Two Essential Aspects of Solid Mechanics: Material Modeling and Computational Mechanics.
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This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.
Environmental fatigue modeling is a complex problem due to multiple failure modes and their intermixing. The failure modes are function of various underlying causes in addition to the corrosive effect of reactor coolant environment. Some of the major causes are time-dependence of material associated with cyclic loading, load sequence effect associated with random/variable amplitude loading, effect of strain amplitude and rates, effect of varying temperature (along both temporal and spatial directions) and the effect of mean strain and stress. The nonlinear intermixing of failure modes associated with above mentioned causing parameters makes the environmental fatigue modeling is a challenging task. Because of this challenge, fatigue is traditionally being modeled based on experimental data. However, test based empirical approach often requires hundreds of fatigue tests to model the above-mentioned intermixing failure causes even for a single material system. The problem is further exaggerated for reactor component made from multi-material systems such as made from both carbon and stainless-steel base metals and their similar and dissimilar metal welds. With the difficulty of conducting hundreds of fatigue tests to capture the above-mentioned intermixing failure causes, fatigue modeling approaches often depends on empirical models based on limited available test data such as available through ASME code and NUREG 6909. However, these limited test-data-based models may not be enough to accurately predict the life of reactor components. Accurate prediction of life of reactor component would become a necessity, particularly when the license of the reactors to be extended for long-term-operation (LTO) that is for well beyond its original design life of 40 years. The requirement of extending the license of reactor under LTO requires hundreds of fatigue tests to be conducted to understand the mechanism associated with the above-mentioned interdependent failure causes. However, conducting large number of fatigue tests is not a feasibility due to the cost involved. To address this issues Argonne National Laboratory (ANL) with the sponsorship of DOE Light Water Reactor Sustainability (LWRS) program trying to develop a hybrid predictive modeling approach. This is based on limited experiment-data, Artificial-intelligence (AI) – Machine-Learning (ML) - Deep-Learning (DL) based techniques and Multiphysics-computational-mechanics based modeling tools. The hybrid approach not-only can improve the accuracy of the existing stress analysis and fatigue modeling approach but also can reduce the over-dependency on test-based approach. Towards this goal following are some of the major contributions based on ANL’s FY-20 environmental fatigue modeling activities: 1) A cyclic plasticity material model database for 82/182 dissimilar metal weld, which can be readily shared with US nuclear industry and regulatory agency on request. 2) A well validated analytical modeling methodology to perform cycle-by-cycle stress prediction under both constant amplitude fatigue loading and variable amplitude fatigue loading (with load-sequence effect). 3) An AI/ML/DL based methodology to predict unmeasurable cyclic strain based on other available sensor signals. This type of approach can be used for estimating strain in real reactor components from other sensor readings. 4) An AI/ML based approach to improve the US capability on environmental fatigue testing. This is by improving ANL’s existing environmental fatigue testing capacity to conduct ASME required strain-controlled tests (by controlling strain amplitudes and its rate), while not measuring the strain (due to the difficulty of placing an extensometer in a narrow autoclave in a PWR-water-test system). 5) A simulation and experiment based probabilistic modeling methodology for time-series fatigue state and life estimation of reactor metal such as dissimilar metal weld.
Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.
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Reactor pressure vessels (RPVs) are safety-critical light-water-reactor components that, under irradiation, experience long-term material degradation in the form of embrittlement. This can increase their susceptibility to fracture under thermal-shock conditions, which could occur during off-normal transients such as loss-of-coolant accidents (LOCAs). During a LOCA, the most severe conditions for the RPV occur when emergency core cooling water is injected through the cold legs into the water-and-steam-filled RPV. The rapid cooling of the downcomer and internal RPV surface causes decreased temperature and elevated thermally driven tensile stresses in the RPV wall. This, combined with long-term material embrittlement, may cause fracture initiation at pre-existing flaws, challenging the integrity of the RPV. Assessing RPV integrity during transients with a large spatial variation in the coolant temperature requires a modeling approach that considers the effects of spatially varying coolant temperature on the fracture probability of a population of flaws distributed throughout the RPV, accounting for spatially varying embrittlement. Here, the present study addresses this need by demonstrating first-of-its-kind coupling of a high-fidelity 3D computational fluid dynamics code with 3D probabilistic fracture mechanics This was accomplished using representative models of a pressurized-water reactor subjected to small- and medium-break LOCA conditions, both of which can result in large spatial temperature variations. While the observed impact of accounting for 3D effects was minimal under the small-break LOCA this study indicates a significant increase in the probability of fracture initiation under the medium-break LOCA when 3D effects are considered, relative to a spatially uniform cooling scenario.
LEU (Low Enriched Uranium) plate-type fuel elements consist of a high-density, low-enrichment U–Mo alloy-based fuel foil encapsulated in an aluminum cladding and is fabricated through the Hot Isostatic Pressing (HIP) technique. Understanding the mechanism of possible failure modes of nuclear fuel is critical to mitigate potential consequences. One of the major contributing factors in various failure modes is stress and it greatly affects the integrity under temperature, pressure, and irradiation. These stresses could originate from various sources, including manufacturing, and operation, and can lead to deformation, cracking, or even complete failure of fuel elements. This study focuses on the development of a computational model that accurately predicts the residual stresses generated in the U10Mo fuel during fabrication. It has been observed that cladding creep has a substantial impact on the residual stresses in the U10Mo fuel post the HIP fabrication process. Furthermore, during the HIP bonding process the fuel plate system is heated to a temperature of 560 oC and as a result, the aluminum cladding transitions from (Al 6061-T6 to -O). This presents a challenge in capturing the change in material properties accurately. Therefore, a temperature dependent creep model such as hyperbolic sine creep model is considered to estimate the creep properties of the Aluminum cladding. The proposed calibrated creep model accurately predicts the residual stresses in the U10Mo fuel foil and agrees well with the experiments.
