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At least 1,495 records · Page 83

Local Power Impact Experiment Design for a New Fuel Type for use in the Advanced Test Reactor

The Advanced Test Reactor (ATR), and complimentary zero-power ATR Critical (ATRC) reactor, located at Idaho National Labs (INL), are undergoing conversion from Highly Enriched Uranium (HEU) to Low Enriched Uranium (LEU). Both have a variety of testing locations that can receive large variations in flux due to its unique serpentine design, consisting of five lobes (see Figure 1). Initial criticality and power distribution throughout the core are controlled by core-external outer shim control cylinders (OSCCs). Distinct test loops allow for testing at specific temperatures, pressures, and irradiation conditions. The ATR is one of the key nuclear engineering research and testing facilities within the DOE National Laboratory Complex, and the ATRC supports its operation [1]. Currently, the Office of Material Management and Minimization (M3) within the National Nuclear Security Administration of the DOE is working to convert the remaining research reactors, including the ATR, from 93% HEU fuel to 19.75% LEU fuel (LEU) to support non-proliferation [2]. Extensive materials testing at INL and internationally has demonstrated that a high-density uranium molybdenum (U 10Mo) alloy can meet the performance requirements of the remaining high powered research reactors. However, there are many technical challenges to address before the conversion to LEU can be successful, including the accurate characterization of the reactor core physics with LEU fuel. Reactor physics safety evaluations currently use Monte Carlo for the 21st Century (MC21), a continuous-energy Monte Carlo radiation transport code [3]. Existing MC21 models of the ATR and ATRC cores have a validation basis for use in neutronics analyses with HEU fuel. The models are used to support safety analyses that include comparisons to the safety requirements for the reactors. However, the use of the LOWE element in the ATR and ATRC is not currently covered by the current model validation basis. To deploy the new fuel type, extensive computational reactor physics support is necessary to support the use of LOWE in the ATR and ATRC. Therefore, LOWE requires a rigorous validation basis, aligned with that of HEU fuel, that takes advantage of the existing software tools and processes currently used for the ATR and ATRC. The experiment to validate of the MC21 models for determining power, the Power Impact Validation Experiment, will consist of two flux runs in the ATRC, one with fully HEU loading and one with a single LOWE element. Both flux runs will be instrumented with 20 sets of azimuthal fission wires and 3 sets of axial fission wires, as shown in Figure 4. Standard flux run methodology will be used [4]. Power Impact Validation Experiment data will be compared against MC21 calculated data, both for absolute fission rate accuracy and to determine the relative change in fission rates between the two runs. The results of the Power Impact Validation Experiment and subsequent evaluations will provide the validation basis for MC21 for use with LOWE elements. Key features of the Power Impact Validation Experiment include: (1) Two flux runs to allow for LOWE perturbed measurements to be compared to already validated measurements taken from a full core of HEU fuel, (2) Optimization of instrumentation to balance analytical needs with practical considerations (e.g., limited time window to count beta particles from fission products), and (3) Standard ATRC core loading, including both driver positions and flux traps, to minimize cost while remaining representative of typical ATR core loading.

42 ENGINEERING↗

Tensile testing and fracture mechanism analysis of polyvinyl alcohol nanofibrous webs

Abstract A tensile properties testing study was conducted to understand the influence of thickness, cross‐head speed (speed of testing), gauge length (GL; specimen test length), and sample shape on important tensile properties of polyvinyl alcohol (PVA) nanofiber webs. The effects of each testing parameter on load at break, extension at break, Young's modulus, and tensile stress–strain curve of PVA nanofiber webs are analyzed. The Welch two sample t ‐tests show the significant difference among tested data. Using interaction plots, two‐way analysis of variance, and margin mean plots, the interaction effects among testing parameters have been analyzed. Of all the factors, cross‐head speed, the interaction among GL, and sample thickness (GL: Thickness) and the interaction among GL, testing speed and sample thickness (GL: Speed: Thickness) have significant influence on the tensile properties of PVA nanofiber webs. Moreover, the hypothesized model of mechanism of tensile strain–stress curve of PVA nanofiber webs has been proposed. Based on the model, the tensile strain–stress curve can be split into three stages: linear elastic, partial break up, and complete breakage. This study will provide a better understanding of tensile testing parameters' effects and their interaction effects on the tensile properties of nanowebs.

