliability of composites (i.e., the Weibull modulus rather than strength itself) is essential to expanding the design margin and benefiting from a probabilistic design approach.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Understanding the effect of specimen size on the properties of fine-grain isotropic nuclear graphite for irradiation studies: Mechanical properties

Programs at Oak Ridge National Laboratory are investigating the effects of neutron irradiation in the High Flux Isotope Reactor (HFIR) on properties of fine-grain isotropic nuclear graphites. Specimens were irradiated in the HFIR flux trap, which requires using specimens that are smaller than the sizes recommended by ASTM standards. Here, this work has investigated whether subsized specimens can be used to reliably predict strength behavior. The results show that (1) tensile strength was loosely coupled to specimen volume, (2) the compression specimens had a slightly higher strength for larger volumes, (3) the uniaxial flexural strength was nearly independent of specimen effective area for one orientation whereas the other orientation showed a slight strength–size scaling Weibull behavior, and (4) equibiaxial flexural strength followed traditional strength–size scaling Weibull behavior. These results suggest that fine-grain graphite is more similar to ceramics than to medium- and large-grained graphite with respect to both the strength-limiting flaws (Griffith theory) and the effect of machining on the strength behavior. This work shows that using specimens that are smaller than ASTM recommendations are suitable for investigating the strength changes caused by neutron irradiation because the primary interest is the relative change in the strength distribution parameters rather than their absolute values.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Determining reference standard strength for neutron-irradiated reduced activation ferritic/martensitic steel F82H by Bayesian method

The deterministic approach widely adopted in the design of structural components relies on systematically defined design limits using empirically determined safety factors. However, this approach is not always appropriate because structures are subjected to a variety of loads in the practical environment, which may result in excessively conservative design limits. In recent years, a more rigorous probabilistic approach that incorporates material strength distributions has become an important solution. In the probabilistic approach, the probability density functions of material strength properties underpin the design criteria. Here, the objective of this study is to identify the density distribution functions that best describe tensile properties of irradiated F82H to define a reference strength for DEMO design. Due to the limited number of existing data, this study specifically employs a Bayesian prediction method based on Monte Carlo simulations to determine a material reference value with statistical reliability and to investigate its effectiveness. For example, the dependence of tensile properties of 300 °C irradiated materials on irradiation damage and the range predicted by 95% Bayesian estimation was evaluated. As a statistical model for the dose dependence of statistical parameters, the normal distribution exhibited a better fit for 0.2% proof strength and tensile strength, whereas the distribution of total elongation data gave comparable reference values for both the normal and Weibull distribution models. Both models gave comparable criteria for the distribution of total elongation data. The Weibull model also gave better results for uniform elongation. The function best describing the model was a logarithmic law for both 0.2% proof strength and tensile strength, while a power law for both total and uniform elongation, which allowed for more comprehensive data prediction of irradiation data with statistical accuracy for DEMO reactor design.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Thermal shock resistance of additively manufactured alumina

The mechanical behavior and cracking patterns of thermally-shocked additively manufactured alumina were investigated. The flexural strength of test specimens that had been heated to temperatures ranging from 200°C to 1000°C and then rapidly quenched in water was determined at ambient temperature by four-point bending. Results indicated that the surface cracking patterns had a multifractal structure and that an increase in the thermal shock temperature led to an increase in the density and uniformity of the crack network. Further, the flexural strength results were analyzed with Weibull statistics, where the Weibull moduli for most of the thermal shock conditions tested were found to be statistically indistinguishable. It was also found that a significant decrease (~50%) in flexural strength occurred for heating temperatures ≥300°C. The effect of the manufacturing method on cracking patterns is discussed, as well as the implication of the material behavior for practical applications of these materials.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Size effects in 3D–printed polymer–derived, zirconium diboride–reinforced ceramic composites

