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At least 1,351 records · Page 75

Observation-constrained kinetic modeling of isoprene SOA formation in the atmosphere

Isoprene has the largest global non-methane hydrocarbon emission, and the oxidation of isoprene plays a crucial role in the formation of secondary organic aerosol (SOA). Two primary processes are known to contribute to SOA formation from isoprene oxidation: (1) the reactive uptake of isoprene-derived epoxides on acidic or aqueous particle surfaces and (2) the absorptive gas–particle partitioning of low-volatility oxidation products. In this study, we developed a new multiphase condensed isoprene oxidation mechanism that includes these processes with key molecular intermediates and products. The new mechanism was applied to simulate isoprene gas-phase oxidation products and SOA formation from previously published chamber experiments under a variety of conditions and atmospheric observations during the Southern Oxidant and Aerosol Studies (SOAS) field campaign. Our results show that SOA formation from most of the chamber experiments is reasonably reproduced using our mechanism, except when the concentration ratios of initial nitric oxide to isoprene exceed ~ 2, the formed SOA is significantly underpredicted. The SOAS simulations also reasonably agree with the measurements regarding the diurnal pattern and concentrations of different product categories, while the total isoprene SOA remains underestimated. The molecular compositions of the modeled SOA indicate that multifunctional low-volatility products contribute to isoprene SOA more significantly than previously thought, with a median mass contribution of ~ 57 % to the total modeled isoprene SOA. However, this contribution is intricately intertwined with IEPOX-derived SOA (IEPOX: isoprene-derived epoxydiols), posing challenges for their differentiation using bulk aerosol composition analysis (e.g., the aerosol mass spectrometer with positive matrix factorization). Furthermore, the SOA from these pathways may vary greatly, mainly dependent on the volatility estimation and treatment of particle-phase processes (i.e., photolysis and hydrolysis). Our findings emphasize that the various pathways to produce these low-volatility species should be considered in models to more accurately predict isoprene SOA formation. The new condensed isoprene chemical mechanism can be further incorporated into regional-scale air quality models, such as the Community Multiscale Air Quality Modelling System (CMAQ), to assess isoprene SOA formation on a larger scale.

54 ENVIRONMENTAL SCIENCES↗

On the Onset of Plasticity: Determination of Strength and Ductility

The analysis of the work hardening variation with stress reveals insight to operative stress-strain mechanisms in material systems. The onset of plasticity can be assessed and related to ensuing plastic deformation up to the structural instability using one constitutive relationship that incorporates both behaviors of rapid work hardening (Stage 3) and the asymptotic leveling of stress (Stage 4). Results are presented for the mechanical behavior analysis of Ti-6Al-4V wherein the work hardening variation of Stages 3 and 4 are found to: be dependent through a constitutive relationship; be useful in a Hall-Petch formulation of yield strength; and provide the basis for a two point-slope fit method to model the experimental work hardening and stress-strain behavior.

36 MATERIALS SCIENCE↗

A Tool Kit for Generating Simulated Radiation Measurements for Advanced Reactor Safeguards and Security

A tool kit was developed to simulate and analyze passive radiation measurements of molten salt reactor (MSR) operations to support development of nuclear safeguards approaches for this emerging reactor technology. A Transient Simulation Framework of Reconfigurable Modules (TRANSFORM) multiphysics simulation of an MSR produces time-dependent isotopic inventories at user-selected locations within the model. The tool kit implements the Gamma Detector Response and Analysis Software (GADRAS) application programming interface to inject the TRANSFORM isotopic inventories extracted/processed by a Python pipeline into GADRAS models of user-defined geometries. The TRANSFORM inventories are the source terms used to obtain synthetic measurements from GADRAS-defined detectors. The speed of TRANSFORM and GADRAS simulations enables surveying the large design space of MSRs (e.g., fuel type, fuel salt composition, number of loops) and the plethora of measurements (e.g., location, detector type, and collimation) within the reactor. This has enabled timely assessment of the various measurement locations and detectors to identify the most effective and efficient safeguards approach for a specific MSR design. Lastly, the tool kit also simulates extracted samples that can be aged to a desired dose, enabling stakeholders to optimize a measurement plan to use sample analysis as an element within a broader material accountancy plan.