Lou, Lihua↗

Understanding and improving anode performance in an alkaline membrane electrolyzer using statistical design of experiments

The behavior of the oxygen-evolving positive electrode (i.e. anode) in the anion exchange membrane water electrolyzer (AEMEL) is complex and influenced by several factors. Very few studies have been performed to understand oxygen evolution reaction (OER) behavior by optimizing the individual factors that influence performance. Here, this study highlights the effects of catalyst loading, catalyst selection, porous transport layer (PTL) type and conductive additive content. The influence of each factor is elucidated through a design of experiments (DoE) approach with a full statistical analysis. Electrochemical data, alongside Pareto charts, parametric trends and their mutual interactions are discussed. This DoE approach is also helpful in making useful predictions and discovering new combinations to be tested. The end result was a high-performance AEMEL able to operate at a current density of 1.0 A/cm 2 at 1.80 V with IrOx OER and PtNi hydrogen evolution reaction (HER) catalysts using 0.3 M KOH fed to the anode. Even lower operating voltage was observed with PbRuOx catalyst at the anode, 1.64 V @ 1.0 A/cm 2 , though the cell decay rate was higher. Lastly, a IrOx/PtNi cell was stably operated continuously for 30 days (720 h) at 1.0 A/cm 2 . This study can serve as a guide for optimal electrode design with insights into component-performance compromises, which can aid in making design choices and performing techno-economic analyses.

08 HYDROGEN↗

Cluster-Spin-Glass Magnetic Behavior and Morphology in the Coordination Polymer Alloys Fe y Co 1– y BTT

We report the synthesis of a series of pseudo-1D coordination polymer (CP) materials with the formula Fe y Co 1–y BTT (BTT = 1,3,5-benzenetrithiolate). These materials were structurally characterized by PXRD Rietveld, EXAFS, and PDF analyses, revealing that the CP superstructure enables a continuous and isomorphous alloy between the two homometallic compounds. Lower Fe loadings exhibit emergent spin glass magnetic behavior, such as memory effects and composition-dependent spin glass response time constants ranging from 6.9 × 10 –9 s to 1.8 × 10 –6 s. These data are consistent with the formation of spin clusters within the lattice. The magnetic behavior in these materials was modeled via replica exchange Monte Carlo simulation, which provides a good match for the experimentally measured spin glassing and magnetic phase transitions. Furthermore, these findings underscore how the rigid superstructure of CP and MOF scaffolds can enable the systematic tuning of physical properties, such as the spin glass behavior described here.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Black carbon-climate interactions regulate dust burdens over India revealed during COVID-19

India as a hotspot for air pollution has heavy black carbon (BC) and dust (DU) loadings. BC has been identified to significantly impact the Indian climate. However, whether BC-climate interactions regulate Indian DU during the premonsoon season is unclear. Here, using long-term Reanalysis data, we show that Indian DU is positively correlated to northern Indian BC while negatively correlated to southern Indian BC. We further identify the mechanism of BC-dust-climate interactions revealed during COVID-19. BC reduction in northern India due to lockdown decreases solar heating in the atmosphere and increases surface albedo of the Tibetan Plateau (TP), inducing a descending atmospheric motion. Colder air from the TP together with warmer southern Indian air heated by biomass burning BC results in easterly wind anomalies, which reduces dust transport from the Middle East and Sahara and local dust emissions. The premonsoon aerosol-climate interactions delay the outbreak of the subsequent Indian summer monsoon.

54 ENVIRONMENTAL SCIENCES↗

A Data-Driven Voltage Control Strategy for Distribution Grids With Distributed Energy Resources

Traditionally, distribution system control approaches have been model-based. The deployment of advanced metering infrastructure has provided electric utilities with the capability of data-driven control with real-time measurements. The shift from model-based to data-driven control represents a significant advancement in the management of distribution systems, offering a more adaptive approach to system control because of the ability to dynamically adapt to changing conditions without the need for system modeling. Here, in this paper, a behavioral data-driven control method is developed to provide voltage regulation to an actual distribution system by controlling the legacy devices and distributed energy resource (DER) assets. The studied distribution system has a load tap changer and three capacitor banks as the legacy devices and photovoltaic systems as the DERs. The performance of the proposed control algorithm is validated using a laboratory test bed setup considering multiple scenarios. The results show that the proposed control achieved 99% voltage regulation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

