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Reactor Pressure Vessel Fracture Mechanics Development and Concrete Application Testing for Grizzly

The Grizzly code is being developed to address degradation issues in nuclear reactor structures and components. For light-water reactors, Grizzly currently has capabilities to simulate degradation processes and their effects on structural integrity in two key areas: reactor pressure vessels (RPVs) and reinforced concrete structures. This report documents improvements made to Grizzly’s ability to address both of these structural systems. For RPVs, the reduced-order models (ROMs) used in fracture mechanics calculations have been expanded to allow their application over a broader range of the parameter space than was permitted by the previous models. The ROMs currently used in Grizzly for the evaluation of flaws that are fully embedded within the RPV (as opposed to surface-breaking flaws) are based on a model that is known to be conservative, indicating higher stress intensity factors than would be obtained from direct simulations. A more accurate model that eliminates these excess conservatisms has been recently included in the American Society of Mechanical Engineers Boiler and Pressure Vessel Code but was not applicable for flaws near the RPV surface, which is where the most critical flaws are usually located. That model has recently been extended for increased applicability in this near-surface region. The ROMs for embedded flaws in the Grizzly code have been expanded to include these recent extensions, which permit their use in a much broader set of cases than previously possible. Direct 3D simulations have been used to check these ROMs and have shown good agreement in most cases, although there are still some cases that need further investigation. There are considerable benefits to using these these more accurate and less conservative ROMs for embedded flaws. On a benchmark probabilistic fracture mechanics problem tested here, the conditional probability of fracture initiation computed for a population of flaws in a single plate in an RPV decreased by over a factor of 3. To address aging in reinforced concrete structures, a capability to simulate multiple degradation mechanisms, including alkali-silica reaction and radiation-induced volumetric expansion has been developed in Grizzly over the past several years. This had previously been demonstrated on laboratory-scale specimens but not on full-scale nuclear concrete structures with reinforcement. To demonstrate the applicability of Grizzly to the analysis of large-scale structures of interest, a full 3D model of a representative reinforced concrete structure, including a complex arrangement of reinforcing bars, was developed and demonstrated in Grizzly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Assessment of Grizzly Capabilities for Reactor Pressure Vessels and Reinforced Concrete Structures

Over the last several years, capabilities to simulate the progression and effects of degradation in critical structures in light water reactor (LWR) nuclear power plants have been under development in the Grizzly code. Age-related material degradation is important for a number of systems in LWRs, but the main focus for Grizzly development has been on reactor pressure vessels (RPVs) and concrete structures because of their central role and the difficulty of replacement of these structures if they are found to be degraded to an unacceptable degree. The capabilities for analyzing both RPVs and concrete structures in Grizzly have reached a point where the feature sets are sufficiently complete to perform credible analyses of those types of structures. Because of this, the emphasis has shifted from foundational development to assessing the accuracy of these modeling capabilities on representative problems of interest and on improving the physical basis of those models to improve their ability to predict the actual response of those structural systems. This report documents a first set of test cases that have been developed to assess the Grizzly code on real-world problems for these two types of structures. For RPVs, these test cases consist of a set of benchmark problems where Grizzly is compared to another code. For concrete structures, a set of models of experimental specimens designed to characterize the multidimensional swelling response of reinforced concrete members due to alkali-silica reaction (ASR) has been developed and compared with experimental results. Both the RPV and concrete test cases developed here are much more computationally intensive than the small regression tests that are used in the testing that Grizzly undergoes every time a proposed set of changes is made to ensure that those changes do not adversely affect previously established behavior. A system for regularly running these large problems to monitor the behavior of the code as it is developed has been instituted. While these test cases generally indicate good comparison with the benchmark results, they also indicate areas where further development is warranted.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Benchmarking of Probabilistic Fracture Mechanics Models in Grizzly

In 2020, as part of contract/task order 31310019N0006/31310020F0060, the Nuclear Regulatory Commission tasked Idaho National Laboratory (INL) with benchmarking the MOOSE/GRIZZLY code against the NRC’s Fracture Analysis of Vessels - Oak Ridge (FAVOR), version 16.1 code. Both codes can predict large light-water reactor vessel integrity deterministically and probabilistically. In fact, such predictions are the primary purpose of the FAVOR code, and are a main focus of the GRIZZLY code, although GRIZZLY is capable of modeling a wider range of geometries and problems. The vessel integrity modeling capabilities of the GRIZZLY code are still under development and being gradually expanded, and the capability to model vessel fracture by crack growth has not yet been integrated into GRIZZLY (although it does exist in pre-release versions). Thus, the present benchmark study focused on comparing predictions for the conditional probability of crack growth initiation (CPI) between GRIZZLY and FAVOR v16.1. The present benchmarking study expands on a previous study completed in 2020, which focused on single plate regions, various flaw types, and full vessel studies. The previous study was limited in scope and revealed some relatively large discrepancies, particularly in the case of weld regions. In the present study, detailed investigations into the sources of discrepancies between GRIZZLY and FAVOR were performed, with a focus on weld regions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Summary of Grizzly Development for Advanced Reactor Structural Materials