Westphal, Greg↗

Experimental Studies of Nonlinear Integrable Optics with Elliptic Potentials

The stable transport of charged particle beams is the core challenge in designing and operating accelerators. The current paradigm for transverse focusing is based on quadrupole and dipole elements, described as a linear integrable Hamiltonian by Courant and Snyder. The operational limits of high intensity accelerators are often determined by collective instabilities within the beam. Nonlinear elements may be added to suppress certain forms of these collective effects, but restrict the range of stable trajectories. These shortcomings motivate extending to a nonlinear integrable system which can offer the benefits of suppressing collective instabilities without limiting the stable trajectories. Danilov and Nagaitsev proposed a novel nonlinear integrable system with elliptical potentials, which could be implemented as magnetic elements in an accelerator. Such a system has been implemented for practical verification in the integrable optics test accelerator (IOTA), a small storage ring constructed for beam dynamics studies. Electron beam studies in IOTA treat the low-emittance beam as a macroparticle for detailed probing of the expected single particle dynamics. This dissertation details new measurements of the nonlinear integrable system relevant for practical implementation. Turn-by-turn measurements of the kicked beam responses are used for phase space reconstruction and analysis of the predicted nonlinear dynamics. The stability and aperture for various nonlinear configurations are measured with beam losses. Amplitude dependent detuning, a core figure of merit for suppressing instabilities, is measured and compared with high fidelity particle tracking simulations. The synchrotron radiation images of circulating beam allow direct measurements of the topology and lifetime in configurations where nonlinear focusing terms dominate.

Wieland, John [Michigan U.] (ORCID:000000028971852↗

Sensitivity analysis of design parameters in RowWise borehole layout for ground heat exchangers

Ground source heat pump systems offer a promising pathway toward energy-efficient building heating and cooling. The performance and cost-effectiveness of these systems heavily depend on the design of the ground heat exchanger (GHE), particularly the spatial placement of boreholes used in large commercial buildings. Among various borefield layout strategies, the RowWise approach generates and optimizes borehole configurations within irregular polygonal land boundaries, providing land-use efficiency and installation flexibility. While multiple geometric design parameters constrain the RowWise layout, their influence on the system thermal performance and total drilling requirements remains unclear. Thus, this study presents a sensitivity analysis of key design parameters influencing the RowWise layout of vertical borehole GHEs, including the perimeter spacing ratio, borehole spacing, borehole field rotation angle, and borehole length. GHEDesigner and Ray Tune are employed to generate and assess different RowWise configurations. A series of parametric simulations was conducted to quantify the impact of each parameter on geometric distribution, economic cost, and computational speed. The results provide critical insights into the sensitivity and relative importance of different design parameters of RowWise method, offering practical guidance for designers aiming to optimize GHE layouts by balancing thermal efficiency, land constraints, and economic feasibility.

Xu, Dikai [Purdue University]↗

Deterministic modelling of the SPERT IV reactor transients using the multi-physics capability of WIMS

The ANSWERS WIMS reactor physics code is being developed for whole core multi-physics modelling. The established neutronics capability for lattice calculations has recently been extended to be suitable for whole core modelling of Small Modular Reactors (SMRs). A whole core transport, SP3 or diffusion flux solution is combined with fuel assembly resonance shielding. An integrated thermal hydraulic solver permits temperature and density variations to feedback to the neutronics calculation. This capability can be applied to both steady state and time dependent transient problems. Nuclear reactor design and safety case development requires assessment of a range of reactor transients, to inform both normal operation limitations and accident scenario analysis. This paper presents new methodology developed in WIMS to couple the core neutronics to the integrated core thermal hydraulics solver for the simulation of reactor transients in whole core models. To support the validation of the multi-physics capability of WIMS, this capability has been applied to the reactivity insertion transient experiments performed in the plate fuelled SPERT-IV reactor. This study employs WIMS using the whole core solver MERLIN, which calculates the time-dependent flux distribution and magnitude, coupled to ARTHUR, which solves for the time-dependent thermal hydraulics solution, and provides thermal feedback via the cross sections generated by GEOM, which performs resonance shielding calculations and generates cross section data for the plate geometry. This spatial kinetics model, with dynamic cross section generation, allows for variations in the temperature and neutron flux profile with time.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Consequence Analysis of Residual Water in a Storage Canister - 20484