ENERGY STAR for Tenants: An Online Energy Estimation Tool for Commercial Office Building Tenants

The commercial building sector consumes over 18% of the total energy in the United States. According to the 2012 Commercial Building Energy Consumption Survey (CBECS), office buildings comprise nearly 16 billion square feet of floor space and consume 253 billion kWh of energy annually. Office buildings represent nearly one-fifth of the energy consumed by commercial buildings, more than any other building type. Therefore, monitoring and reducing energy consumption in office buildings has become an increasingly important focus across the United States. The goal of the ENERGY STAR for Tenants program is to recognize office building tenants who demonstrate commitment to energy efficiency and environmental stewardship. Tenants seeking recognition must complete five major steps: estimate energy use, meter energy use, use efficient lighting, use efficient equipment, and share data. NREL is responsible for the underlying analysis performed for step one, estimating energy use. An online survey was developed for tenants to input information about their office space and its internal loads. NREL performed a parametric analysis across a large parameter space of office buildings. The analysis results were processed to map the user inputs to output energy ranges. The mappings enable the web tool to provide users with instant energy usage estimates based on a limited number of inputs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Electrification Futures Study: Scenarios of Power System Evolution and Infrastructure Development for the United States

This report is one in a series of Electrification Futures Study (EFS) publications. The EFS is a multiyear research project to explore potential widespread electrification in the future energy system of the United States. Electrification is defined as the substitution of electricity for direct combustion of non-electricity-based fuels used to provide similar services. The EFS is specifically designed to examine electric technology advancement and adoption for end uses in the major economic sectors of the United States, electricity consumption growth and load profiles, future power system infrastructure development and operations, and economic and environmental implications of electrification. Because of the expansive scope and the multiyear duration of the study, research findings and supporting data will be published as a series of reports, with each report being released on its own time frame.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Reducing Memory Consumption in Calico with Shared Memory

This document details the work to reduce memory consumption in Calico. Calico is SimTools’ Constructive Solid Geometry (CSG) and geometry painting library. It is primarily used to paint material volume fractions in the Eulerian meshes of the physics codes. Calico provides point-in-body checks for the geometry supplied by an Oso model, which are then aggregated by the host codes. In addition, Calico can be used to build Oso models and is used by Ingen for that purpose. Oso models, and thus Calico, provide support for various CSG primitives such as spheres, cylinders, surfaces generated by rotating tabular curve data, and STL files as well as binary combinations of those primitives. Prior to refactoring Calico will run out of memory on CTS-1 machines when 36 MPI ranks are used per node when reading STL models on the order of 1.5 GB. This limitation is a bottleneck in designer workflow. This problem has been alleviated through the use of data structures to both reduce memory consumption and to leverage MPI-3 shared memory. This report details the data structures targeted for refactoring in Calico, the methods and implementation details for reducing memory consumption and leveraging shared memory, and results for one test problem. Results show a memory reduction when loading a 1 GB STL file by a factor of 27.5, from 93.4 to 3.4 GB.