This summary report contains an overview of work performed during Fiscal Year 2019 under the Nuclear Engineering Advanced Modeling and Simulation (NEAMS) Fuels Product Line work package entitled "MS-19IN020106 - GRIZZLY - INL". Grizzly is a code based on the MOOSE framework that has been under development for several years funded by the US Department of Energy’s Light Water Reactor Sustainability (LWRS) program. Prior to 2019, Grizzly development was focused on development of capabilities needed to simulate the effects of aging mechanisms in light water reactor (LWR) components. The goal of this LWR-focused work has been to develop tools that can be used to assess the ability of existing LWRs to perform safety in long term operation (LTO) scenarios. This LWR-focused work has primarily focused on the effects of reactor pressure vessel (RPV) embrittlement and aging of reinforced concrete structures. Grizzly development to support LWR degradation needs is still ongoing, but starting in 2019, Grizzly’s capabilities are being expanded to also meet growing needs for a tool to address structural component integrity and degradation in advanced reactors. A simulation capability for advanced reactor components has many of the same basic requirements that one for LWRs does, such as the ability to solve coupled systems of partial differential equations that arise from the fact that many of the problems of interest involve multiple coupled physics. The materials issues also inherently involve multiple length scales, with the response at the engineering scale being strongly affected by mechanisms occurring at atomistic and mesoscopic scales.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

VERA-Grizzly Ex-Core Calculations: Watts Bar Unit 1 Cycles 1-2

The critical structures that comprise light-water reactor (LWR) nuclear power plants are subjected to operating environments that can challenge their integrity. Structures in close proximity to the reactor core, such as the reactor pressure vessel (RPV) and the biological shield wall, are subjected to high levels of radiation emanating from the core, as well as elevated temperatures. As the US fleet of operating LWRs ages, the effects of these operating environments on the integrity of these structures must be considered to ensure their continued safe operation. Extending the lifetime of commercial reactors and maintaining the aging reactor fleet require accurate prediction of the exposure of ex-core components to neutron and photon radiation. In particular, concrete degradation studies must be performed to evaluate the safety and long-term operation of reactors with lifetime extensions. The concrete reactor bioshield is important for providing radiological protection during operation and must last for the entire lifetime of the reactor. Recent interest in lifetime extensions furthers the need to accurately simulate concrete material degradation in the reactor bioshield. As a result of this need, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has funded this study to couple its tools, Virtual Environment for Reactor Applications (VERA) and Grizzly. VERA allows users to set up models to calculate time-dependent and fully coupled solutions (with thermal feedback) for ex-core quantities of interest such as vessel and coupon fluence and detector responses for multiple statepoints and cycles. Grizzly is a finite-element application based on the Multiphysics Object Oriented Simulation Environment (MOOSE) framework that is used to enable aging materials calculations. This report highlights the work performed to calculate the fluence in the vessel and concrete for Watts Bar Nuclear Plant Unit 1 (WBN1) Cycles 1 and 2. The fluences obtained from VERA were successfully transferred to Grizzly using a Python script. Four simulations were run with Grizzly: (1) the Mazars model with the initial Young’s modulus being the instantaneous modulus, (2) the Mazars model with the initial Young’s modulus being the delayed modulus, (3) the Mazars model with the initial Young’s modulus being the delayed modulus with the addition of the effects of micro-damage caused by irradiation, and (4) the Mazars model with the initial Young’s modulus being the instantaneous modulus, and with the addition of micro-damage and creep. Details regarding the methods used to obtain the fluence and the statistical errors associated with the VERA Monte Carlo Shift calculations are discussed in greater detail in this report. The results obtained from the four Grizzly models are also presented in this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Modular system for probabilistic fracture mechanics analysis of embrittled reactor pressure vessels in the Grizzly code

In light water reactor (LWR) nuclear power plants, the reactor pressure vessel (RPV) plays an essential safety role, and its integrity must be ensured during a variety of transient loading conditions. These can include off-normal conditions such as a pressurized thermal shock (PTS), as well as transients encountered during normal startup, shutdown, and testing of the reactor. Exposure to irradiation and elevated temperatures embrittles the RPV’s steel over time, making it increasingly susceptible to failure due to propagation of fractures that could initiate at the locations of flaws introduced during the manufacturing process. As long-term operation scenarios are being considered for LWRs in the United States, it is important to have a flexible simulation tool that can be used to perform probabilistic evaluations of RPV integrity under a wide variety of conditions and incorporate improved predictive models of RPV steel embrittlement. The Grizzly code is being developed to meet these needs. This paper describes Grizzly’s modular architecture, provides results of benchmarking studies of various components of Grizzly, and demonstrates the application of Grizzly on a model that includes plume effects that are difficult to represent in other codes being used in current practice.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Enhancements to Concrete Modeling Capabilities in Grizzly 2.0

