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Initial framework for engineering-scale statistical creep-fatigue modeling

This report describes the integration of new solid and interface-cohesive mechanics systems into MOOSE. The purpose of these new systems is to support the ability of MOOSE to run full-field crystal plasticity finite element method simulations of key material processes in high temperature metallic materials. These simulations could be used to help accurately predict the performance of key high temperature structural materials in future advanced nuclear reactor components. Previous work implemented preliminary versions of many of these systems in MOOSE Apps. The current work reports on their integration into the main MOOSE tensor mechanics module along with associated improvements to the basic formulations and numerical implementations. Finally, the report provides an example of the full-field crystal plasticity simulations now possible in MOOSE, including examples of realistic geometries requiring millions of degrees of freedom to resolve the microstructural features and macroscale geometry.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

In-situ strain behavior and BISON simulations of Zircaloy cladding subjected to temperature cycling separate-effects tests in a steam environment

Understanding fuel system performance during anticipated transients without scram (ATWSs) in boiling water reactors (BWRs) is necessary for refining current and future safety limits. High-fidelity material models and simulations are fundamental to rigorous assessment of zirconium-based cladding performance. However, experimental thermomechanical data during simulated ATWSs to validate these modes are limited. To provide relevant in-situ data, Zircaloy-4 cladding was subjected to cyclic heating in a steam environment to simulate an out-of-pile BWR ATWS. Digital image correlation was used to capture the cladding strain behavior in-situ for comparison against simulations using the BISON finite element code. Conventional high-temperature models were compared using multiple schemes to gain a better understanding of the applicability of three BISON models to BWR ATWS: (1) the default combination of creep models in BISON, (2) the high-temperature Erbacher model alone, and (3) the low-temperature Limback-Andersson model alone. The cases run with the Limback-Andersson model alone produced the lowest root mean square error (RMSE). The lowest RMSE for the Limback-Andersson model alone was 0.659%, and the highest RMSE reported was 4.22%. A data gap within the model in the temperature regime of interest was also identified, and to account for this gap, the current model in BISON is linearly interpolated between two separate datasets. In conclusion, this evaluation highlights the need to either develop a new model or to improve the existing model to capture transient creep effects resulting from a cyclic temperature transient.

Anticipated transient without SCRAM↗

Diffusional creep in UO 2 informed by lower length scale simulations

Using molecular dynamics, we predict information at the atomistic scale used to develop a mechanistic UO 2 creep model for use in higher length-scale fuel performance codes. The ultimate objective of the model is to not only to capture the creep rates of UO 2 but to determine the dominant mechanism in the diffusional regime, which is still debated in the literature. It is important to have a model to capture the correct mechanisms for creep in UO 2 as this can be used as the foundation when applying to other fuels, such as doped UO 2 , and when irradiation is accounted. In last years NEAMS milestone (FY22), we developed a prelimnary model, however there were issues, for example, excessively high values of uranium vacancy concentrations at the grain boundary. This year we have addressed the issues with the previous version of the model, added a new term that accounts for the nucleation of dislocations at stress raisers (e.g., triple junctions) within the microstructure and discussed where there was disagreement in the literature about the underpinning physics (uranium self-diffusion at the grain boundary).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluation of Mechanistic and Empirical Models against Existing FFRD and LOCA Experimental Databases

The desire of the nuclear industry to improve the economics of existing nuclear power plants has necessitated research into the potential of a phenomenon known as fuel fragmentation, relocation, and dispersal (FFRD). This phenomenon is possible during a loss-of-coolant accident (LOCA) at relatively high burnup. The Nuclear Energy Advanced Modeling and Simulation program has been developing simulation capabilities for FFRD and LOCA in the BISON fuel performance code for multiple years. This year, the effort has been focused on evaluating new lower length scale informed pulverization thresholds as well as updating and adding new empirical models for various phenomena. Models added or updated this year include a preliminary transient fission gas release model, new high-temperature Zircaloy creep models, a Zircaloy rupture opening area model, and a temperature-dependent emissivity during radiation from the fuel rod to the surrounding atmosphere. The models are verified through implementation tests to demonstrate code correctness after addition to BISON. The models are then assessed against a subset of the existing BISON validation suite for LOCA and FFRD cases. Two new cases, Studsvik Rods 192 and 193, have been added. The results indicate that the inclusion of a bubble pressure evolution model in the bubbles in the high-burnup structure has the largest impact compared to the 3D fracture criterion on reducing the calculated amount of pulverized fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Effects of time-dependent deformation of shale on the integrity of a geological nuclear waste repository