97 MATHEMATICS AND COMPUTING↗

Extraction of Vibration Data with Imaging

To date, the primary sensing technology used to measure the vibration response has been accelerometers and strain gages mounted directly to the structure and using either wired or, more recently, wireless telemetry. Cost issues with these sensors and the associated data acquisition systems typically limit the numbers that are deployed on in situ structures. Although there are a few structures with larger sensing counts that in some cases exceed over 1000 sensors, more typical numbers range from ten to one hundred sensors resulting in low spatial resolution when they are applied to physically large systems. When one considers that nuclear power plant structures usually have complex geometries, material properties, connectivity and boundary conditions, it is clear these current approaches to vibration measurements can only provide limited information about a system’s dynamics response characteristics. As an alternative, many non-contact measurement technologies have emerged, including point wise measurement methods such as Global Positioning System (GPS), microwave interferometry, and laser Doppler vibrometry (LDV), as well as simultaneous full-field measurement methods such as electronic speckle pattern interferometry, holography interferometry, and muon tomography, some of which can provide high spatial resolution measurements. Among these methods, digital video imaging techniques have emerged as a feasible solution for full-field vibration measurements that provide significantly more detailed dynamic response information because every pixel becomes a measurement point. Furthermore, recent advances in image processing and computer vision algorithms have been successfully used to process video data for experimental and operational modal analysis. Such full-field measurements have the potential to significantly improve many current structural assessment procedures including system identification (modal parameter estimation), structural health monitoring, load reconstruction, model validation, and model updating. Furthermore, more recent full-field imaging techniques can be accomplished with relatively low-cost, commercially-available off-the-shelf cameras. However, these measurement procedures have other limitations that must be considered such as the ability to only measure visibly accessible points on a structure and a more limited dynamic range and bandwidth than can be achieved with accelerometers or strain gages.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

National Modeling of Geothermal District Energy Systems with Ambient-Temperature Loops Using dGeo: Preprint

Geothermal district energy systems (DES) with ambient-temperature loops, also known as thermal energy networks, are one option for decarbonizing space heating and cooling loads. Geothermal fifth-generation DES include an "ambient" temperature thermal loop that connects heat pumps at each building with thermal balancing sources such as geothermal borehole fields. Heating and cooling are provided via a water-source heat pump at each end-user. This project seeks to analyze the nationwide potential for ambient-temperature loop districts by creating a new module within the Distributed Geothermal Market Demand Model (dGeo). dGeo is an agent-based modeling tool for distributed geothermal resources; it can investigate potential on a nationwide or statewide scale using geospatial data for all 50 states and thermal demands for existing buildings. This process allows for high-level estimates of technical and economic potential for ambient-temperature loop districts across the United States. Using GHEDesigner, a lookup table was created to size borehole fields for different thermal loads and ground conditions experienced across the country. A cost and financing structure, along with incentives, were applied. Cost estimates include costs for the distribution network, borehole field installation and operation, and circulation pump operation, while savings are calculated based on agent energy bills. This newly developed module can be used for assessing which areas of the country have the highest potential for agent benefits from ambient-temperature loop installation and assess the impact of different costing and pricing future scenarios. While the code is still under development and nationwide simulations are ongoing, initial results for two states are provided. Future work includes expanding the module to consider mixed residential and commercial districts and considering multiple costing scenarios.

ambient temperature loop↗

National Modeling of Geothermal District Energy Systems with Ambient-Temperature Loops Using dGeo

Geothermal district energy systems (DES) with ambient-temperature loops, also known as thermal energy networks, are one option for decarbonizing space heating and cooling loads. Geothermal fifth-generation DES include an "ambient" temperature thermal loop that connects heat pumps at each building with thermal balancing sources such as geothermal borehole fields. Heating and cooling are provided via a water-source heat pump at each end-user. This project seeks to analyze the nationwide potential for ambient-temperature loop districts by creating a new module within the Distributed Geothermal Market Demand Model (dGeo). dGeo is an agent-based modeling tool for distributed geothermal resources; it can investigate potential on a nationwide or statewide scale using geospatial data for all 50 states and thermal demands for existing buildings. This process allows for high-level estimates of technical and economic potential for ambient-temperature loop districts across the United States. A lookup table was created using GHEDesigner to size borehole fields for different thermal loads and ground conditions experienced across the country. A cost and financing structure, along with incentives, were applied. Cost estimates include costs for the distribution network, borehole field installation and operation, and circulation pump operation, while savings are calculated based on energy bills for building owners (agents). This newly developed module can be used for assessing which areas of the country have the highest potential for agent benefits from ambient-temperature loop installation and assess the impact of future cost and price scenarios. Initial results for statewide analysis (for Vermont) and nationwide (for United States) are provided. Future work includes expanding the module to consider mixed residential and commercial districts as well as evaluating multiple cost scenarios.

ambient-temperature loop↗

Distribution System State Estimation With High Penetration of Demand Response Enabled Loads

