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Title: Graphite Characterization: Baseline Variability Analysis Report

Abstract

The Idaho National INL’s Baseline Material Property program provides many measurements of different material properties on a variety of nuclear graphite grades being investigated for irradiation-induced changes in material properties. The baseline material properties provide an unirradiated reference for comparison with measurements of those properties after irradiation. This study describes how uncertainty, or variance, in estimates of important material properties, like compressive strength, may depend on sample size, sample distribution and parameter estimation methods. Compressive strength data from two large collections of specimens from a billet of PCEA graphite (sample size = 230) and a billet of IG-110 graphite (sample size = 48) are used to illustrate these dependencies. The grades of graphite used represent approximate end members in terms of relative variability in strength measurements. Monte Carlo simulation and bootstrapping methods were used to examine variance in Weibull-parameter estimates as a function of sample size. Results were consistent with what previous statistical analyses have shown about the relationship between sample size and width of the confidence interval for maximum likelihood (ML) estimated parameters when samples are repeatedly drawn from a Weibull distribution. As a function of sample size, the precision of the modulus estimate increases faster than that ofmore » the characteristic strength. The modulus maximum likelihood estimates (MLEs) are biased for low sample sizes. The American Society for Testing and Materials document ASTM D7846-16 provides equations that describe the dependence of the variance of parameter MLEs on sample size. Using the same methodology, we show that the polynomials provided for variance dependence on sample size are inaccurate for sample sizes greater than ~120. We provide approximations to that relationship that illustrate relative constancy for sample size > ~10, in the logspace relationship of the modulus variance and the log transformed characteristic strength variance. Bootstrapping provided a means of comparing Weibull parameters obtained using ASME’s guidance for specimen collection to those obtained using different weighting in a case where strength is related to position in a billet and to grain orientation and a single distribution is used to characterize the billet. ASME specifies that samples be collected with equal representation in all locations and grain orientations. Parameter values obtained using ASME’s method were different from those obtained using random sampling of the complete data sets, and this was particularly true for the PCEA data. In addition, while the ASME approach yielded more conservative parameters for the PCEA data, the opposite was true for the IG-110 data. The difference observed for the PCEA data set likely reflects the larger number of against-grain specimens collected, which had generally higher strength than the with-grain specimens. This emphasizes the importance of the dependence of strength on location or grain orientation and suggests that it may be prudent to weight specimen collection toward the weaker subgroups if a conservative estimate as desired, as the equal weighting method recommended by ASME would will not always provide the most conservative Weibull parameters. Because spatial correlations commonly exist in certain grades of graphite, future work may involve developing a methodology for parameter inference that relaxes the assumption of independent specimens. ASTM and ASME codes recommend different parameter estimation methods and models of the Weibull distribution in different situations. Descriptions of the effects on parameter estimates for the example billets used in this study provide an example of how the method may affect the parameter estimate, and how—in this case—that compares to differences due to other factors, such as sample size and dependence on grain orientation or sample location.« less

Authors:
 [1];  [1]
  1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1467487
Report Number(s):
INL/EXT-18-45315-Rev000
TRN: US1902753
DOE Contract Number:  
AC07-05ID14517
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; 36 MATERIALS SCIENCE; GRAPHITE; GRAIN ORIENTATION; MAXIMUM-LIKELIHOOD FIT; COMPARATIVE EVALUATIONS; high-temperature gas-cooled reactor (HTGR); Advanced Reactor Technologies (ART)

Citation Formats

Plummer, Mitch, and Mack, Andrea. Graphite Characterization: Baseline Variability Analysis Report. United States: N. p., 2018. Web. doi:10.2172/1467487.
Plummer, Mitch, & Mack, Andrea. Graphite Characterization: Baseline Variability Analysis Report. United States. https://doi.org/10.2172/1467487
Plummer, Mitch, and Mack, Andrea. 2018. "Graphite Characterization: Baseline Variability Analysis Report". United States. https://doi.org/10.2172/1467487. https://www.osti.gov/servlets/purl/1467487.
@article{osti_1467487,
title = {Graphite Characterization: Baseline Variability Analysis Report},
author = {Plummer, Mitch and Mack, Andrea},
abstractNote = {The Idaho National INL’s Baseline Material Property program provides many measurements of different material properties on a variety of nuclear graphite grades being investigated for irradiation-induced changes in material properties. The baseline material properties provide an unirradiated reference for comparison with measurements of those properties after irradiation. This study describes how uncertainty, or variance, in estimates of important material properties, like compressive strength, may depend on sample size, sample distribution and parameter estimation methods. Compressive strength data from two large collections of specimens from a billet of PCEA graphite (sample size = 230) and a billet of IG-110 graphite (sample size = 48) are used to illustrate these dependencies. The grades of graphite used represent approximate end members in terms of relative variability in strength measurements. Monte Carlo simulation and bootstrapping methods were used to examine variance in Weibull-parameter estimates as a function of sample size. Results were consistent with what previous statistical analyses have shown about the relationship between sample size and width of the confidence interval for maximum likelihood (ML) estimated parameters when samples are repeatedly drawn from a Weibull distribution. As a function of sample size, the precision of the modulus estimate increases faster than that of the characteristic strength. The modulus maximum likelihood estimates (MLEs) are biased for low sample sizes. The American Society for Testing and Materials document ASTM D7846-16 provides equations that describe the dependence of the variance of parameter MLEs on sample size. Using the same methodology, we show that the polynomials provided for variance dependence on sample size are inaccurate for sample sizes greater than ~120. We provide approximations to that relationship that illustrate relative constancy for sample size > ~10, in the logspace relationship of the modulus variance and the log transformed characteristic strength variance. Bootstrapping provided a means of comparing Weibull parameters obtained using ASME’s guidance for specimen collection to those obtained using different weighting in a case where strength is related to position in a billet and to grain orientation and a single distribution is used to characterize the billet. ASME specifies that samples be collected with equal representation in all locations and grain orientations. Parameter values obtained using ASME’s method were different from those obtained using random sampling of the complete data sets, and this was particularly true for the PCEA data. In addition, while the ASME approach yielded more conservative parameters for the PCEA data, the opposite was true for the IG-110 data. The difference observed for the PCEA data set likely reflects the larger number of against-grain specimens collected, which had generally higher strength than the with-grain specimens. This emphasizes the importance of the dependence of strength on location or grain orientation and suggests that it may be prudent to weight specimen collection toward the weaker subgroups if a conservative estimate as desired, as the equal weighting method recommended by ASME would will not always provide the most conservative Weibull parameters. Because spatial correlations commonly exist in certain grades of graphite, future work may involve developing a methodology for parameter inference that relaxes the assumption of independent specimens. ASTM and ASME codes recommend different parameter estimation methods and models of the Weibull distribution in different situations. Descriptions of the effects on parameter estimates for the example billets used in this study provide an example of how the method may affect the parameter estimate, and how—in this case—that compares to differences due to other factors, such as sample size and dependence on grain orientation or sample location.},
doi = {10.2172/1467487},
url = {https://www.osti.gov/biblio/1467487}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jun 01 00:00:00 EDT 2018},
month = {Fri Jun 01 00:00:00 EDT 2018}
}