The Grizzly code has been under development for several years with the goal of modeling aging effects in a variety of nuclear power plant systems, components, and structures. Version 2.0 of Grizzly was recently released, including both major improvements to its probabilistic fracture mechanics capabilities for evaluation of irradiated reactor pressure vessels, as well as multiple improvements to its capability for modeling degradation of concrete structures. This report summarizes recent development in the Grizzly code specific to concrete modeling that are included in this release. Major highlights of this work include the release of much of the concrete modeling capabilities of Grizzly in an open-source code called BlackBear, modernization of the models and documentation of the code, support for including nonlinear mechanical constitutive models, including creep and damage, re-architecting the anisotropic expansion model to allow its use for modeling both expansion due to alkali-silica reaction and radiation-induced volumetric expansion, and developing a preliminary capability for modeling connection of reinforcing bars to a concrete matrix.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Use of Neutron Flux Calculated by Shift in a Grizzly Reactor Pressure Vessel Fracture Simulation

The reactor pressure vessel (RPV) plays the critical role of containing the reactor and coolant in a light water reactor nuclear power plant, and must be able to safely perform this function under a variety of normal and off-normal transient loading conditions. The RPV is subjected to harsh environmental conditions (elevated temperature and high neutron flux) whenever the plant is operating, which leads to embrittlement of the steel over time. RPVs contain populations of flaws introduced during the manufacturing process, and the primary safety concern is that during a transient event, a fracture could initiate at the site of one of these flaws and lead to rupture of the RPV. RPVs are very rugged structures, and the probability of this occurring is very low, but as the RPV's steel becomes embrittled over time, its resistance to fracture decreases and this becomes more likely. Assessing the likelihood of RPV fracture during a transient event involves performing a probabilistic fracture mechanics analysis, in which random sampling procedures are used to assess the probability of fracture of a population of flaws. Grizzly offers unique capabilities for modeling the RPV using 1D, 2D, or 3D representations, taking advantage of parallel computing for this type of analysis. One of the important inputs to Grizzly is the spatial distribution of the neutron fluence, which has a large impact on the material embrittlement, and should thus be characterized as accurately as possible. The VERA core simulator developed by the CASL program takes advantage of high performance computing resources to perform high-fidelity multiphysics simulations of reactor physics, including the effects of neutron transport, fuel performance, and thermal hydraulics. Recently a capability was developed to also evaluate neutron fluxes away from the reactor core through the Shift code. This allows for a detailed 3D map of the spatial variation of the fluence in components such as the RPV to be computed, which is ideal for use with Grizzly. This report documents a procedure developed to use the fluences computed in Shift in a Grizzly simulation, which allows for improved realisim in the prediction of the effects of environmental exposure on propensity for reactor pressure vessel fracture. This capability demonstrated on RPVs with multiple types of configurations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Progress on Grizzly Development for Reactor Pressure Vessels and Reinforced Concrete Structures

The Grizzly code has been under development for the U.S. Department of Energy’s Light Water Reactor Sustainability program to provide predictive tools for the evolution of material degradation in critical light water reactor structural components due to long-term exposure to the environmental conditions of normal reactor operation, and for the effects of this degradation on the safety of these components. This development has primarily targeted reactor pressure vessels and reinforced concrete structures. Work performed during Fiscal Year 2019 added important features for both of these types of structures. For probabilistic fracture mechanics analysis of reactor pressure vessels, capabilities were added to account for the effects of warm prestressing and residual stresses, as well as to model crack initiation, growth, and arrest. For modeling microstructure evolution in reactor pressure vessels, a cluster dynamics model for evolution of Mn-Ni-Si phases has been implemented. For modeling degraded reinforced concrete structures, capabilities to consider the combined effects of damage and creep in the concrete constitutive model and model nonlinear behavior of reinforcing bars has been added. These newly-developed features fill important gaps in Grizzly’s feature set for engineering-scale analysis of degraded reactor pressure vessels and reinforced concrete structures. Grizzly development in both of these areas has reached a point where it is ready for extensive testing on relevant engineering problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

High-Temperature Creep Test Suite for Grizzly

A recent development in the Grizzly has focused on improving its ability to model the high-temperature response of alloys, enabling its use for predictive modeling of material response for advanced reactor applications. This report documents an effort to expand the example and assessment test suites in Grizzly to include a set of problems that exercise the models for high-temperature response of components relevant to advanced reactors. These problems can be used to assess the accuracy of models, provide examples for users interested in modeling this class of problems, monitoring performance on large-scale problems and as test cases for future feature development.

