A proposed model for the effect of oxidation on the high-temperature deformation of nickel
Dynamic creep model to determine oxidation effects on high temperature deformation of nickel
Wolf, J. S.↗
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Results for “Creep modeling”
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The constitutive representation of high-temperature creep damage
The elastic-viscoplastic constitutive equations of Bodner-Partom were applied to modeling creep damage in a high temperature Ni-alloy, B1900 + Hf. Both tertiary creep in bulk materials and creep crack growth in flawed materials were considered. In the latter case, the energy rate line integral was used for characterizing the crack driving force, and the rate of crack extension was computed using a local damage formulation that assumed fracture was controlled by cavitation occurring within the crack-tip process zone. The results of this investigation were used to assess the evolution equation for isotropic damage utilized in the Bodner-Partom constitutive equations.
Chan, K. S.↗
Materials constitutive models for nonlinear analysis of thermally cycled structures
Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis.
Kaufman, A.↗
Evaluation of Inelastic Constitutive Models for Nonlinear Structural Analysis
The influence of inelastic material models on computed stress-strain states, and therefore predicted lives, was studied for thermomechanically loaded structures. Nonlinear structural analyses were performed on a fatigue specimen which was subjected to thermal cycling in fluidized beds and on a mechanically load cycled benchmark notch specimen. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic-kinematic, combined plus transient creep) were exercised. Of the plasticity models, kinematic hardening gave results most consistent with experimental observations. Life predictions using the computed strain histories at the critical location with a Strainrange Partitioning approach considerably overpredicted the crack initiation life of the thermal fatigue specimen.
Kaufman, A.↗
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↗
Evaluation of inelastic constitutive models for nonlinear structural analysis
The influence of inelastic material models on computed stress-strain states, and therefore predicted lives, was studied for thermomechanically loaded structures. Nonlinear structural analyses were performed on a fatigue specimen which had been subjected to thermal cycling in fluidized beds and on a mechanically load cycled benchmark notch specimen. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, combined plus transient creep) were exercised using the MARC program. Of the plasticity models, kinematic hardening gave results most consistent with experimental observations. Life predictions using the computed strain histories at the critical location with a strainrange partitioning approach considerably overpredicted the crack initiation life of the thermal fatigue specimen.
Kaufman, A.↗
Determination of Creep Behavior of Thermal Barrier Coatings Under Laser Imposed High Thermal and Stress Gradient Conditions
A laser sintering/creep technique has been established to determine the creep behavior of thermal barrier coatings under steady-state high heat flux conditions. For a plasma sprayed zirconia-8 wt. % yttria coating, a significant primary creep strain and a low apparent creep activation energy were observed. Possible creep mechanisms involved include stress induced mechanical sliding and temperature and stress enhanced cation diffusion through the splat and grain boundaries. The elastic modulus evolution, stress response, and total accumulated creep strain variation across the ceramic coating are simulated using a finite difference approach. The modeled creep response is consistent with experimental observations.
Zhu, Dongming↗
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↗
Application of two creep fatigue life models for the prediction of elevated temperature crack initiation of a nickel base alloy
Cyclic Damage Accumulation (CDA) and Total Strain-Strain Range Partitioning (TS-SRP) models for predicting the creep-fatigue crack initiation life of high temperature alloys are presented. The models differ in their fundamental assumptions regarding the controlling parameters for fatigue crack initiation and in the amount of data required to determine model constants. The CDA model represents a ductility exhaustion approach and uses stress quantities to calculate the cyclic fatigue damage. The TS-SRP model is based on the use of total mechanical strain and earlier concepts of the Strain Range Partitioning Method. Both models were applied to a well controlled fatigue data set at a high temperature nickel base alloy, B1900 + Hf, tested at 1600 F and 1800 F. The tests were divided into a baseline data set required to determine model constants and a verification data set for evaluation of the predictive capability of the models. Both models correlated the baseline data set to within factors of two in life, and predicted the verification data set to within a factor of three or better. In addition, sample calculations to demonstrate the application of each model and discusions of the predictive capabilities and areas requiring further development are presented.
Moreno, V.↗
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↗
Constitutive Theory Developed for Monolithic Ceramic Materials
With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated with these service conditions by developing a multiaxial viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (such as creep and stress relaxation) in monolithic structural ceramics. Using continuum principles of engineering mechanics, we derived the complete viscoplastic theory from a scalar dissipative potential function.
Janosik, Lesley A.↗
Uncertainty quantification for Bayesian active learning in rupture life prediction of ferritic steels
Abstract Three probabilistic methodologies are developed for predicting the long-term creep rupture life of 9–12 wt%Cr ferritic-martensitic steels using their chemical and processing parameters. The framework developed in this research strives to simultaneously make efficient inference along with associated risk, i.e., the uncertainty of estimation. The study highlights the limitations of applying probabilistic machine learning to model creep life and provides suggestions as to how this might be alleviated to make an efficient and accurate model with the evaluation of epistemic uncertainty of each prediction. Based on extensive experimentation, Gaussian Process Regression yielded more accurate inference ( $$Pearson\;correlation\;coefficent> 0.95$$ P e a r s o n c o r r e l a t i o n c o e f f i c e n t > 0.95 for the holdout test set) in addition to meaningful uncertainty estimate (i.e., coverage ranges from 94 to 98% for the test set) as compared to quantile regression and natural gradient boosting algorithm. Furthermore, the possibility of an active learning framework to iteratively explore the material space intelligently was demonstrated by simulating the experimental data collection process. This framework can be subsequently deployed to improve model performance or to explore new alloy domains with minimal experimental effort.
20 FOSSIL-FUELED POWER PLANTS↗
A comparison of surrogate constitutive models for viscoplastic creep simulation of HT-9 steel
Mechanistic microstructure-informed constitutive models for the mechanical response of polycrystals are a cornerstone of computational materials science. However, as these models become increasingly more complex – often involving coupled differential equations describing the effect of specific deformation modes – their associated computational costs can become prohibitive, particularly in optimization or uncertainty quantification tasks that require numerous model evaluations. To address this challenge, surrogate constitutive models that balance accuracy and computational efficiency are highly desirable. Data-driven surrogate models, that learn the constitutive relation directly from data, have emerged as a promising solution. In this work, we develop two local surrogate models for the viscoplastic response of a steel: a piecewise response surface method and a mixture of experts model. These surrogates are designed to adapt to complex material behavior, which may vary with material parameters or operating conditions. The surrogate constitutive models are applied to creep simulations of HT-9 steel, an alloy of considerable interest to the nuclear energy sector due to its high tolerance to radiation damage, using training data generated from viscoplastic self-consistent (VPSC) simulations. In conclusion, we define a set of test metrics to numerically assess the accuracy of our surrogate models for predicting viscoplastic material behavior, and show that the mixture of experts model outperforms the piecewise response surface method in terms of accuracy.
36 MATERIALS SCIENCE↗
Outer magnetospheric fluctuations and pulsar timing noise
The Cheng, Ho, and Ruderman (1986) outer-magnetosphere gap model was used to investigate the stability of Crab-type outer magnetosphere gaps for pulsars having the parameter (Omega-square B) similar to that of the Crab pulsar. The Lamb, Pines, and Shaham (1978) fluctuating magnetosphere noise model was applied to the Crab pulsar to examine the type of the equation of state that best describes the structure of the neutron star. The noise model was also applied to other pulsars, and the theoretical results were compared with observational data. The results of the comparison are consistent with the stiff equation of state, as suggested by the vortex creep model of the neutron star interior. The timing-noise observations also contribute to the evidence for the existence of superfluid in the core of the neutron star.
Cheng, K. S.↗