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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Statistical analysis of S—N type environmental fatigue data of Ni-base alloy welds using weibull distribution

In this study, the probabilistic fatigue life model for Ni-base alloys was developed based on the Weibull distribution using statistical analysis of fatigue data reported in NUREG/CR-6909 and the new fatigue data of Alloy 52M/152 and 82/182. The developed Weibull model can consider right-censored data (i.e., non-failed data) and quantify the improved safety (or reliability) based on the level of failure probability. The overall margin in the current fatigue design limit model (ASME design curve + NUREG/CR-6909 F en model) is similar to that of the Weibull model with a cumulative failure probability of approximately 2.5%. The margin in the current fatigue design limit model demonstrated inconsistencies for the Ni-base alloy weld data, whereas the Weibull model showed a consistent margin. Therefore, the Weibull model can systematically mitigate the excessive safety margin.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Employing Weibull Analysis and Weakest Link Theory to Resolve Crystalline Silicon PV Cell Strength Between Bare Cells and Reduced- and Full-Sized Modules

Weibull analysis and weakest link theory are employed to resolve the probability of crystalline silicon PV cell fracture when measured as bare cells and when stressed in reduced- and full-sized modules. Experimental results indicated that the characteristic cell strength is reduced by ~20% once packaged into the laminate of a one-cell module and loaded in four-point flexure (4PF). This experimental observation was shown consistent with a weakest link theory prediction that the strength limiting flaws reside on the surface of the cell's edge. Here, the analysis is ultimately extended to present the equivalent loading of four-cell modules by uniform pressure and 4PF and a uniformly loaded full-sized module and demonstrates that smaller, representative, modules must be loaded to a much higher level than their parent full-sized modules to achieve an equivalent probability for cell fracture.

14 SOLAR ENERGY↗
DOE OSTI2022

Equibiaxial Flexure Strength of a Superfine-Grained Nuclear Graphite

The strength of advanced graphite is reported in accordance with ASTM D7846-16 using a two-parameter Weibull distribution for uniaxial strength testing. The rule of thumb for Weibull distributions is to use a minimum of 30 strength measurements to have a high level of confidence in the Weibull characteristic strength and the Weibull modulus. These large sample sets for statistical confidence are easily obtained for as-manufactured graphite, but determination of the Weibull two-factor parameters on graphite that has been exposed to neutron irradiation is nearly impossible due to irradiation testing restraints on specimen size and space limitations in test reactors for the accommodation of specimens. These restrictions have resulted in irradiation programs that use sub-sized specimens to measure uniaxial strength change, but the specimen geometries still hinder the number of replicate specimens for each irradiation condition. In contrast, this work used an advanced ceramic standard, ASTM C1499-05, as the foundation for equibiaxial strength testing of a superfine-grained nuclear graphite to investigate the irradiation-induced strength change and any changes to the two-parameter Weibull distribution. The goal was to investigate the effect of specimen size on the two-parameter Weibull distribution parameters in support of the small specimens and geometry desired for irradiation. A study of the effect of a reduced sample population was also undertaken to investigate the reliability of using the two-parameter Weibull distribution to study changes to the materials properties caused by neutron irradiation damage. The results of this work suggest that these equibiaxial specimens would be ideal for statistically significant studies of the effects of irradiation on the Weibull characteristic strength (but not the modulus) and for providing a method for surveillance specimen campaigns for future operating commercial reactors.

Campbell, Anne↗
DOE OSTI2022

Sensitivity analysis applied to SiC failure probability in TRISO modeled with BISON