Recent observations from projects sponsored under the DOE-Nuclear Energy Spent Fuel and Waste Disposition campaign show that residual free water, well above the 0.4 gm-moles that correspond to a 3 torr rebound pressure after a 30-minute hold following prototypic drying, may remain within SNF canisters used for long-term dry storage. Specifically, experimental observations in an Integrated Research Project showed subzero temperatures and a local pocket of frozen water in a mockup fuel assembly subjected to an industry practiced drying process. In gas sampling and analysis from the High Burnup (HBU) Demonstration project, using a fully loaded and dried SNF canister, indicated presence of 100 g of residual water had remained in the canister. The effects of residual water in terms of potential adverse impacts on the condition of the SNF and the canister internals during long-term dry storage has been rigorously evaluated to address inadvertent residual water contents. The impact of residual water on the fuel and canister internals, with a focus on the oxidation of the cladding and of postulated exposed (breached-clad) fuel, were evaluated using an integrated set of time-dependent environmental conditions with semi-empirical materials oxidation models. An 'integration model,' with coupled sub-models, developed and previously used by the Center for Nuclear Waste Regulatory Analysis (CNWRA), was applied and expanded with improved sub-models for water radiolysis, and for cladding and fuel oxidations. Cladding oxidation models for various alloys were developed using the rate constants for various cladding alloys in the dry storage temperature range. A burnup-dependent fuel oxidation model was developed; it accounted for inhibition effect of fission products on fuel oxidation rates. The potential for extension of the initial breach flaw (1 mm hole) was evaluated by two separate mechanics criteria. In the first case, a critical cladding strain criterion was used. In the second case, a critical stress intensity was used to evaluate stability of a planar axial flaw postulate. A failure condition exists when a sufficient amount of fuel oxidation (at the postulated breached-clad location) causes fuel pellet swelling to load the cladding to meet a mechanics criterion for flaw extension. The integration model's results provide the following insights. The radiolysis-generated oxygen is consumed with a partitioning between the cladding and the fuel. The extent of cladding oxidation is no more than 2 μm additional consumption of the cladding metal even with 10 moles of residual water, indicating that changes in cladding conditions due to water are expected to be negligible. The conditions for cladding failure (breach opening size extension) directly correlates with the extent of fuel oxidation. Fuel oxidation significant to extend the breach could occur even with 5.5 moles of residual water. The results indicate that fuel oxidation vis-a-vis cladding oxidation is more likely under a higher radiation field, i.e., when radiolytic decomposition of the residual water occurs in few years compared to several decades, and that the conditions to cause failure are increased with fuel and cladding temperatures approaching the peak storage temperature limit of 400 deg. C. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Develop a Fast Analysis Solver for Welding Sequence Optimization

During the shipbuilding manufacturing process, materials are exposed to significant stresses, as induced both thermally and mechanically, that alter the intended design and significantly affect the production schedule, labor hours (fitting, welding, rework, etc.), and material structural performance. The type and magnitude of deformation of a given structure depends on many factors such as the material, thickness and quality of components, the process heat input, preheat and inter-pass temperatures, type and size of welds, welding sequence and direction, location, sequence, and degree of fixturing. Numerical simulations using finite element analysis (FEA) have long been used to analyze welding-induced structural distortion. For large assemblies, transient thermal elastic-plastic analysis (TEPA) can take days or weeks to run, and optimization of welding sequence is not feasible. Simplified analysis methods were developed to reduce computational time. However, it is challenging to use these techniques to fully optimize welding sequencing because of their applied simplifications in modeling weld details. A fast analysis solver that could be used by the shipbuilding industry is being developed for optimizing welding sequences by taking full advantage of modern GPU-based HPC hardware and incorporating patented acceleration schemes. The accelerated processing factors are up to 2200 times greater for large, multi-pass welded structures.

