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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 OSTI2017

On Weibull's Spectrum of Nonrelativistic Energetic Particles at IP Shocks: Observations and Theoretical Interpretation

Some interplanetary shocks are associated with short-term and sharp particle flux enhancements near the shock front. Such intensity enhancements, known as shock-spike events (SSEs), represent a class of relatively energetic phenomena as they may extend to energies of some tens of MeV or even beyond. Here we present an SSE case study in order to shed light on the nature of the particle acceleration involved in this kind of event. Our observations refer to an SSE registered on 2011 October 3 at 22:23 UT, by STEREO B instrumentation when, at a heliocentric distance of 1.08 au, the spacecraft was swept by a perpendicular shock moving away from the Sun. The main finding from the data analysis is that a Weibull distribution represents a good fitting function to the measured particle spectrum over the energy range from 0.1 to 30 MeV. To interpret such an observational result, we provide a theoretical derivation of the Weibull spectrum in the framework of the acceleration by “killed” stochastic processes exhibiting power-law growth in time of the velocity expectation, such as the classical Fermi process. We find an overall coherence between the experimental values of the Weibull spectrum parameters and their physical meaning within the above scenario. Hence, our approach based on the Weibull distribution proves to be useful for understanding SSEs. With regard to the present event, we also provide an alternative explanation of the Weibull spectrum in terms of shock-surfing acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Integrating GLL-Weibull Distribution Within a Bayesian Framework for Life Prediction of Shape Memory Alloy Spring Undergoing Thermo-mechanical Fatigue

The present paper tackles an important but unmapped problem of the reliability estimations of smart materials. First, an experimental setup is developed for accelerated life testing of the shape memory alloy (SMA) springs. Generalized log-linear Weibull (GLL-Weibull) distribution-based novel approach is then developed for SMA spring life estimation. Applied stimulus (voltage), elongation and cycles of operation are used as inputs for the life prediction model. The values of the parameter coefficients of the model provide better interpretability compared to artificial intelligence based life prediction approaches. In addition, the model also considers the effect of operating conditions, making it generic for a range of the operating conditions. Moreover, a Bayesian framework is used to continuously update the prediction with the actual degradation value of the springs, thereby reducing the uncertainty in the data and improving the prediction accuracy. In addition, the deterioration of material with number of cycles is also investigated using thermogravimetric analysis and scanning electron microscopy.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Structure-property relation and Weibull analysis of calcium aluminate cement pastes

Highlights: • Weibull distribution analysis was conducted for calcium aluminate cement pastes with 52 wt% and 71 wt% of alumina contents. • Compressive strength ranged from 10 to 45 MPa. • The hydrated phases found showed diverse polymorphisms of Gibbsite (Nordstrandite, Bayerite, Hidrogarnet and Gehlenite). - Abstract: In this investigation calcium aluminate cement (CAC) pastes with 52 wt% and 71 wt% of alumina contents were fabricated and characterized with different techniques. Samples were made with 0.4 and 0.5 water to cement (W/C) ratios. Both the raw cement powders and their corresponding samples after hydration were characterized in their microstructure by scanning electron microscopy, X-ray diffraction (with Rietveld refinement), X-ray fluorescence (XRF), Fourier Transform Infrared Spectroscopy (FTIR), density, and compression tests. With the compressive strength results, Weibull distribution analysis was conducted for 20 samples per composition. The higher compression strength obtained was about 45 MPa, which corresponds to samples with the higher W/C contents. The hydrated phases found showed diverse polymorphisms of Gibbsite (Nordstrandite, Bayerite, Hidrogarnet and Gehlenite).

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 OSTI2019

Weibull and Bootstrap-Based Data-Analytics Framework for Fatigue Life Prognosis of the Pressurized Water Nuclear Reactor Component Under Harsh Reactor Coolant Environment

In general, the fatigue life of a safety critical pressure component is estimated using best-fit fatigue life curves (S-N curves). These curves are estimated based on underlying in-air condition fatigue test data. The best-fitting approach requires a large safety factor to accommodate the uncertainty associated with large scatter in fatigue test data. In addition to this safety factor, reactor component fatigue life prognostics requires an additional correction factor that in general is also estimated deterministically. This additional factor known as the environmental correction factor F en is to cater the effect of the harsh coolant environment that severely reduces the life of these components. The deterministic F en factor may also lead to further conservative estimation of fatigue life leading to unnecessary early retirement of costly reactor components. To address the above-mentioned issues, we propose a data-analytics framework which uses Weibull and Bootstrap probabilistic modeling techniques for explicitly quantifying the uncertainty/scatter associated with fatigue life rather than estimating the lives based on a best-fit based deterministic approach. We assume the proposed probabilistic approach would provide the first hand information for assessing the maximum and minimum effects of pressurized water reactor water on the reactor component. In the discussed approach, in addition to the probabilistic fatigue curves, we suggest using a probabilistic environment correction factor F en . Here, we assume the probabilistic fatigue curve and F en would capture the S-N data scatter associated with the bulk effect of material grades, surface finish, strain rate, etc. on the material/component fatigue life.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Effects of the addition of boron nitride nanoplate on the fracture toughness, flexural strength, and Weibull Distribution of hydroxyapatite composites prepared by spark plasma sintering

Hydroxyapatite (HA) has inherently low fracture toughness and low flexural strength, thus limiting it from wide scale application as an implant material in the biomedical field. To increase the fracture toughness and flexural strength, HA composites were fabricated by adding boron nitride nanoplatelets (BNNP) as reinforcement. Spark plasma sintering was utilized to achieve fine grain structure. The addition of BNNP facilitated grain size refinement. The BNNP reinforced HA composites exhibited increased fracture toughness (2.3 MPa m 1/2 ) and flexural strength (79.79 MPa) of HA over previous published values (1.0 MPa m 1/2 ). Despite that the Weibull Distribution indicated a sacrifice in mechanical reliability, all the composites fabricated in this study showed a low probability of failure and a factor of safety (~ 5.6) that is consistent with that of human bones (~ 6). In addition, the current study provides an approach to statistically design sintering parameters and mechanical loading for fabrication of ceramics.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Progressive failure site generation in AlGaN/GaN high electron mobility transistors under OFF-state stress: Weibull statistics and temperature dependence

Gate leakage degradation of AlGaN/GaN high electron mobility transistors under OFF-state stress is investigated using a combination of electrical, optical, and surface morphology characterizations. The generation of leakage “hot spots” at the edge of the gate is found to be strongly temperature accelerated. The time for the formation of each failure site follows a Weibull distribution with a shape parameter in the range of 0.7–0.9 from room temperature up to 120 °C. The average leakage per failure site is only weakly temperature dependent. The stress-induced structural degradation at the leakage sites exhibits a temperature dependence in the surface morphology, which is consistent with a surface defect generation process involving temperature-associated changes in the breakdown sites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