Demand-side operations incentivize utility customers to take part in various grid services. A demand response enabled load (DREL) is a flexible grid asset that schedules electricity consumption in response to a time-of-use (TOU) energy price. Consequently, its energy profile differs from that of a conventional load that is insensitive to price. This difference may cause new challenges for distribution system state estimation (DSSE). It is well known that DSSE often needs to use pseudo-measurements based on historic load profiles to increase system observability. However, historic profiles of conventional loads are not representative of DREL behaviors. Additionally, the inaccuracy impacts DSSE results and other DSSE-dependent operations. In this paper, we propose an online pseudo-measurement generation approach for DSSE with DRELs. We formulate an optimization model to represent DRELs self-adjusting actions. Sampling-based stochastic optimization techniques are proposed to account for uncertainties in DRELs. A set of representative DREL behavior data corresponding to the samples are used to characterize DREL pseudo-measurements. Case studies with modified IEEE 123-bus test system verify the validity of the proposed work.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Second ARM Aerosol Chemical Speciation Monitor Users’ Meeting Report

The aerosol chemical speciation monitor (ACSM) was developed to adapt the technology of the aerosol mass spectrometer (AMS) to routine, long-term, standalone monitoring. The calculation of particulate mass concentration from ACSM data requires the measurement of the response of the instrument to aerosol of specific size and composition as well as assumptions about the instrument response based on laboratory measurements and field experience acquired over more than two decades of operation of AMS and a decade of operation of the ACSM. Three parameters in the concentration calculations that are particularly important are the NO3 response factor (RFNO3), relative ionization efficiency (RIE), and the collection efficiency (CE). The values of RFNO3 and RIEs are determined from calibration, however the jump calibration method previously used in calibration can result in errors in the RIE for sulfate. This has been corrected by implementing a continuous calibration method. The default collection efficiency is 0.5. This has been shown to result in mass loadings that do not agree with mass determinations from other instruments because of effects of composition on the vaporization of the particles. The previous work of investigators addressing this issue is discussed. After preliminary work on ACSM and scanning mobility particle sizer (SMPS) data from the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) user facility Southern Great Plains (SGP) observatory collected in late 2016 and 2017 produced a parameterization of composition dependent collection efficiency very different from the results of previous studies, SMPS data were examined and we determined that there was significant mass that the instrument did not capture because the particles with diameters larger than 465 nm are not counted by this instrument. Data for the ultra-high-sensitivity aerosol spectrometer (UHSAS), SMPS, and ACSM are available for nearly all of 2019. The data from UHSAS and SMPS collected in 2019 were compared. We found that the UHSAS data has particle counts and total volumes significantly less than measured by the condensation particle counter (CPC) and SMPS. The SMPS data were extended by fitting the average volume distribution with a log normal curve and using this relationship to estimate a mass value for the SMPS over extended diameter range. The extended SMPS mass values result in a CDCE parameterization that is in better agreement with the results of other investigators, but is still different from other formulations. The working group recommends that the ACSM data be processed with a collective efficiency (CE)=1, that this be documented clearly in the metadata, and the use of the default CE of 0.5 or a formulation of composition-dependent collection efficiencies (CDCE) chosen by the user should be implemented based on the ammonium nitrate mass fraction. This is clearly necessary for the wintertime SGP ACSM data because of the high nitrate concentrations.

47 OTHER INSTRUMENTATION↗

An improved Method for Determining Transient Fuel Dilution of Oil in an Internal-Combustion Engine Using Laser-Induced Florescence and Multivariate Least Square Calibration

An optical diagnostic, based on laser-induced fluorescence (LIF), has been developed for on-engine measurements of real-time fuel dilution of engine oil or fuel in oil (FIO). Fuel dilution of oil is broadly relevant to advancing engine technology including durability, calibration, and catalyst-system management, and believed to promote destructive stochastic pre-ignition (SPI) during high-load engine operations. While standard (e.g., ASTM D3524-90) methods are not capable of real-time transient measurements, the LIF technique resolves transient dilution on the minutes time scale. We have expanded on our original FIO instrument development by introducing an improved analysis based on multivariate least square chemometrics analysis. The measurement uses a fuel dye (180–1300 parts per million, by mass) and monitors for its presence in the oil using 532 nm excitation and LIF. While the original FIO instrument utilized a two-color ratio method for analysis, the improved chemometric analysis uses the fully resolved LIF dye spectra to provide better predictive FIO accuracy (>92%) over a wide FIO range (1.5–14%) typical of engine application. We also investigate the effect of oil temperature on the LIF signal. Limited engine applications for demonstrating and validating the improved FIO instrument are shown, and the related data used to quantify practical detection limit and sensitivity. The improved analysis is insensitive to laser power fluctuation and change in detector integration time, providing an excellent FIO sensitivity (1–2%) and detection limit (0.01 %FIO) over a wide range of loads and injection timings, illustrating this updated approach to be a promising tool for advancing engine technology.