Here, a sensitivity analysis on the failure probability of the Silicon Carbide (SiC) layer in tristructural isotropic (TRISO) nuclear fuel during transient conditions predicted by the BISON fuel performance code is performed. The principal goal of the analysis is to understand the most important parameters dictating SiC failure behavior in BISON during Reactivity Initiated Accidents (RIAs). SiC brittle fracture probability is modeled using Weibull statistics. A total of seven inputs related to SiC failure has been selected for the analysis, including the Weibull statistics parameters, elastic moduli for SiC and Pyrolitic Carbon (PyC) and SiC stress-free temperature. A 1D TRISO BISON model has been established for various reactivity insertions performed at the Nuclear Safety Research Reactor (NSRR). The principal advantage associated with the 1D TRISO model developed in this work is its computational efficiency. The Sobol variance decomposition method is used, and the sensitivity indices are presented for eight different values of the energy deposition. The results show that the two most important parameters impacting the predicted SiC failure probability are the Weibull modulus and the characteristic stress, and a co-variance amongst these parameters is obtained for low reactivity insertions. An additional new finding of this work is that the relative importance of Weibull parameters depends on the energy deposition, and thus reactivity, regime. For low energy depositions, two parameters are of influence on SiC failure probability, while for high energy depositions only one parameter impacts failure probability results. Moreover, optimization of the Weibull modulus and characteristic stress is performed by minimizing the RMSE between BISON failure probability predictions and experimental failure fractions for each energy deposition. This work also demonstrates the validity of the NSRR tests BISON simulations and of the respective sensitivity analysis results as conservative, yet indicative for slower transients characterized by lower deposited energies. Such verification is achieved through the partial extension of the analysis to a group Control Rod Withdrawal reproduced from a previous study. Another novel result of this analysis is that no single set of Weibull parameters can reproduce all reactivity insertion experimental failure results, which is related to the intrinsic nature of SiC failure properties, and a new range for the parameters is proposed to produce a failure probability envelope that encompasses the experimental fractions. Additionaly, this work proposes a new approach for future failure analysis with BISON, consisting in the use of Weibull parameters ranges, rather than fixed sets, along with failure envelopes generation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Equibiaxial flexural strength determination of UO 2 using a ball-on-ring test

To increase nuclear fuel performance and reliability, their mechanical properties require an accurate and statistically relevant assessment. Biaxial flexural strength tests provide an alternative to bend bar techniques for assessing mechanical behavior; namely, the transverse rupture strength (TRS) of ceramic samples. Biaxial test samples require simple geometries and minimal surface preparation, reducing fabrication costs and handling hazards. This study investigated the TRS of polycrystalline UO 2 fuel forms at room temperature using a ball-on-ring test fixture. Here, pellets were fabricated from UO 2 powder using conventional powder processing and sintering techniques. The TRS and Weibull parameters were obtained through Weibull statistics on over 60 UO 2 samples tested under equibiaxial flexure. The larger sample size in this study enabled a more robust Weibull statistical analysis than alternative test methods, which may not capture the stochastic failure of typical ceramics. Furthermore, two different loading ball diameters were employed to assess the impact of contact damage on fracture strength. While Hertzian contact damage was observed with the smaller loading ball, the fracture strength remained unaffected. A fracture analysis of the tested UO 2 samples indicated a mixture of intergranular and transgranular fracture that transitions to transgranular fracture with increasing distance from the fracture origin. The characteristic strength of the combined data sets was determined to be 148 MPa, and the Weibull modulus was determined to be 9.1. The TRS values and Weibull parameters were close to values found in the literature for alternative testing techniques using samples with similar microstructure and density. The findings in this study validate the ball-on-ring method used to obtain the TRS of UO 2 with a sample geometry more representative of nuclear fuels. Additionally, experimental TRS results from this study can be implemented in modeling codes to predict fuel performance, which is critical to fuel burnup extension and advanced nuclear fuel technologies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

TRISO SiC Failure Probability for Reactivity Initiated Accidents in High-Temperature Gas-Cooled Reactors

This work analyzes the failure process of the silicon carbide (SiC) layer in tristructural isotropic (TRISO) during reactivity-initiated accident scenarios for a high-temperature gas-cooled reactor (HTGR) with BISON. Two cases are considered—a group control rod withdrawal (CRW) and a control rod ejection (CRE)—reproduced from a previous study. Failure probability is modeled using Weibull statistics, and worst-case scenario Weibull parameters are adopted to simulate the envelopes in BISON with a one-dimensional TRISO model. CRW scenario results are characterized by higher values of maximum energy deposition and final temperature and volumetric strain with respect to the CRE ones, but the latter have remarkably higher SiC failure probability, mainly due to the offset in strain rates between the two cases. This work also confirms the validity and conservatism of the performance envelopes produced in a previous work by replicating the envelope formulation using RELAP5-3D and RAVEN with a different sampling technique and obtaining consistent results. A sensitivity analysis using the Sobol variance decomposition method on SiC failure probability is then performed involving a set of inputs on both CRW and CRE. The two most important parameters are Weibull modulus and characteristic stress, and their relative importance depends on the specific case. The proposed interpretation of the results is that both energy deposition and strain rate influence the relative degree of importance of the failure parameters. Computation of 95% confidence intervals around worst-case scenario SiC failure probability values is also carried out for four different sets of Weibull parameters. Heren a new criterion for SiC TRISO quality classification built upon safety-based ranges of Weibull parameters is proposed to be integrated in future Fuel-Production Quality Assurance Plans.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Ball-on-ring test validation for equibiaxial flexural strength testing of engineered ceramics