Preceramic polymers are of interest for use in many manufacturing techniques such as injection molding, ceramic fiber infiltration, and additive manufacturing. However, off-gassing of low molecular weight oligomers occurs when these polymers cure, potentially leading to porosity in the cured part. Here to study how porosity and strength are affected by the size of the printed part, and the presence of a high surface area nano-scale filler, polycarbosilane (PCS) microrods of varying diameter were fabricated via direct ink writing (DIW), an additive manufacturing technique, with two ink formulations containing either zirconium diboride (ZrB 2 ) alone, or ZrB 2 and fumed alumina (FA). Sets of microrods were printed in a range of sizes by using print nozzles of 450, 634, 979, 1 346, or 1 702 μm in diameter, which were thermally cured, pyrolyzed to form ceramic composite microrods, and tested in 3-pt flexure. Porosity increased with increasing diameter, while failure strength decreased. For a given nozzle size, the microrods containing FA displayed lower porosity and higher strength (up to ~500 MPa) compared to the microrods containing only ZrB 2 . Weibull strength analysis was performed on each group of microrods and shows that the addition of FA increased Weibull modulus from 4.63 ± 1.56 to 9.35 ± 0.601. In conjunction with optical microscopy, this analysis indicates two distinct flaw populations in the printed materials, porosity which arises during the curing step and cracking which arises during pyrolysis of the larger specimens.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Integrating high resolution drone imagery and forest inventory to distinguish canopy and understory trees and quantify their contributions to forest structure and dynamics

Tree growth and survival differ strongly between canopy trees (those directly exposed to overhead light), and understory trees. However, the structural complexity of many tropical forests makes it difficult to determine canopy positions. The integration of remote sensing and ground-based data enables this determination and measurements of how canopy and understory trees differ in structure and dynamics. Here we analyzed 2 cm resolution RGB imagery collected by a Remotely Piloted Aircraft System (RPAS), also known as drone, together with two decades of bi-annual tree censuses for 2 ha of old growth forest in the Central Amazon. We delineated all crowns visible in the imagery and linked each crown to a tagged stem through field work. Canopy trees constituted 40% of the 1244 inventoried trees with diameter at breast height (DBH) > 10 cm, and accounted for ~70% of aboveground carbon stocks and wood productivity. The probability of being in the canopy increased logistically with tree diameter, passing through 50% at 23.5 cm DBH. Diameter growth was on average twice as large in canopy trees as in understory trees. Growth rates were unrelated to diameter in canopy trees and positively related to diameter in understory trees, consistent with the idea that light availability increases with diameter in the understory but not the canopy. The whole stand size distribution was best fit by a Weibull distribution, whereas the separate size distributions of understory trees or canopy trees > 25 cm DBH were equally well fit by exponential and Weibull distributions, consistent with mechanistic forest models. The identification and field mapping of crowns seen in a high resolution orthomosaic revealed new patterns in the structure and dynamics of trees of canopy vs. understory at this site, demonstrating the value of traditional tree censuses with drone remote sensing.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Comparative Study of Wind Energy Potential Estimation Methods for Wind Sites in Togo and Benin (West Sub-Saharan Africa)

The characterization of wind speed distribution and the optimal assessment of wind energy potential are critical factors in selecting a suitable site for wind power plants (WPP). The Weibull distribution law has been used extensively to analyze the wind characteristics of candidate WPP sites, and to estimate the available and deliverable energy. This paper presents a comparative study of five wind energy resource assessment methods as they applied to the context of wind sites in West Sub-Saharan Africa. We investigated three numerical approaches, namely, the adaptive neuro-fuzzy inference system (ANFIS), the multilayer perceptron method (MLP), and support vector regression (SVR), to derive the distribution law of wind speeds and to optimally quantify the corresponding wind energy potential. Next, we compared these three approaches to two well-known Weibull distribution law-based methods: the empirical method of Justus (EMJ) and the maximum likelihood method (MLM). Case study results indicated that the neural network-based methods, ANFIS and MLP, yielded the most accurate distribution fits and wind energy potential estimates, and consequently, are the most recommended methods for the wind sites in Togo and Benin. The orders of magnitude of the root mean squared error (RMSE) in estimating the recoverable energy using ANFIS were, respectively, 10-4 and 10-5 for Lomé and Cotonou, while MLP achieved an RMSE order of magnitude of 10-3 for both sites.