Safety assessment of geological nuclear waste repositories is essential for the permanent disposal of spent nuclear fuels and high-level radioactive waste. The long-term integrity of the host rock as well as the engineered barrier system (e.g., bentonite buffer) surrounding nuclear waste canisters is of particular importance as decay heat from nuclear waste canisters, which will last over thousands of years, significantly disturbs the thermo-hydromechanical (THM) state of the repository. In this study, THM coupled simulations were carried out to investigate the effect of time-dependent deformation (i.e., creep) of shale on the long-term integrity of a generic subsurface nuclear waste repository. The Norton-Bailey creep model, which is also known as the Lemaitre-Menzel-Schreiner model, was employed to simulate the power-law type creep that is observed in shales. The TOUGH-FLAC simulator was employed for the THM coupled modeling of the repository. The objective of this study is to assess the effect of creep in different shales (i.e., high creep shale vs. low creep shale) on long-term stress and permeability changes in the repository. Results show potential advantages of constructing repositories in the high creep shale, as deviatoric stress levels in the formation decreased to zero in 100 years since the emplacement of nuclear waste canisters and the permeability also decreased to the undamaged, intrinsic levels in 10,000 years. Also, mean effective stress levels in the bentonite buffer increased by 100% in the high creep shale case relative to the low creep shale case at 10,000 years due to creep-induced contraction of the nuclear waste disposal tunnel. However, in earlier periods (e.g., 1000 years), the stress levels in the bentonite buffer were twice smaller in the high creep shale case than in the low creep shale case, which shows a tradeoff between the intermediate- (~1000 years) and long-term (>10,000 years) compaction levels in the bentonite buffer depending on the creep characteristics of the host shale.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Heterogeneous creep deformation behavior of functionally graded transition joints (GTJs)

Dissimilar metal welds (DMWs) made between ferritic steels and austenitic alloys are used extensively in high-temperature power plant components. These DMWs experience premature creep failure in the ferritic steel’s heat affected zone (HAZ), close to the weld interface. Steep variations in microstructure and chemical composition across the dissimilar weld interface have been the contributing factors for the failure. Graded transition joints (GTJs), developed by functionally grading the chemical composition in layers, have been proposed as potential candidates to replace DMWs. In this research, GTJ coupons were fabricated between 2.25Cr-1Mo steel and Alloy 800H base material using two filler materials: (i) Inconel 82 and (ii) P87. These samples were aged at 600°C for 2000h to accelerate high-temperature microstructural evolution seen in service conditions, before subjecting them to short-term (~1 month) creep tests. Surface strains were measured using digital image correlation (DIC) technique to extract creep strain rates at different locations within GTJs. Both the GTJs exhibited heterogeneous creep strain distribution. Creep strain accumulated in the FGHAZ of 2.25Cr-1Mo steel, similar to type IV failure associated with Cr-Mo steel weldments. Microstructure based creep model framework was developed to describe the discrete creep strain rates observed in various 2.25Cr-1Mo steel regions of GTJs.

36 MATERIALS SCIENCE↗

Irradiation enhanced diffusion and diffusional creep in U₃Si₂

U₃Si₂ is a candidate as an advanced fuel for light water reactors (LWRs). Compared to UO₂, there are significant data gaps for the thermophysical and thermomechanical properties of U₃Si₂. Atomic scale simulations can help fill in those gaps, while also providing a more mechanistic understanding of the material properties. Creep is an important property for fuel performance as it influences the pellet-cladding gap, which in turn affects the temperature of the fuel (a key parameter in many other aspects of fuel behavior). In this work, we employed a DFT-informed cluster dynamics framework to predict point defect concentrations in U₃Si₂. The concentrations, diffusivities, and volumes of these defects were used to develop a diffusional creep model based on bulk (Nabarro-Herring) and grain boundary (Coble) diffusion processes. It was found that irradiation enhanced Nabarro-Herring creep is dominant at low temperatures, while Coble creep dominates for high temperatures. The model compares well against available experimental data and has been implemented in BISON. A demonstration case using simple power profiles has been carried out, showing that negligible creep occurs due to the low temperatures experienced by U₃Si₂, a consequence of its high thermal conductivity.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Computational Tools for Additive Manufacture of Tailored Microstructure and Properties

Additive manufacturing has the potential to revolutionize industrial hardware and unlock efficiency gains through the fabrication of geometries and architectures not possible by conventional processing. Currently most additive builds use a single set of process parameters (e.g. laser power and scan speed) which results in a part with a homogenous microstructure that provides a singular performance level. To move beyond this state, Raytheon Technologies Research Center worked to create a set of computational tools to track material evolution through each step of the additive process. Computational fluid dynamics and phase field models for microstructure evolution as a function of processing parameters, and crystal plasticity models fully coupling microstructure and mechanical properties for performance predictions were leveraged to establish a connection between additive parameters and the final microstructure. This framework was utilized to tailor spatially-varying mechanical properties in a part by appropriately controlling the microstructure evolution during the additive process. Specifically, a turbine blade was 3D printed from nickel superalloy IN718 using laser powder bed fusion with coarse grains in the airfoil section which experiences the highest temperatures and is creep limited while finer grains were printed in the root of the blade which experience higher stresses but at lower temperatures and is therefore fatigue limited. The benefit of being able to intentionally insert coarse grains in the high temperature region of the blade was showcased with a microstructure sensitive creep model that indicates longer creep life for coarser grains.