The validation of a ball-on-ring, equibiaxial flexural strength method to obtain the transverse rupture strength (TRS) of right cylindrical ceramic specimens was performed in this study. Validation of the test method was achieved using commercially available engineered high purity alumina disks and finite element (FE) model analysis. The validated fixture was then used to obtain the TRS and Weibull statistical analysis of MgO-partially stabilized zirconia (MSZ) and Y 2 O 3 -partially stabilized zirconia (YSZ) ceramic disks. TRS data for alumina, MSZ, and YSZ agreed with the TRS values reported in the literature. A statistically relevant number of samples (N > 30) for each material were tested to allow for a Weibull statistical analysis. Weibull parameters for these materials were within the expected values for engineered ceramics. The characteristic strength for alumina, MSZ, and YSZ were determined to be 289, 786, and 814 MPa, respectively. The Weibull modulus was determined between 10 and 25 for each material, which is typical of engineered ceramics. In addition, FE model results were in close agreement with experimental fracture values for the three ceramic materials tested in this study.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Clutter Distributions for Tomographic Image Standardization in Ground-Penetrating Radar

Multistatic ground-penetrating radar (GPR) signals can be imaged tomographically to produce 3-D distributions of image intensities. In the absence of objects of interest, these intensities can be considered to be estimates of clutter. These clutter intensities spatially vary over several orders of magnitude and vary across different arrays, which makes a direct comparison of these raw intensities difficult. However, by gathering statistics on these intensities and their spatial variation, a variety of metrics can be determined. In this study, the clutter distribution is found to fit better to a two-parameter Weibull distribution than Gaussian or log-normal distributions. Based on the spatial variation of the two Weibull parameters, scale and shape, more information may be gleaned from these data. How well the GPR array is illuminating various parts of the ground, in depth and cross track, may be determined from the spatial variation of the Weibull scale parameter, which may in turn be used to estimate an effective attenuation coefficient in the soil. The transition in depth from clutter- to noise-limited conditions (which is one possible definition of GPR penetration depth) can be estimated from the spatial variation of the Weibull shape parameter. Lastly, the underlying clutter distributions also provide an opportunity to standardize image intensities to determine when a statistically significant deviation from background (clutter) has occurred, which is convenient for buried threat detection algorithm development that needs to be robust across multiple different arrays.

42 ENGINEERING↗
DOE OSTI2024

Microstructural characterization and equibiaxial flexural strength of CeO 2 and Ti-doped CeO 2

In this study, the synthesis of CeO 2 and titanium dioxide (TiO 2 ) doped CeO 2 (TDC) monoliths are investigated, and their fracture strength is assessed using an equibiaxial flexure testing technique at room temperature. Pellets were synthesized using conventional powder processing and sintering methods to produce the desired characteristics. The TiO 2 dopant concentration was optimized at 0.1 wt % TiO 2 to obtain dense, solid-solution pellets with an enhanced grain microstructure. A ball-on-ring fixture was used to obtain the TRS and Weibull parameters of over 30 pellets for CeO 2 and 0.1 wt % TDC to compare fracture behavior. The TRS of CeO 2 pellets ranged from 88 to 160 MPa and the TRS of 0.1 wt % TDC pellets ranged from 102 to 171 MPa, both being consistent with published values. Weibull parameters, such as characteristic strength and Weibull modulus, were extracted as 129 MPa and 8.5 for CeO 2 and 150 MPa and 9.3 for 0.1 wt % TDC, respectively. Although Hertzian contact damage was observed on compressive surfaces, failure initiation occurred on the tensile surfaces of both types of samples. Fracture surface analysis for CeO 2 indicated a predominantly intergranular fracture while 0.1 wt % TDC had a predominantly transgranular fracture mode. Finally, the TRS of 0.1 wt % TDC resulted in increased Weibull parameters when compared to CeO 2 , indicating sample chemistry and microstructure impact mechanical behavior for these samples.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Flexural strength of a conventionally processed and additively manufactured debased 94% alumina

