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Data-driven reduced-order models for rank-ordering the high cycle fatigue performance of polycrystalline microstructures
Computationally efficient estimation of the fatigue response of polycrystalline materials is critical for the development of next generation materials in application domains such as transportation, health, security, and energy industries. This is non-trivial for fatigue of polycrystalline metals since the initiation and growth of fatigue cracks depends strongly on attributes of the microstructure, such as the sizes, shapes, orientations, and neighbors of individual grains. Furthermore, regions of microstructure most likely to initiate cracks correspond to the tails of the distributions of the microstructure features. This requires the execution of large numbers of experiments or simulations to capture the response of the material in a statistically meaningful manner. In this work, a linkage is described to connect polycrystalline microstructures to the statistically signified driving forces controlling the high cycle fatigue (HCF) responses. This is achieved through protocols that quantify these microstructures using 2-pt spatial correlations and represent them in a reduced-dimensional space using principal component analysis. Reduced-order relationships are then constructed to link microstructures to performance characteristics related to their HCF responses. As a result, these protocols are demonstrated for α-titanium, which exhibits heterogeneous microstructure features along with significant elastic and inelastic anisotropies at both the microscale and the macroscale.
Development and preliminary validation of a mechanistic multiscale model for fuel-cladding chemical interaction in metallic nuclear fuels
Despite decades of fuel rod material and design improvements, fuel-cladding chemical interaction (FCCI) remains the single-most lifetime-limiting behavior for modern metallic fuel rods. Constraining fuel lifetime increases operating costs, limiting the economic viability of commercializing metallic nuclear fuel technology. A mechanistic multiscale model utilizing the finite element method-based MARMOT and BISON codes was developed to more confidently predict cladding-side FCCI and its impact on fuel performance. The new BISON model incorporates mesoscale models for the effects of fuel microstructure evolution on the transport of wastage-inducing lanthanides through the fuel and for the kinetics of cladding wastage layer growth. The mesoscale models, in turn, build on lanthanide transport property data obtained from the atomistic scale. Preliminary validation studies using wastage thickness and cladding profilometry data from four fuel rods irradiated in Experimental Breeder Reactor II experiment X447 and one fuel rod from Fast Flux Test Facility experiment IFR1 show that the new model predicts cladding wastage and its effects on cladding deformation as well as existing empirical FCCI correlations. The new model is expected to aid in the design of new metallic fuel concepts, including fuel additives, cladding liners, and sodium-free annular fuel geometries. In conclusion, future work will focus on broader validation and refinement of the model’s treatment of different fuel alloys and cladding materials.
Tritium Transport Modeling at the Pore Scale in Ceramic Breeder Materials Using TMAP8
Fusion reactors depend on the blanket material to breed and release tritium at the same rate or faster than it is consumed by the fusion reaction. Cellular ceramic breeders (CCBs) are dense materials that can maintain a high tritium breeding ratio while promoting tritium release because of highly connected pores. Assessing the tritium breeding capabilities of these materials requires a combination of extensive experimental and modeling efforts. In this work, we develop and calibrate a multiphysics model of tritium transport. This novel model accounts for ceramic and pore diffusion, trapping and detrapping, and several surface reactions at the pore surface. We perform a sensitivity analysis and calibrate the model by comparing its predictions against experimental measurements of deuterium absorption. The calibrated model is then used to model tritium absorption in samples with different pore microstructures to investigate the effect of pore interconnectivity on tritium absorption. The model is part of the development of the multiscale, multiphysics framework for tritium transport [i.e., the Tritium Migration Analysis Program (TMAP8)], which is itself built on top of the finite-element multiphysics framework multiphysics object-oriented simulation environment (MOOSE). This study demonstrates some of TMAP8’s capabilities and is the first step toward assessing the tritium breeding capabilities of ceramic breeder material designs.