This corrigendum clarifies the conditions under which the proof of convergence of Theorem 1 from the original article is valid. We erroneously stated as one of the conditions for the Schwarz alternating method to converge that the energy functional be strictly convex for the solid mechanics problem. Finally, we have relaxed that assumption and changed the corresponding parts of the text. None of the results or other parts of the original article are affected.
This paper presents an overview of added features in a new version of the FAVOR (Fracture Analysis of Vessels Oak Ridge) computer code called FAVOR-OCI. The original FAVOR code was developed at the US Department of Energy’s Oak Ridge National Laboratory (ORNL) under the sponsorship of the US Nuclear Regulatory Commission (NRC). FAVOR is applied by US and international nuclear power industries to perform deterministic and probabilistic fracture mechanics analyses of commercial nuclear reactor pressure vessels (RPVs). Appli-cations of FAVOR are focused on insuring that the structural integrity of aging, and increasingly embrittled, RPVs is main-tained throughout their licensed service life. Based on the final ORNL release of FAVOR, v16.1, FAVOR-OCI extends existing deterministic features of FAVOR while preserving all prev-iously-existing probabilistic capabilities of FAVOR.The objective of this paper is to describe new deterministic features in FAVOR-OCI that can be applied to analytical evaluations of planar flaws. These evaluations are consistent with the acceptance criteria of ASME Code, Section XI, Article IWB-3610, including Subarticles IWB-3611 (acceptance based on flaw size) and IWB-3612 (acceptance based on applied stress intensity factor). The linear elastic fracture mechanics (LEFM) capabilities of FAVOR-OCI also incorporate the analytical procedures presented in the Nonmandatory Appendix A, Analysis of Flaws, Article A-3000, Method of KI Determination, for both surface and subsurface (embedded) flaws.The paper describes a computational methodology for determining critical values of fracture-related parameters that satisfy ASME Code Section XI acceptance criteria for flaws exposed to multiple thermal-hydraulic transients. These com-pute-intensive analyses can be carried out with a single execution of FAVOR-OCI. The new methodology determines critical values by solving for either the point of tangency or point of intersection between applied KI versus time histories and a user-selected fracture toughness material property (e.g., ASME KIc, FAVOR Weibull KIc, or Master Curve Weibull KJc) for surface or subsurface flaws. Situations where warm prestress conditions apply can also be addressed. The paper highlights a need for this new capability via applications to a recent independent review of safety cases for RPVs in two Belgian nuclear power plants (NPPs). That review required ASME Section XI assessments of several thousand embedded, quasi-laminar flaws in the wall of each RPV. Analysis results provided by the new capability contributed to the technical bases compiled from several sources by the Belgian nuclear regulatory agency (FANC) and eventually used by FANC to justify the restart of these NPPs.
Porous liquids (PLs) based on the zeolitic imidazole framework ZIF-8 are attractive systems for carbon capture since the hydrophobic ZIF framework can be solvated in aqueous solvent systems without porous host degradation. However, solid ZIF-8 is known to degrade when exposed to CO 2 in wet environments, and therefore the long-term stability of ZIF-8-based PLs is unknown. Here, through aging experiments, the long-term stability of a ZIF-8 PL formed using the water, ethylene glycol, and 2-methylimidazole solvent system was systematically examined, and the mechanisms of degradation were elucidated. The PL was found to be stable for several weeks, with no ZIF framework degradation observed after aging in N 2 or air. However, for PLs aged in a CO 2 atmosphere, formation of a secondary phase occurred within 1 day from the degradation of the ZIF-8 framework. From the computational and structural evaluation of the effects of CO 2 on the PL solvent mixture, it was identified that the basic environment of the PL caused ethylene glycol to react with CO 2 forming carbonate species. These carbonate species further react within the PL to degrade ZIF-8. The mechanisms governing this process involves a multistep pathway for PL degradation and lays out a long-term evaluation strategy of PLs for carbon capture. Additionally, it clearly demonstrates the need to examine the reactivity and aging properties of all components in these complex PL systems in order to fully assess their stabilities and lifetimes.
The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation, the lack of direct measurement of these internal variables for calibration and validation, and the weak physical underpinning of those phenomenological laws have long been criticized as barriers to creating realistic models. In this work, geometric machine learning on graph data (e.g. finite element solutions) is used as a means to establish a connection between nonlinear dimensional reduction techniques and plasticity models. Geometric learning-based encoding on graphs allows the embedding of rich time-history data onto a low-dimensional Euclidean space such that the evolution of plastic deformation can be predicted in the embedded feature space. Finally, a corresponding decoder can then convert these low-dimensional internal variables back into a weighted graph such that the dominating topological features of plastic deformation can be observed and analyzed.
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