Mechanical strength of a 94 wt% debased alumina was measured using ASTM-C1161 specimens fabricated via conventional and lithography-based ceramic manufacturing (LCM) methods. The effects of build orientation and a 1500°C wet hydrogen fire added to the LCM firing sequence on strength were evaluated. Additionally, a Weibull fit to the conventional flexural specimen data yielded 20 and 356 MPa for the modulus and characteristic strength, respectively. Weibull fits of the data from the LCM specimens yielded moduli between 7.5 and 11.3 and characteristics strengths between 333 and 339 MPa. A Weibull fit to data from LCM specimens subjected to the wet hydrogen fire yielded 14.2 and 376 MPa for the modulus and characteristic strength, respectively. The 95% confidence intervals for all Weibull parameters are reported. Average Archimedes bulk densities of LCM and conventional specimens were 3.732 and 3.730 g/cm 3 , respectively. Process dependent differences in surface morphology were observed in scanning electron microscope (SEM) images of specimen surfaces. SEM images of LCM specimen cross-sections showed alumina grain texture dependent on build direction, but no evidence of porosity concentrated in planes between printed layers. Fracture surfaces of LCM and conventionally processed specimens revealed hackle lines and mirror regions indicative of fracture initiation at the sample surface rather than the interior.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Joint Modeling of Wind Speed and Wind Direction Through a Conditional Approach

Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. In this work, we develop a conditional approach to model these two variables, where the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. To accommodate the circular nature of wind direction, a von Mises mixture model is used; the conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the dependence of the Weibull parameters on wind direction. A Monte Carlo simulation study indicates that our method outperforms two other approaches in estimation efficiency: one that utilizes periodic spline quantile regression and another that generates data from the commonly used Abe-Ley distribution for cylindrical data. We illustrate our method by using the output from a regional climate model to investigate how the joint distribution of wind speed and direction may change under some future climate scenarios. Our method indicates significant changes in the variation of wind speed with respect to some directions.

17 WIND ENERGY↗
DOE OSTI2024

Fracture mechanics approach to TRISO fuel particle failure analysis

Weibull stress-based methods for failure probability assessment have been developed and analyzed to assess the integrity of tristructural isotropic (TRISO) fuel particles during fuel life cycles and accident operating conditions. While simple, these methods entail a number of drawbacks when stress concentrates near crack tips, including finite element mesh size dependency when the Weibull stress is averaged over the finite element domain. Fracture mechanics approaches involving the use of interaction integrals eliminate this lack of mesh convergence and produce consistent fracture predictions. In this work, we use an interaction integral approach to computing stress intensity factors for a crack in the inner pyrolytic carbon layer perpendicular to the silicon carbide layer, which is simplified representation of a failure mode in TRISO particles. Further, the interface between these two TRISO layers has been shown to become porous, which we simulate by considering a transition of mechanical properties over such porous length, i.e. the layers are modeled as a functionally graded material. Aspects such as porosity and thermal and irradiation eigenstrains are considered in computing the stress intensity factor from a fracture mechanics approach and compared with the known Weibull stress failure approach. The methodology introduced in this paper enables a more general fracture probability assessment in TRISO particles and eliminates the need to identify best suited parameters when using local or averaged stress-based failure criterion. Finally, the numerical sensitivity studies show how parameters such as the porous transition zone length, the material stiffness, and creep affect the probability of TRISO fuel particle failure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Accelerated statistical failure analysis of multifidelity TRISO fuel models

Statistical nuclear fuel failure analysis is critical for the design and development of advanced reactor technologies. Although Monte Carlo Sampling (MCS) is a standard method of statistical failure analysis for fuels, the low failure probabilities of some advanced fuel forms and the correspondingly large number of required model evaluations limit its application to low-fidelity (e.g., 1-D) fuel models. In this paper, we present four other statistical methods for fuel failure analysis in Bison, considering tri-structural isotropic (TRISO)-coated particle fuel as a case study. The statistical methods considered are Latin hypercube sampling (LHS), adaptive importance sampling (AIS), subset simulation (SS), and the Weibull theory. Using these methods, we analyzed both 1-D and 2-D representations of TRISO models to compute failure probabilities and the distributions of fuel properties that result in failures. The results of these methods compare well across all TRISO models considered. Overall, SS and the Weibull theory were deemed the most efficient, and can be applied to both 1-D and 2-D TRISO models to compute failure probabilities. Moreover, since SS also characterizes the distribution of parameters that cause TRISO failures, and can consider failure modes not described by the Weibull criterion, it may be preferred over the other methods. Finally, a discussion on the efficacy of different statistical methods of assessing nuclear fuel safety is provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Determining the tensile strength of fuel surrogate TRISO-coated particle buffer, IPyC, and buffer-IPyC interlayer regions

