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Mack, Andrea L

Publications and source records attributed to Mack, Andrea L.

UNDERSTANDING THE SEMI-PROBABILISTIC APPROACHES IN STRUCTURAL RELIABILITY USED TO SET DESIGN RELIABILITY TARGETS FOR GRAPHITE COMPONENTS USING ASME BPVC METHODS

Graphite is a quasi-brittle material, resulting in random variability in tensile strength distributions. To account for the random variability in strength, HHA-3000 of the ASME BPVC provides two semi-probabilistic methods for qualifying nuclear graphite components in the design stage, the simplified and full assessments. The full and simplified assessments apply statistical methods to engineering-based design problems. This is often referred to as reliability-based design. Reliability-based design (RBD) is a method to develop reliable designs by accounting for uncertainties and result in small chances of failure when also considering safety factors. RBDs provide reliability targets using semi-probabilistic approaches. RBD is implemented in ASME BPVC HHA-3000 for nuclear graphite components, but is not specific to that application. There has been much confusion around the methods implemented in ASME BPVC HHA-3000 for qualifying nuclear graphite components. To address the confusion, this paper takes a hierarchical approach. First, the general RBD framework is presented. Then, the semi-probabilistic methods and the underlying assumptions implemented in the assessments are presented. The semi-probabilistic methods are separated from the engineering modifications that have been made to the assessments. After building the framework and underlying assumptions, the specific methods in the full and simplified assessments are explained in three steps: inputs, methods, outputs. The methods are applied to an H-451 reflector block. Tensile strength properties for other graphite grades are provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluation of the Simplified Assessment Peak Equivalent Stress Design Limit Probability of Failure

The ASME Boiler and Pressure Vessel Code Section III Division 5 Subsection HH Subpart A (HHA) outlines requirements and qualification methods for graphite core components in high temperature reactor environments. One such structural qualification method is the Simplified Assessment outlined in HHA-3220, which represents a comparison of service level specific equivalent stresses to allowable stress values derived from target probability of failures (POFs). The target POF is based on the structural reliability class (SRC) for the components and service condition of interest, and is used to establish design limits for combined membrane and peak equivalent stresses. Combined membrane stress limits are derived from two parameter Weibull distribution fits of the graphite grade specific tensile strength data and the target POF. The combined membrane stress limits are then scaled based on the ratio of flexural strength to tensile strength (referred hereinafter as Rtf) to establish the corresponding peak equivalent stress limits. It is desired that the target POF is at least maintained for both combined membrane and peak equivalent design limits, especially with the use of Rtf. The assessment presented herein examines tensile and flexural data for medium and fine grade graphites relative to the calculated combined membrane and peak equivalent stress limits per HHA-3220 and illustrates the simplified assessment method results in anticipated, or at least conservative, peak equivalent design stress limits.

36 - MATERIALS SCIENCE↗

ASME Design Code Rule Changes for Nuclear Graphite

The American Society of Mechanical Engineers Boiler Pressure and Vessel Code (ASME BPVC) Section III, Division 5, Article HHA-3000 outlines graphite core component and graphite core assembly design guidelines. Graphite core components are defined as ?components manufactured from graphite that are installed to form a graphite core assembly within the reactor pressure vessel of a high temperature, graphite moderated fission reactor.? (p. 413) Graphites? inherent defect distributions do not allow for deterministic material reliability. Rather, graphite has variable strength distributions which change by grade. Article HHA-3000 outlines two semi-probabilistic methods, the full and simplified assessments, which set design load limit targets for each of three component structural reliability classes. The Design Task Group was officially recognized as a specialized task group within ASME November of 2023, though we?ve been collaborating since 2022. The purpose of the Design Task Group is to correct, clarify, and make HHA-3000 function as intended. The Design Task Group will sunset once we?ve achieved our objectives. The Design Task Group was specifically told to not write new Code. While there may be more precise and more accurate methods to determine reliability targets, the current methods are conservative, relatively simple to implement, and have thus far been considered satisfactory for setting design reliability targets. Much of the ground-work to write proposal files and background documents for records to make the changes needed to achieve our objective have been completed. The Design Task Group has documented much of their work through papers, presentations, and memorandums. Three memorandums in which INL team members had substantial contributions are found in the Appendices: FEA Modeling for the Baseline Program, Evaluating the Effects on Margin of Updating the Threshold and Shape Parameters in the Full Assessment, and Interpretations of the Full and Simplified Assessments in ASME BPVC. Most of the on-going work to achieve the Design Task Group?s objective will be addressing comments on existing records and moving records through the balloting process. The Design Task Group met bi-weekly mostly through the end of FY2023. Since February 2024, the Design Task Group has mostly been completed with solving and documenting the technical issues associated with the assessments. Unless new tasks are identified, the remaining work of the Design Task Group will be political and editorial.

97 MATHEMATICS AND COMPUTING↗

ASME Code Development: Design Rules

ASME Code Development: Design Rules, ASME BPVC, and ASME BPVC HHA-3000, Design Task Group Papers, Presentations, and Memorandums, and records.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Qualifying nuclear graphite components using ASME guidelines

Qualifying nuclear graphite components using ASME guidelines, including Semi-probabilistic, probabilistic, and deterministic approaches to design, theory of methods, pre-assessment analysis inputs, post assessment analysis outputs, simplified assessment, full assessment, and application.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Design Task Group Update

Slides detailing Primary Subtask 1 and 2 with the Graphite Review, accomplishments, studies, and on-going subtasks for the timeline of January 2023 through May 2023.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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↗

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↗

Data Collection and Analysis Challenges and Mitigation Strategies for Quantitative Human Factors Research Studies in Nuclear Power Plant Modernization

The United States (U.S.) Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) program Plant Modernization Pathway is conducting targeted research and development (R&D) to address aging and reliability concerns with the legacy instrumentation and control and related information systems of the U.S. LWR fleet. In this effort, the application of human factors engineering (HFE) provides an important role in ensuring new digital plant technologies enable broad innovation and business improvement with continued operational safety. Evaluation is a key activity in HFE, which often occurs iteratively through the system design lifecycle. While qualitative methods are important in collecting information of how users perform tasks through observations, quantitative methods are equally important in assessing system design based on performance. In collecting and analyzing this quantitative data, there are notable challenges in the nuclear HFE domain that may threaten the validity and reliability of the inferences made in these studies. Notable challenges include small sample size and limited resources, large error variance and small effect size, an “adding test features to losing degrees of freedom” dilemma, non-normal distribution, and heterogeneity of variance. The results in control room usability studies are often statistically non-significant, which makes it hard to interpret. This work discusses these challenges across different scientific viewpoints and provides real-world examples of these challenges in practice. Collectively, the objective of this work is to position these challenges to the larger data science community as a means of identifying future opportunities to address these issues.

99 GENERAL AND MISCELLANEOUS↗