Yang, Yu-Ping↗

Soft matter approach for creating novel protein hydrogels using fractal whey protein assemblies as building blocks

In this study, mesoscopic sized fractal assembly (FA) particles were prepared using whey protein isolate; the coldset gelation properties of FA particles were investigated in-depth. Two types of FA particles (FA -62 and FA -90) with different mean sizes were synthesized through controlled thermal treatment of whey protein solutions at two concentrations (62 g/L and 90 g/L). Particle characteristics e.g. hydrodynamic radius, ζ-potential and surface hydrophobicity were dependent on pH and structure of FA. Transmission electron microscopy (TEM) observation confirmed the fractal morphology and small-angle X-ray scattering (SAXS) analysis suggested an internal fractal structure for the obtained FA particles. Eight cold-set FA protein gels (2 % w/v) were manufactured by controlling two gelling factors at two levels: pH (5.8 and 7.0) and Ca 2+ content (5 mM and 10 mM). Rheological characteristics in the large amplitude oscillatory shear regime revealed that pH 7.0 gels were softer and elastic while pH 5.8 gels were harder and brittle. Rheology Pipkin diagrams demonstrated that the strain softening/stiffening and the shear-thinning/thickening behaviors may be fine-tuned by manipulating the key gelation factors: e.g. FA structure, pH, and Ca 2+ . The entrainment speed-dependent friction coefficient curves showed that at an intermediate velocity regime (6-250 mm s -1 ), FA -90 particles induced hydrogels had superior lubrication effect compared to FA -62 gels. Further, this work demonstrated a food structure design approach regarding tuning texture and lubrication properties of protein gels without changing protein content and protein composition. The optimized protein hydrogels may be used as texturizer for "cleaner label" food formulas and/or as delivery system for carrying micronutrients.

60 APPLIED LIFE SCIENCES↗

Low-temperature solar thermal-power systems for residential electricity supply under various seasonal and climate conditions

In this work, the performance of low-temperature (<100 degrees C) solar thermal-power systems to satisfy residential electric loads was analyzed. The solar-driven system was designed to provide a fraction of the total electricity demand in a complementary operation with the electric grid. The analysis was conducted for an coperation during seven days each season, considering real solar and climate variables and residential loads at different climate zones in the United States. The efficiency of the system strongly depends on the solar radiation profile and the ambient temperature. Maximum efficiencies of around 9.5% were obtained in the cold and marine climate zones due to the high solar energy input and low heat dissipation temperatures. In these two zones, the system could supply more than 98% of the electricity demand all seasons. At mixed-humid and hot-humid regions, the system supplied around 50% of the electric load in three of the four seasons, but it only supplies about 27% of the electricity needs in the mixed-humid zone during summer and hot-humid zone during winter. The effect of the solar collector field area and the tank volume was also analyzed. In general, larger solar fields positively impact the efficiency. However, the impact of the tank volume varies depending on the solar radiation profile and the load requirements. Average efficiencies for the seven-day operation can be larger than 6% with a proper selection of the solar collector area and tank volume for an Organic Rankine Cycle with a capacity of about 2.6 kW. Finally, an economic analysis of the system was conducted, and the results were compared with a solar PV + battery system of similar capacity. It is expected that the cost for the analyzed solar-thermal system decreases in the coming years with the increased interest on low temperature applications.

14 SOLAR ENERGY↗

Analysis of RF losses and material characterization of samples removed from a Nb 3 Sn-coated superconducting RF cavity

Nb 3 Sn (T c ≈18 K and H sh ≈400 mT) is a prospective material to replace Nb (T c ≈9 K and H sh ≈200 mT) in SRF accelerator cavities for significant cost reduction and performance enhancement. Because of its material properties, Nb3Sn is best employed as a thin film (coating) inside an already built RF cavity structure. A particular test cavity noted as C3C4 was a 1.5 GHz single-cell Nb cavity, coated with Nb3Sn using Sn vapor diffusion process at Jefferson Lab. Cold measurements of the coated cavity indicated the superconducting transition temperature of about 18 K. Subsequent RF measurements indicated field-dependent surface resistance both at 4.3 K and 2.0 K. After initial cold measurements, the cavity RF loss distribution was studied with a thermometry mapping system. Loss regions were identified with thermometry and were cut out for material analysis. The presence of significantly thin patchy regions and other carbon-rich defects is associated with strong local field-dependent surface resistance. This paper summarizes RF and thermometry results correlated with material science findings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Analysis of precooling optimization for residential buildings