A Novel Constitutive Model for Ti-6Al-4V Selective Laser Melting Based on a Microstructural Material Representation
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TRITIUM TRANSPORT MODELING AT THE PORE SCALE IN CERAMIC BEEDER MATERIALS USING TMAP8
Fusion reactors depend on the blanket material to breed and release tritium at the same rate or faster than it is consumed by the fusion reaction. Cellular ceramic breeders are dense materials that can maintain a high tritium breeding ratio while promoting tritium release thanks to highly connected pores. Assessing the tritium breeding capabilities of these materials requires a combination of extensive experimental and modeling efforts. In this work, we develop and calibrate a multiphysics model of tritium transport. This novel model accounts for ceramic and pore diffusion, trapping and detrapping, and several surface reactions at the pore surface. We perform a sensitivity analysis and calibrate the model by comparing its predictions against experimental measurements of deuterium absorption. The calibrated model is then used to model tritium absorption in samples with different pore microstructures to investigate the effect of pore interconnectivity on tritium absorption. The model is part of the development of the multiscale, multiphysics framework for tritium transport (i.e., the Tritium Migration Analysis Program [TMAP8]), which is itself built on top of the finite element multiphysics framework MOOSE. This study demonstrates some of TMAP8’s capabilities, and is the first step toward assessing the tritium breeding capabilities of ceramic breeder material designs.
Role of crystallographic orientation on intragranular void growth in polycrystalline FCC materials
In this study, we study the effect of crystallographic orientation and applied triaxiality on the growth of intragranular voids. Two 3D full-field micromechanics methods are used, the dilatational visco-plastic fast-Fourier transform (DVP-FFT) and the crystal plasticity Finite Elements (CP-FE), both of which incorporate a combination of crystalline plasticity and dilatational plasticity. We demonstrate with several select cases that predictions of void growth from both formulations agree qualitatively. With the more computationally efficient DVP-FFT, additional effects of polycrystalline microstructure and the influence of nearest neighborhood are investigated. Crystals bearing a single intracrystalline void are studied in three types of 3D microstructural environments: isolated single crystals, individual equal-sized grains within a regular polycrystal, and individual variable sized grains within a polycrystal with grains and voids randomly located. We show that loading type plays a significant role. In strain-rate controlled conditions, voids in the hardest [111]-crystals grow the fastest in time, whereas in stress-controlled conditions, voids in the softest [100]-crystal grow the fastest in time. The analysis reveals that on average void growth is slower for the same starting orientation in the polycrystal than in the single crystal. We find that at the highest triaxiality tested that the correlation between crystal orientation and void growth rate in the polycrystal strengthens, drawing closer to that seen in the isolated single crystals. These results and model can help guide the microstructural design of polycrystalline materials with high strength and damage-tolerance in high-rate deformation.
Sparse thermal data for cellular automata modeling of grain structure in additive manufacturing
Grain growth in the wake of the melt pool formed during alloy-based additive manufacturing (AM) is complex and multifaceted, depending on parameters governing heat transport, fluid flow, and solidification itself. Cellular automata (CA) models have proven effective in providing computationally efficient and physically sound predictions of grain structure for several AM problems, but their efficiency is tied to the performance of heat transport models. CA models use only a small portion of the problem's temperature data (near the moving melt pool boundary), and much of the CA calculations do not affect the final result due to re-melting of material. Coupling of and communication between heat transport and solidification models, and eliminating operations irrelevant towards final grain structure prediction, will be necessary for using these methods for efficient simulation of large parts. In this work, we introduce a procedure of decoupling the CA from temperature field simulation, using files of relevant temperature data written by the heat transport model. This approach is validated against the standard coupling approach using data obtained through the computational fluid dynamics software OpenFOAM. Negligible differences are seen in grain size, volume, and texture distributions for multilayer simulation of test problems, while the quantity of temperature data for these test problems was reduced by four orders of magnitude (from 100s of GB to 10s of MB) and the code performance sped up by a factor of around 50. Furthermore, variability in microstructure as a function of cell size, substrate, time step, and nucleation parameters is studied, and it is found that cell sizes less than or equal to 1.67 μm and sufficiently small time steps yield Αstatistically equivalent microstructures. Finally, a potential use case for this CA approach—the layer-wise convergence in grain structure starting from extremes in initial grain size—is examined. This approach's ability to simulate expected trends in nucleation and epitaxial grain growth for large regions of microstructure, simulated independently of heat transport models themselves, should prove useful for investigation of various microstructure uncertainties and prediction of part-scale experimental results.