42 ENGINEERING↗

Enhancement of phase change material hysteresis model: A case study of modeling building envelope in EnergyPlus

Nowadays, buildings are expected to offer demand side services to the power grid to enhance the electrical load flexibility, which leads to the concepts of grid-interactive efficient buildings (GEBs). Phase change material (PCM)-based thermal energy storage has seen increasing attention in recent years for peak load shifting of grid-interactive efficient buildings (GEBs). Numerical models are critical tools for design and evaluation of PCM-integrated systems. Most industrial-grade PCMs are reported to melt/freeze over a temperature range instead of at a unique temperature. Such thermal hysteresis effect significantly affects the reliability of simulation results because not only the heat transfer process depends on melting and freezing temperatures, the PCM thermal properties change significantly during the phase change process as well. This study is aimed to develop a model for the PCMs used in the building envelope with the capability to accurately simulate hysteretic behaviors. Further, this model is based on a two-phase assumption and is implemented in a whole building energy performance simulation program (i.e., EnergyPlus). A comparison between numerical results and experimental data shows that during a complete phase transition, the two-phase model could achieve a good agreement with the experimental data. During a partial phase transition, the two-phase model could lead to significant improvements compared to other alternative PCM models, including the existing PCM model in EnergyPlus. Last, whole building simulations were performed to study this model's performance regarding heating/cooling loads and zone mean air temperature of a given building. The results show that the difference in hourly heating/cooling loads introduced by the models was less than 1% in design conditions, while significant changes were observed in both hourly heating/cooling loads and zone mean air temperature when the PCM envelope underwent partial phase transition processes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Temperature-dependent mechanical properties and crystal plasticity parameters for additively manufactured Haynes-214 alloy: Experiments and numerical modeling

Our experimental mechanical testing data demonstrated that the additively manufactured (AM) laser powder bed fusion (L-PBF) Haynes-214 alloy exhibits non-linear mechanical properties as the temperature rises from ambient to 870 °C. Crystal plasticity (CP) simulations provide an effective approach to gaining deeper insights into microstructure-property linkages under thermomechanical loading. This method can reduce the need for costly high-temperature mechanical testing while accounting for the effects of crystallographic texture and grain morphology on the mechanical behavior of AM materials. However, calibrating a CP model is time-consuming because individual simulations are computationally expensive and hundreds (or more) of iterations over parameter sets may be required. To address this issue, we have designed a machine learning-differential evolution (ML-DE) CP framework that can accurately interpolate the tensile properties of AM L-PBF Haynes-214 alloy across a wide temperature range from ambient to 870 °C, with minimal reliance on experimental data. The framework uses electron backscatter diffraction (EBSD) measurements to generate statistically equivalent microstructural volume elements to serve as inputs to the CP modeling framework. Stress–strain curves were generated from 1000 CP simulations, which serve as the training data set for the three ML regression algorithms explored: linear, extra-trees, and multi-layer perceptron. These three regression models were independently evaluated to compare their efficiency and identify the most suitable algorithm for the given problem. Results revealed that the extra-trees ML regressor outperforms the other models in both qualitative and quantitative aspects with an R 2 of 0.98. Subsequently, the differential evolution optimization approach is employed to calibrate the ML-based CP material parameters with experimental results obtained at various temperatures. Finally, temperature-dependent CP material parameters are formulated. The effectiveness and efficiency of the designed framework are validated through comparison with experimental results, demonstrating a high degree of agreement. These calibrated parametric constitutive equations enable further use of the CP model to study the deformation behavior of this alloy under a wide range of thermo-mechanical loading conditions.

36 MATERIALS SCIENCE↗

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