A novel micro tensile sample fabrication technique for determining the tensile strength of the buffer, IPyC, and buffer -IPyC interlayer regions of surrogate (ZrO2) TRISO fuel particle layers was refined and implemented. Copper micro tensile samples served as baseline materials to verify the methods used. Tensile tests performed in this study, while limited in number, were analyzed using standard and Weibull statistics. As expected, the buffer layer was weakest, with an average ultimate tensile strength of 138.70 MPa, and the IPyC layer samples, were strongest, with an average ultimate tensile strength of 189.74 MPa. In the buffer -IPyC interface samples, all breaks occurred in the buffer region, though the average ultimate tensile strength of the samples, 159.80 MPa, was between the pure buffer and IPyC samples. These results suggest the interlayer region has unique properties, perhaps associated with pyrocarbon infiltration into the buffer layer during particle coating. All interlayer samples fractured within the buffer side; however, the stress strain behavior of some of these samples resembled the behavior of the IPyC layer samples. Here, the buffer and IPyC layer strengths had a normal distribution under Weibull analysis, while the interlayer region had a Rayleigh distribution. Further testing is needed to clarify both the standard and Weibull statistical results

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Residual Stress Limits Gridline Bridging in Cracked Solar Cells

Cracks in solar cells can be generated in various ways, but this does not mean immediate power loss. Previous studies showed that gridlines bridge cracked silicon cells, and the bridging behavior decreases during the contact and separation of gridlines within bare cells. In this study, we investigate bridging behavior in laminated monocrystalline cells. We characterize the behavior with Weibull analysis of critical crack opening distance (COD), at which the gridline is completely separated. The Weibull analysis of the laminated cell shows a good agreement with bare cells at the first cycle. However, we observe different behavior during cyclic bending. Bare cells show gradual decay of critical COD, while laminated cells show instant decay and plateau. We hypothesize that the difference is due to residual stress, squeezing gridlines, and causing plastic deformation. This is justified by the correlation between critical COD and gridline morphology. In the presentation, we shall present a Weibull analysis of the cyclic bending of a laminated cell with a reduced residual stress effect.

bending↗
DOE OSTI2025

Statistical fracture behavior of doped UO 2 using a ball-on-ring equibiaxial flexure test method

Metal oxide dopants, such as titanium and chromium oxides, have garnered considerable attention for their potential to increase grain size (≥ 30 µm) in UO 2 fuel, purportedly enhancing fission gas retention during reactor operation. Fuel performance is significantly impacted by fuel fracture behavior, so it is important to understand the effects of enhanced grain size and dopant content on UO 2 fuel fracture. UO 2 pellets were doped with 0.1 wt% TiO 2 and 0.3 wt% Cr 2 O 3 to alter density and grain size. Inductively coupled plasma mass spectroscopy measured dopant levels pre- and post-sintering. X-ray diffraction revealed lattice changes and microstrain via Rietveld refinement. Field emission scanning electron microscopy determined grain sizes of approximately 30 µm for TiO 2 doping and 7 µm for Cr 2 O 3 doping. Transverse rupture strength tests were performed on over 30 samples per dataset to obtain characteristic strength and Weibull modulus. Results indicate no statistical difference in fracture strength between 0.1 wt% TiO 2 doped UO 2 and undoped UO 2 , while 0.3 wt% Cr 2 O 3 doped UO 2 exhibited a 20% decrease in fracture strength. Doped UO 2 samples also showed reduced Weibull modulus compared to undoped UO 2 , suggesting increased scatter in fracture strength. This study's findings suggest that titanium and chromium oxide doping in UO 2 , regardless of grain size, induce residual stresses, decreasing fracture strength and increasing variability in fracture behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