17 WIND ENERGY↗

DOE OSTI2022

Initial ASME code rule analysis on Simple and Full assessment

ASME & ASTM codes present simple and full assessment methodologies to qualify nuclear grade graphite components. This report explains the theory behind the statistical portion of the codes and describes the issues discussed in a 2020 workshop in the simple assessment, as well as the full assessment. The methodology for the full assessment was developed by Hindley []. He used a validation methodology to match the experimental average failure load of test specimens from several geometries to the calculated 50% POF load to tune the grouping criteria parameters based on an RMSE penalty function. The grouping criteria consists of a minimum volume to satisfy the weakest link theory of the Weibull distribution and a minimum stress range parameter. Hindley’s work found a minimum link volume of 10 times the grain size and a stress range parameter of 7% [satisfy the validation requirements. Several studies found that the link volume of 10 times the grain size was not satisfactory for the volume grouping criteria for graphite grades with fine grains. ASME 2021 code adopted a new volume grouping criteria based on fracture toughness for calculation of the process zone volume. However, errors were found in the ASME 2021 code process zone volume equation and the question is now open as to what volume grouping criteria is satisfactory. This report presents results from sensitivity studies that were done to evaluate the volume grouping criteria effect on the full assessment POF. This report also presents results from sensitivity studies on other aspects of the code that affect the POF, the mesh size and the choice of the Weibull threshold parameter. All three sensitivity studies: the volume grouping criteria, the mesh size, and the threshold parameter choice are found to affect the component qualification decision for components of structural reliability class 1 (SRC-1). The sensitivity analysis results are presented in the body of the report for NBG-18, which is the same grade of graphite as Hindley used in his thesis. Results from NBG-17, IG-110, 2114, and PCEA are presented in the Appendix. For NBG-18, it was found that increasing the threshold increases the POF, finer meshes result in higher POFs, and that smaller link volume requirements lead to higher POFs (which is inconsistent with Hindley’s findings). This report proposes a new validation study similar to Hindley’s []. The purpose of the new validation study is to tune the threshold, mesh size and grouping criteria based on results from multiple grades of graphite, including finer grain graphites T220 (1-3 microns) and NG-CT-50 (5 microns). The test specimens will be broken at 3 labs, such that we can measure between lab measurement variability, with at least 5 test specimens per lab such that the within lab uncertainty can also be measured. Hindley’s validation method tried matching the average experimental load with the median. The future study will attempt to match failures at lower percentiles, which would be closer to the SRC POF limit. We are currently looking into what geometries make sense and the best method to measure multi-axial stress states. These design decisions are still being set.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A method for predicting failure statistics for steady state elevated temperature structural components

This paper presents the initial development of a high temperature life prediction method that accounts for the variability in the material properties of Grade 91 steel. The method accounts for material variability by fitting a variable 3-parameter Weibull distribution to experimental rupture data and accounts for the variability of creep deformation on the steady-state stresses via a Monte Carlo approach. To ensure reasonable computational times, the model represents the material as an extremely viscous Stokes fluid with a non-Newtonian viscosity, therefore solving the stress relaxation problem with a steady, static, instead of transient, analysis. Furthermore, the complete statistical analysis combines this model for creep deformation with a probabilistic model for creep rupture to evaluate the probability of premature failure for a set of sample problems, comparing the predicted failure statistics to the design life predicted by the ASME Boiler and Pressure Vessel Code rules.