20 FOSSIL-FUELED POWER PLANTS↗

Initial microstructural model for creep-fatigue damage in Grade 91 steel

This report describes an initial Crystal Plasticity Finite Element Method (CPFEM) model for cyclic plasticity and damage in Grade 91 steel. The objective of this work is to develop a framework for modeling creep-fatigue interaction in Grade 91 steel to better predict the onset of damage in high temperature microreactor components. Many microreactor concepts envision low operating pressures but relatively high thermal stresses. Under these conditions, creep-fatigue will likely be the dominant design failure mechanism. Physically based models, like the one under development here, could lead to a better understanding of creep-fatigue mechanisms and the effect of stress multiaxiality and hold time on creep-fatigue damage. In turn, this could lead to more efficient microreactor component designs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Prediction of Creep-Induced Strain Using a Symbolic Regression-Based Model

Material creep under high-temperature conditions limits the lifetime and safety of structural systems such as advanced nuclear reactors. Conventional creep testing is slow and often produces inconsistent results across nominally identical experiments, making lifetime prediction uncertain. Here, to address these challenges, this work develops a data-driven symbolic regression (SR) model that consolidates results from duplicate creep tests and predicts the remaining strain-time curve of an ongoing experiment. The method uses piece-wise multi-objective SR with physical constraints to generate analytic, interpretable functions describing transient creep strain. Applied to Inconel Alloy 617 data, the approach achieved relative mean absolute errors of 1.0–9.5%, providing closed-form predictions of strain evolution. These results demonstrate a first step toward reducing the duration and cost of long-term creep testing while retaining physically interpretable model forms.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

BISON Capability to Account for Dopant Sensitivity in Relevant UO 2 Material Models

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program aims to develop predictive capabilities using computational methods for the analysis and design of advanced reactor and fuel cycle systems. This program has been supporting the development of BISON, a high-fidelity and high-resolution fuel performance tool at the engineering scale. Incorporation of more physics-based models in BISON for the accident tolerant fuel applications motivated this study. This document details integration of new modeling capabilities in BISON, including: a tensile strength model for uranium dioxide (UO 2 ) fuel to incorporate the microstructural effects (e.g., grain size, fabrication pore size, and porosity), and atomistic-informed creep model for UO 2 fuel that is developed by Los Alamos National Laboratory. Sensitivity analyses are conducted on these models separately as well as a two-dimensional full rod application under normal operating conditions. Lastly, these new modeling capabilities in BISON are exercised in Halden IFA-677.1 and IFA-716.1 assessment cases.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Development of High-Performance Ni-base Alloys for Gas Turbine Wheels Using a Coprecipitation Approach (Final Technical Report)

In this project, a synergistic approach involving experiments informed by modelling was used to develop γ'/γ'' coprecipitation-strengthened Ni-base superalloys for land-based gas turbine wheels. In thick sections of such turbine wheels, the slow cooling rate normally observed, as well as variations in cooling rate could potentially result in drastically inhomogeneous and coarsened microstructure. Thus, ten alloy compositions were selected based on coprecipitation and sluggish γ’ growth and coarsening during three iterations of alloy development, assisted by extensive CALPHAD modeling. Phase equilibrium calculations, informed by the characterization of early alloys, were successful in predicting suitable aging treatments to obtain bimodal coprecipitate distribution in several alloys. These aging treatments were applied to the subsequent round of alloys and the resulting microstructures were characterized in detail. Two different cooling rates were used during each of these heat treatments to simulate the range of cooling rates observed in a thick section forging. The microstructures were used to calibrate a multi-phase field model (MPF), which was used to study the formation mechanisms of various coprecipitate morphologies observed in the experiments. Following this, the most promising alloys in each round were selected and studied using high temperature tensile and creep tests. Considering that a slower cooling rate would lead to a strength debit, while a faster cooling rate might lead to a decline in creep rupture life of a full-scale wheel, tensile tests were carried out for slower cooled samples, while creep tests were carried out for faster cooled samples. The deformation microstructures were then characterized using advanced characterization techniques such as Diffraction Contrast-Scanning Transmission Electron Microscopy (DC-STEM) and Electron Channeling Contrast Imaging (ECCI). Further, a mean-field creep model was developed and calibrated using these experimental findings to predict long-term creep behavior of these coprecipitation-strengthened alloys.

36 MATERIALS SCIENCE↗

BISON Development and Validation for Priority LWR-ATF concepts

Over the years, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) (2015-2018, 2020) and Consortium for Advanced Simulation of Light Water Reactors (CASL) (2019) programs have provided support for development of Accident Tolerant Fuel (ATF) material models in the BISON fuel performance code. Since the beginning, the goal has been to utilize a multiscale modeling approach to gain a physical understanding of the fuel concepts of interest and to develop mechanistic models in the absence of a large amount of experimental data. This work builds upon that of previous years. In particular we present newly updated fission gas release models for both gas behavior in Cr 2 O 3 -doped UO 2 and U 3 Si 2 fuels, and a new creep model for U 3 Si 2 . The validation exercises completed last year are revisited with the latest models and the results updated. A brief summary of recent modeling activities for FeCrAl cladding is also provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