Predicting the creep-rupture lifetime of a cast austenitic stainless steel using Larson-Miller and Wilshire parametric approaches
An experimental dataset of just over 100 creep tests of a cast austenitic stainless steel, CF8C-Plus, was analyzed by two temperature-compensated parametric models (Larson-Miller, Wilshire et al.) to predict long-term lifetimes as functions of temperature and stress. The dataset and associated regression analyses showed greater scatter than typically found in recent similar studies of wrought Ni-based alloys by the same two models and was attributed to the microstructural inhomogeneity of the cast stainless steel. Qualitatively, the Larson-Miller formalism showed greater lifetime prediction accuracy than the Wilshire approach, with the latter model's predictive ability being particularly degraded by the presence of two very significant outlier results. This observation suggests that the Larson-Miller approach is more robust when treating rupture-time datasets that show particularly wide experimental scatter. Despite the differences in the overall predictive ability, both models yielded similar predictions of the applied stress at which CF8C-Plus would have a creep-limited lifetime of 100,000 h when loaded below the yield point.
Rationalization of the tensile creep behavior of the Nb45Ta25Ti15Hf15 bcc refractory complex concentrated alloy using Rao-Suzuki screw dislocation glide model
Published experimental tensile creep data for refractory body-centered cubic alloy Nb45Ta25Ti15Hf15 (NTTH) at temperatures ranging from 850–950 °C and applied tensile stresses 50–300 MPa are analyzed using the Rao-Suzuki screw dislocation glide model of solid solution strengthening. It is shown that the experimental creep data as well as transmission electron microscopy observations of post- creep deformation dislocation microstructure are in agreement with the model results. This suggests that the creep deformation of NTTH at 850–950 °C is controlled by screw dislocation glide.
A sensitivity analysis of the columnar-to-equiaxed transition for Ni-based superalloys in electron beam additive manufacturing
Solidification conditions experienced during Selective-Electron Beam Melting (S-EBM) of Nickel-Base superalloys generally lead to epitaxial grain growth from previous layers, resulting in highly textured columnar grain structures, and consequently, highly anisotropic mechanical properties. However, in recent work, researchers have been able to produce equiaxed grain structures by changing the scan strategy to influence the solidification conditions, thereby obtaining isotropic properties. The competition between columnar and equiaxed grain formation is governed by both the local thermal conditions and alloy thermodynamics. The above examples demonstrate successful manipulation of the thermal conditions through changes in process parameters. However, there is no guarantee that process conditions that encourage the formation of equiaxed grains for a given alloy will coincide with the production of defect free material. The goal of this work is therefore to understand the influence of alloy composition on the columnar-to-equiaxed transition (CET) so that alloys may be designed such that grain structure control is accessible to a wider range of S-EBM process conditions. A CET model originally developed by Hunt and extended by Gäumann was used to relate processing conditions to resulting microstructure. A sensitivity analysis of the CET model was performed using the Element Effects Methods. Furthermore, the results lead to a comparison of the relative effects of various alloying additions on the CET, as well as an assessment of other model parameters, including, most significantly, the nucleation density of equiaxed grains.
Predicting oxidation damage in ultra high-temperature borides: A machine learning approach
Ultra-high temperature (UHT) borides are ceramics materials with melting points above 3000 °C for structural applications in extreme environments. However, at temperatures exceeding 1600 °C and under oxidizing conditions, the material suffers from detrimental degradation. Optimized design and performance of diboride materials under such extreme conditions requires filling the missing composition-microstructure-oxidation gap. This study proposes a computational data-driven framework to connect the processing and microstructure of Ultra-high temperature borides with the oxidation damage. Random Forest Regressor (RFR) model is adopted to forecast the oxide scale thickness developed after oxidation testing based on processing variables and microstructural features. The model trained on a dataset consisting of 107 samples of experimental data extracted from the literature aims to predict oxidation damage. With proper data manipulation and fine model tuning, the predictor could forecast the oxide scale thickness of UHT diborides with a Mean Absolute Error of 37.45 μm and an R-square of 0.83. This model could be used as a high-throughput scheme to design and test new UHT diborides materials computationally. Furthermore, a model with larger composition capabilities could also be developed in the future as more experimental data become available.