To reduce peak demand and/or energy cost for residential buildings, optimal precooling strategies are becoming important as an alternative to rule-based precooling strategies that are intuitive but may not be optimal. Since precooling optimization is heavily dependent on a variety of factors such as the home thermal properties, HVAC system, weather, thermal comfort criteria, and utility rate structure, the individual and collective impact of these factors on precooling performance needs to be analyzed. In addition, since the indoor air temperature is affected by heat transfer to and from the interior wall surface, performance analysis in view of the interior wall surface temperature is also essential. Therefore, in this paper, an optimal precooling strategy that accounts for the aforementioned factors and utilizes a second-order thermal network model, is proposed. With this strategy, the HVAC on/off control signal that minimizes 24-hour energy cost while maintaining thermal comfort, is determined. Through extensive simulations, it is found that the proposed optimal precooling strategy is able to adapt to changing conditions and that having a sufficiently low interior wall surface temperature during precooling is critical for avoiding expensive on-peak operation. Here, the reason for the latter is that such a temperature indicates that enough “cooling energy” has been stored. It is also found that weather has the most dominant impact on the precooling performance, followed by home thermal condition, with the rated cooling capacity and utility rate structure having the least impact.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Magnetic phase diagram of (Mo 2/3 RE 1/3 ) 2 AlC, RE = Tb and Dy, studied by magnetization, specific heat, and neutron diffraction analysis

We report the results of magnetization, heat capacity, and neutron diffraction measurements on (Mo 2/3 RE 1/3 ) 2 AlC with RE = Dy and Tb. Temperature and field-dependent magnetization as well as heat capacity were measured on a powder sample and on a single crystal allowing the construction of the magnetic field-temperature phase diagram. To study the magnetic structure of each magnetic phase, we applied neutron diffraction in a magnetic field up to 6 T. For (Mo 2/3 Dy 1/3 ) 2 AlC in zero field, a spin density wave is stabilized at 16 K, with antiferromagnetic ordering at 13 K. Furthermore, we identify the coexistence of ferromagnetic and antiferromagnetic phases induced by magnetic fields for both RE = Tb and Dy. The origin of the field induced phases is resulting from the competing ferromagnetic and antiferromagnetic interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DPC Disposal Thermal Scoping Analysis

This is a progress report on thermal modeling for dual-purpose canister (DPCs) direct disposal that covers several available calculation methods and addresses creep and temperature-dependent properties in a salt repository. Three modeling approaches are demonstrated: A semi-analytical calculation method that uses linear solutions with superposition and imaging, to represent a central waste package in a larger array; A finite difference model of coupled thermal creep, implemented in FLAC2D; and An integrated finite difference thermal-hydrologic modeling approach for repositories in different generic host media, implemented in PFLOTRAN. These approaches are at different levels of maturity, and future work is expected to add refinements and establish the best applications for each.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Time dependent supervisory control update with FARM using rolling window

This report describes improvements to the Feasible Actuator Range Modifier (FARM) component of the RAVEN-based HYBRID framework for analysis of Integrated Energy Systems (IES). FARM supports the HERON plug-in that solves the power dispatch problem. The solution to the dispatch problem involves economically optimal dispatches that satisfy limits on production variables and their rates of variation (explicit constraints) as well as process variables tied to the service life of equipment (implicit constraints). FARM serves to validate or confirm that a HERON solution for explicit constraints also satisfies the implicit constraints. FARM-alpha was released by Argonne National Laboratory in January 2021 followed by FARM-Beta in January 2022 with the latter providing increased flexibility for the user. In this report, FARM-Gamma, the latest version of the code, is described. The major improvement is the implementation of a system identification algorithm based on the Dynamic Mode Decomposition with Control (DMDc) coupled with a “Rolling Window” scheme that allows obtaining linear time-varying state-space models. This feature equips FARM with the most accurate approximation of system dynamics, and it relieves the user from the burden of performing an exhaustive off-line characterization of the dynamics. FARM-Gamma capabilities are assessed by solving the power dispatch problem for a representative IES unit. The simulation times corresponding to the different releases are estimated and compared. These values capture the increasing computational burden of the successively higher fidelity state-space models adopted by FARM-Alpha, FARM-Beta and FARM-Gamma. The code implementation provides significant flexibility, i.e., the user can always select the most suitable version of FARM according to the problem to be solved and the available computational resources. It is anticipated that FARM will play a role in addressing several future IES applications. We outline how it can support the coordinated management and safe operation of a nuclear plant coupled to industrial processes to produce hydrogen and synfuels.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Evaluation of Modeled Precipitation in Oceanic Extratropical Cyclones Using IMERG