42 ENGINEERING↗

DOE OSTI2022

Mechanical evaluation of WC-Co materials with varying microstructures

Tungsten carbide–cobalt materials are useful in a variety of extreme applications due to a desirable blend of properties, yet the technology has not significantly changed since their initial development in the 1920s. The mechanical properties of this class of materials is highly dependent on two variables, the size of the tungsten carbide grains, and the amount of binder phase present in the final body. In this study, the amount of binder phase is isolated across three commercial materials from the same manufacturer with three different grain sizes to investigate the effect on mechanical properties. The mechanical properties investigated are indentation hardness, flexure and tensile strength, as well as fracture toughness. In general, an increase in hardness and tensile strength with decreasing grain size was observed, while the fracture toughness showed the opposite trend with toughness increasing with increasing grain size. The flexure strength results did not show a correlation to grain size. Fractographic analysis identified the dominant strength-limiting flaw for each sample, which largely were in the form of porosity. Other flaws types, such as inclusions from the milling process, clusters of large grains, and machining cracks from the surface finishing process, were also identified. Finally, Weibull analysis was performed and deemed appropriate for analysis of these materials, but strength-size scaling was not conducted due to the variability in the strength-limiting feature between the different specimen geometries.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Mechanical Properties of Irradiated U-10 wt. %Mo Alloy Degraded by Porosity Development

In this study, a plate-type nuclear fuel consisting of a solid monolithic foil of U-10 wt. %Mo is under development for use in the United States' high-performance research reactors. In support of developing this fuel, the fuel has been fabricated for the first time by a commercial fuel vendor and subsequently irradiated in a test reactor. This provides an opportunity to evaluate postirradiation mechanical properties of the commercially fabricated fuel. Four-point bend testing was conducted on the irradiated U-10Mo samples to generate the fuel material properties, including the modulus of elasticity and the bending strength. Although the material behaves in a brittle manner due to the accumulated porosity, a general trend of strength and modulus reduction was found as fission density increases. The data produced was evaluated using both Weibull statistics and a modulus degradation model with recommendations provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Thermo-Mechanical Modeling and Evaluation of the Cracking Response of Additively Manufactured Monolithic SiC Lattice Structures Subjected to Laser Heating

Increasing operating temperatures of solar receivers is paramount to the efficiency of concentrated solar thermal (CST) and solar power (CSP) systems. Owing to its high temperature stability combined with excellent thermal and optical properties, SiC has been the material of choice for application in high-temperature solar receivers. The state-of-the-art SiC volumetric concentrating solar air receivers such as honeycomb design have been demonstrated in field tests to achieve exit air temperatures approaching 800oC. However, successful application of CST systems for decarbonization requires significant increase in temperature capability of SiC receiver technology. Supported by an award from the Solar Technology Office (SETO), US Department of Energy (DOE), GE Research in collaboration with Heliogen Holdings Inc, is engaged in the development of ultra-High Operating Temperature SiC-matrix Solar Thermal Air Receiver (HOTSSTAR) enabled by additive manufacturing. The program objective is to design and to demonstrate a techno-economically viable SiC air receiver technology to achieve exit air temperature of 1100oC for CST applications. This report summarizes the learnings of a computational study on additively manufactured SiC lattice structures subjected to laser heating. The results from this study aim to help guide the design of a SiC receiver through a better understanding of lattice structure geometric parameters and their implications on the cracking response of the structure. In the study, a heat flux was applied to the surface of a 2”-diameter cylindrical lattice structure to simulate a 4kW CO2 laser. The resulting temperature distribution was applied to a structural model to approximate the stress distribution within the lattice structure and a Weibull analysis was performed to gain insight into the probability of failure and to evaluate the cracking response of the structure. With this approach, the influence of lattice density on temperature, stress, and probability of failure was explored for two different lattice beam spacings. A discussion on modeling assumptions, a comparison with experimental results, and an evaluation of the lattice cracking response is provided.

14 SOLAR ENERGY↗