36 MATERIALS SCIENCE↗

An evaluation of the use of ERTS-1 satellite imagery for grizzly bear habitat analysis

Multispectral scanner images taken by the ERTS-1 satellite in August and October, 1972, were examined to determine if they would be useful in identifying and mapping favorable habitat for grizzly bears. It was possible to identify areas having a suitable mixture of alpine meadow and timber, and to eliminate those which did not meet the isolation requirements of grizzlies because of farming or grazing activity. High altitude timbered areas mapped from satellite imagery agreed reasonably well with the distribution of whitebark pine, an important food species. Analysis of satellite imagery appears to be a valuable supplement to present ground observation methods, since it allows the most important areas to be identified for intensive study and many others to be eliminated from consideration. A sampling plan can be developed from such data which will minimize field effort and overall program cost.

Varney, J. R.↗

Grizzly Development for Light Water Reactor and Advanced Reactor Applications in Fiscal Year 2021

This report summarizes work performed during Fiscal Year (FY) 2021 at Idaho National Laboratory (INL) for the U.S. Department of Energy’s Nuclear Engineering Advanced Modeling and Simulation (NEAMS) program for the Structural Materials and Chemistry Technical Area in the work package entitled “MS-21IN050106 - Structural Materials - INL.” This effort mainly focused on development and application of capabilities for engineering-scale analysis of nuclear reactor structural components in the Grizzly and BlackBear codes. These efforts include performance improvements and application of models for high-temperature component response, cluster dynamics modeling of precipitation in light water reactor pressure vessel steel, engineering-scale capability development in the areas of concrete simulation and reactor pressure vessel analysis, and preparation for and conducting an independent assessment of the adherence of these codes to software quality standards.

36 MATERIALS SCIENCE↗

Initial Fracture Propagation Modeling of Graphite Components with Grizzly

Graphite has historically been extensively used in power reactor cores and will be used in multiple types of advanced reactors currently under development. These graphite structural components can experience significant stresses due to nonuniform volumetric strains induced by irradiation and thermal expansion, which can lead to fracture. Robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors are important for evaluating component integrity, developing design standards, and interpreting experimental results to characterize graphite performance. The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program has been developing degradation models for other structural components in nuclear reactors within the Grizzly and BlackBear codes. This report documents an effort to develop initial capabilities for modeling graphite fracture within these codes, building on prior efforts to model fracture in other materials. Major elements of this effort include developing a new system for modeling fracture nucleation and growth in two dimensions using the extended finite element method and incorporating a damage and plasticity model. These capabilities are applied here to model a representative graphite component and a splitting disc experiment used to obtain tensile strength.

36 MATERIALS SCIENCE↗

Development of Graphite Thermal and Mechanical Modeling Capabilities in Grizzly

Nuclear-grade graphites are used extensively in the core designs of multiple types of advanced nuclear reactors. In the reactor environment, graphite is exposed over long durations to extreme conditions, including high temperatures, radiation and potentially molten salt and oxygen. Exposure to these conditions can cause several degradation mechanisms in graphite, including nonuniform volumetric strains induced by irradiation and thermal expansion, which lead to stresses that can compromise the performance of graphite components. Evaluating component integrity, predicting component performance over the reactor lifetime, and developing design standards all require robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors. This report documents progress in an ongoing effort to develop modeling and simulation tools in the Grizzly code for predicting the performance of graphite exposed to reactor conditions. Recent developments include a set of thermal and mechanical models that now include the IG-110, NBG-18, and H-451 graphite grades. Improvements have also been made to a nonlinear damaged plasticity model applicable to predicting damage under tension and compression to quasibrittle materials, including graphite. In addition, enhancements have been made to the extended finite element method implementation targeted at simulating graphite fracture. These include new capabilities for crack nucleation in the interior of a solid body, improved treatment of crack nucleation on free surfaces, and more robust modeling approaches for crack growth approaching free surfaces or other cracks.

36 MATERIALS SCIENCE↗

An evaluation of the use of ERTS-1 satellite imagery for grizzly bear habitat analysis

Improved classification and mapping of grizzly habitat will permit better estimates of population density and distribution, and allow accurate evaluation of the potential effects of changes in land use, hunting regulation, and management policies on existing populations. Methods of identifying favorable habitat from ERTS-1 multispectral scanner imagery were investigated and described. This technique could reduce the time and effort required to classify large wilderness areas in the Western United States.

Varney, J. R.↗