Using a high-spatial- and high-temporal-resolution precipitation dataset, Integrated Multi-satellite Retrievals for GPM (IMERG), extratropical cyclone precipitation is evaluated in two reanalyses and two climate models. Based on cyclone-centered composites, all four models overestimate precipitation in the western subsiding and dry side of the cyclones, and underestimate the precipitation in the eastern ascending and moist side. By decomposing the composites into frequency of occurrence and intensity (mean precipitation rate when precipitating), the analysis reveals a tendency for all four models to overestimate frequency and underestimate intensity, with the former issue dominating in the western half and the latter in the eastern half of the cyclones. Differences in frequency are strongly dependent on cyclone environmental moisture, while the differences in intensity are strongly impacted by the strength of ascent within the cyclone. There are some uncertainties associated with the observations: IMERG might underreport frozen precipitation and possibly exaggerate rates in vigorously ascending regions. Nevertheless, the analysis suggests that all models produce extratropical cyclone precipitation too often and too lightly. These biases have consequences when evaluating the changes in precipitation characteristics with changes in cyclone properties: the models disagree on the magnitude of the change in precipitation intensity with a change in environmental moisture and in precipitation frequency with a change in cyclone strength. This complicates accurate predictions of precipitation changes in a changing climate.

54 ENVIRONMENTAL SCIENCES↗

PET-FBA: A lightweight enzyme allocation and thermodynamics-constrained flux analysis approach to explore Escherichia coli metabolic adaptation to intracellular acidification

Escherichia coli employs diverse strategies to adapt to acidic environments that disrupt enzyme activity and the thermodynamic feasibility of essential reactions. To understand the impact of pH stress on cell metabolism, we present the PET-FBA (pH-, Enzyme protein allocation-, and Thermodynamics-constrained Flux Balance Analysis) framework. PET-FBA extends genome-scale modeling by integrating enzyme protein costs and reaction Gibbs free energy changes. Additionally, by incorporating pH-dependent enzyme kinetics in response to intracellular acidification, this framework enables the simulation of E. coli's metabolic adjustments across varying external pH levels. The model's accuracy is validated by comparing in silico growth simulations with experimental measurements under both anaerobic and aerobic conditions, as well as in silico gene knockouts of essential genes. By explicitly incorporating pH effects, our model accurately replicates the metabolic shift towards lactate production as the primary fermentation product at low pH in anaerobic conditions. This shift is only predicted when enzyme kinetics are dynamically adjusted as a function of pH. Further analysis revealed that this shift can be attributed to the reduced protein efficiency of the acetyl-CoA branch compared to lactate dehydrogenase under acidic stress, which then becomes crucial for maintaining NAD regeneration and cell growth at low pH. Furthermore, we identified strategies for enhancing cell growth under acidic anaerobic conditions by improving the enzyme activity of lactate dehydrogenase and pyruvate formate lyase, which increases NAD production efficiency and reduces enzyme protein allocation costs. Designed as a lightweight yet versatile framework, PET-FBA enables efficient genome-scale metabolic analysis. Using E. coli as a model system, our framework provides a systematic approach to understanding metabolic responses to environmental stress, pinpointing key metabolic bottlenecks, and identifying potential targets for strain optimization.

42 ENGINEERING↗

Phase-field modeling and experiments of dynamic fracture in single crystal quartz

Predicting the onset and characteristics of brittle fracture is important for a wide range of engineering and geological material applications. In this paper, we study important aspects of brittle fracture in α-quartz by phase-field modeling and experiments using a top-down approach. In the modeling framework, the work term in the Griffith energy balance is replaced with internal energy contributions that represent surface energy, thermal energy, and elastic strain energy stored in defects. This allows parametrization of individual energy contributions in terms of internal state variables and keeps track of energy partitioning after the onset of fracture. The path and history dependence of fracture is included in evolution laws for internal state variables, e.g., entropy evolution, while the energy remains a true potential. In the experimental part, dynamic compression experiments coupled with X-ray phase contrast imaging are performed on cube-like samples with a hole. In the top-down analysis, dynamic compression and three point bending experiments from the literature are simulated with the developed phase-field damage model. In conclusion, the fitted model highlights the strain rate, size, and stress state dependence of damage nucleation and evolution in single crystal α-quartz.

36 MATERIALS SCIENCE↗