Time-dependent water vapor desorption isotherm model of hardened cement paste
Highlights: • Short-term and long-term desorption isotherms of hardened cement paste are reviewed. • Water content at RH depends on both thermodynamic and microstructural equilibria. • An extended GAB equation is proposed to fit the cavitation drop during desorption. • A dynamic time-dependent sorption isotherm model is shown and used for simulations. • Numerical results capture anomalous drying in the same RH as seen experimentally. This study aims to enhance moisture transport modeling by elucidating the so-called anomalous water diffusion in cementitious materials. Water desorption isotherms are measured from samples at various drying stages using techniques with different durations to quantify the impact of the drying duration on the water sorption ability. A single water sorption isotherm does not solely give a relationship between the water content and relative humidity but also represents the state of microstructure. The continuous evolution of a desorption isotherm due to drying-induced microstructural rearrangement is demonstrated. For numerical modeling, the microstructural alteration can be explicitly considered through a dynamic desorption isotherm model, which governs the local thermodynamic equilibrium at the capillary meniscus. This approach is implemented into a multiphase transport code, whose ability to predict drying is validated using literature data. Finally, the effect of prolonged drying on the colloidal nature of the calcium-silicate-hydrate gel is discussed.
The Effect of CO 2 Pressure on Chromia Scale Microstructure at 750°C
To understand and model performance in supercritical CO 2 (sCO 2 ) for high-efficiency, concentrating solar power (CSP) and fossil energy power cycles, reaction rates are compared at 750°C in 0.1 MPa CO 2 and 30 MPa sCO 2 as well as laboratory air as a baseline on structural materials such as Ni-based alloy 625. Due to the thin reaction products formed even after 5000 h, scanning transmission electron microscopy was used to study the Cr-rich surface oxide scale. The scales formed in CO 2 and sCO 2 had a much finer grain size with more voids observed in CO 2 . However, the observations on alloy 625 were complicated by Mo and Nb-rich precipitates in the adjacent substrate and Al internal oxidation. To simplify the system, a binary Ni-22Cr alloy was exposed for 1000 h in similar environments. After exposure in sCO 2 , there was an indication of carbon segregation detected on the Cr 2 O 3 grain boundaries. After exposure in air, metallic Ni precipitates were observed in the scale that were not observed in the scale formed on alloy 625. The scale formed in air on a second Ni-22Cr model alloy with Mn and Si additions did not contain Ni precipitates, suggesting caution when drawing conclusions from model alloys.
Fatigue life prediction of powder bed fused–laser beam AlSi10Mg: Incorporating critical defects via crystal plasticity modelling
The current study provides a microstructurally-based computational framework to predict the fatigue life of additive manufactured (AM), i.e., powder bed fused–laser beam (PBF-LB), AlSi10Mg specimens using the crystal plasticity finite element method (CPFEM). The fractography analysis, electron backscatter diffraction (EBSD), uniaxial and cyclic responses, and fatigue life of specimens were used to inform the computational framework. CPFE simulation was used to compute fatigue indicator parameters (FIPs) as fatigue driving forces. A new fatigue criterion is introduced based on FIPs, which was calibrated using experimental fatigue data. The proposed fatigue measure was evaluated versus the specimens with critical defects of various sizes and locations subjected to different stress amplitudes. The results show that the developed framework can capture the fatigue life of samples with different critical defect locations and sizes along with different stress amplitudes for both high-cycle fatigue (HCF) and very high-cycle fatigue (VHCF) regimes.
A mechanistic interpretation of Nelson curves for PVP failures under high temperature hydrogen attack
As an empirically established design criterion, Nelson curves that relate the service temperature and the allowable hydrogen partial pressure have been developed and utilized for more than sixty years in pressure vessels and piping (PVP) safety design. Despite a relatively clear thermodynamic understanding of the high-temperature-hydrogen-attack (HTHA) problem, the detailed fracture process on the microstructural length scales, however, remains elusive, and a quantitative assessment of the PVP lifetime under HTHA from the available creep fracture dataset is still not possible. This work develops a microstructure-informed and micromechanics-based model by incorporating a synergy between hydrogen transport and intergranular-cavity-based fracture process. Based on the available creep lifetime data of C-0.5Mo steels, we are able to calibrate material constitutive parameters, and then conduct nonlinear finite element simulations that reveal a real-time stress-induced hydrogen diffusional transport along grain boundaries, coupled with a microstructure-explicit failure process, from which Nelson curves can be computed. Such failure analyses allow us to delineate two distinct regimes on the Nelson curves, i.e., dislocation-creep-controlled or grain boundary diffusion-assisted cavity growth. More importantly, we found that a small change of the pipe thickness and applied stresses can significantly shift these lifetime curves. However, these two parameters are usually not provided in Nelson curves, thus limiting their usage in material selection and safety design. In conclusion, this discrepancy can clearly be mitigated by extensive parametric studies from our micromechanical modeling/simulation framework.
Mesoscale Modeling for Restructuring and Fragmentation in High Burnup UO 2
This report summarizes the mesoscale modeling conducted in fiscal year 2025 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, focusing on the microstructural evolution and restructuring in high burnup UO 2 nuclear fuel and its impact on fuel fragmentation. We developed a pioneering phase-field model to simulate restructuring behavior across different regions of high burnup fuel, including the dark zone and rim region. A grand-potential-based phase-field model is employed to concurrently evaluate subgrain formation and the growth of fission gas bubbles within the fuel. An energy-based subgrain formation criterion was introduced to simulate the restructuring process. The effects of temperature and burnup rate were studied to capture how each of these parameters influences the characteristics of the restructured fuel. Subgrain formation was observed to initiate around existing fission gas bubbles and proceed toward triple junctions, grain boundaries, and grain interiors. Under a given subgrain formation rate, the rate of restructuring increases with rising fuel temperature. The restructuring occurs faster with higher burnup rate. A restructuring bias was observed within the microstructure, due to the variation in defect accumulation when comparing different grains. Microstructures corresponding to the dark zone and rim region can be obtained by parameterizing the model with the appropriate defect production rate, as determined based on the burnup rate and temperature. The predicted microstructures are consistent with experimental observations of the restructured regions. Based on the mesoscale simulations, a mechanistic model for restructuring and grain size evolution was implemented in BISON. Thus, this work provides a first-of-its-kind restructuring model for different regions of high-burnup fuel to BISON. It was shown that the model predicts appropriate grain size evolution along fuel radius as those observed in experiments. This model enables BISON to predict the effect of restructuring on the fission gas release. Finally, the phase-field fracture simulation with dark zone specific microstructures were presented to provide the fragmentation criteria for the dark zone. This work introduces a first-of-its-kind restructuring model for high burnup fuel, significantly enhancing BISON's predictive capabilities.
Bayesian strategies for uncertainty quantification of the thermodynamic properties of materials
Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution. The goal of thermodynamic models is to capture data from both experimental and computational studies and then make reliable predictions when extrapolating to new regions of parameter space. These predictions will be impacted by artifacts present in real data sets such as outliers, systematic errors, and unreliable or missing uncertainty bounds. Such issues increase the probability of the thermodynamic model producing erroneous predictions. We present a Bayesian framework for the selection, calibration, and quantification of uncertainty of thermodynamic property models. The modular framework addresses numerous concerns regarding thermodynamic models including thermodynamic consistency, robustness to outliers, and systematic errors by the use of hyperparameter weightings and robust Likelihood and Prior distribution choices. Furthermore, the framework’s inherent transparency (e.g. our choice of probability functions and associated parameters) enables insights into the complex process of thermodynamic assessment. We introduce these concepts through examples where the true property model is known. Additionally, we demonstrate the utility of the framework through the creation of a property model from a large set of experimental specific heat and enthalpy measurements of Hafnium metal from 0 to 4900K.