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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4

A Bayesian nonparametric analysis for zero-inflated multivariate count data with application to microbiome study

High-throughput sequencing technology has enabled researchers to profile microbial communities from a variety of environments, but analysis of multivariate taxon count data remains challenging. Here, we develop a Bayesian nonparametric (BNP) regression model with zero inflation to analyse multivariate count data from microbiome studies. A BNP approach flexibly models microbial associations with covariates, such as environmental factors and clinical characteristics. The model produces estimates for probability distributions which relate microbial diversity and differential abundance to covariates, and facilitates community comparisons beyond those provided by simple statistical tests. We compare the model to simpler models and popular alternatives in simulation studies, showing, in addition to these additional community-level insights, it yields superior parameter estimates and model fit in various settings. The model's utility is demonstrated by applying it to a chronic wound microbiome data set and a Human Microbiome Project data set, where it is used to compare microbial communities present in different environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Search for Sterile-Neutrino-Based Muon Neutrino Disappearance Using the MicroBooNe Deep Learning Analysis

We describe a search for νµ disappearance using the MicroBooNE Deep Learning analysis 1µ1p selection. Presently, the unexplained MiniBooNE and LSND anomalies could be explained by a sterile neutrino impacting neutrino oscillations. Our analysis searches for the allowed parameter space that could describe such a sterile neutrino. We determine the allowed and excluded region of a 3+1 sterile-based muon neutrino disappearance model in MicroBooNE at 90% confidence. Our allowed region includes both the null model, and current global best fit model. Context for the underlying Deep Learning analysis is provided and several validation studies surrounding both the disappearance search, and originating 1µ1p selection are performed to strengthen confidence in the result. In addition, a next-generation deep learning tool for cosmic-ray-muon event discrimination is proposed and evaluated, demonstrating a removal of 70% of the remaining event background when added to current methods, under the cut criteria used.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Search for Sterile-Neutrino-Based Muon Neutrino Disappearance Using the MicroBooNe Deep Learning Analysis

We describe a search for νµ disappearance using the MicroBooNE Deep Learning analysis 1µ1p selection. Presently, the unexplained MiniBooNE and LSND anomalies could be explained by a sterile neutrino impacting neutrino oscillations. Our analysis searches for the allowed parameter space that could describe such a sterile neutrino. We determine the allowed and excluded region of a 3+1 sterile-based muon neutrino disappearance model in MicroBooNE at 90% confidence. Our allowed region includes both the null model, and current global best fit model. Context for the underlying Deep Learning analysis is provided and several validation studies surrounding both the disappearance search, and originating 1µ1p selection are performed to strengthen confidence in the result. In addition, a next-generation deep learning tool for cosmic-ray-muon event discrimination is proposed and evaluated, demonstrating a removal of 70% of the remaining event background when added to current methods, under the cut criteria used.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Suppressing simulation bias in multi-modal data using transfer learning

Abstract Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is multi-dimensional. Simulations, however, often suffer from an inherent bias. Estimation of this bias may be poorly constrained not only because of data sparsity, but also because traditional predictive models fit only one type of observed outputs, such as scalars or images, instead of all available output data modalities, which might have been acquired and simulated at great cost. To break this limitation and open up the path for multi-modal calibration, we propose to combine a novel, transfer learning technique for suppressing the bias with recent developments in deep learning, which allow building predictive models with multi-modal outputs. First, we train an initial neural network model on simulated data to learn important correlations between different output modalities and between simulation inputs and outputs. Then, the model is partially retrained, or transfer learned, to fit the experiments; a method that has never been implemented in this type of architecture. Using fewer than 10 inertial confinement fusion experiments for training, transfer learning systematically improves the simulation predictions while a simple output calibration, which we design as a baseline, makes the predictions worse. We also offer extensive cross-validation with real and carefully designed synthetic data. The method described in this paper can be applied to a wide range of problems that require transferring knowledge from simulations to the domain of experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Active learning using hybrid surrogate tool life modeling for machining process optimization

Here, this paper describes an active learning approach for part-to-part iterative machining process optimization using a hybrid surrogate tool life model. A probabilistic interpolating tool life model is developed by combining the empirical Taylor-type tool life equation and the model fit error. The probabilistic tool life model is then used to calculate the machining cost per part distribution. The optimal machining parameters are selected using an expected improvement in machining cost per part criterion. The method is validated numerically using experimental results; the results show a median convergence error of 2.2% after three tests over 400 simulations. The method is validated experimentally on two industrial applications for Ti-6Al-4V roughing resulting in a cost per part reduction greater than 23% after two tests. The described method is a robust solution for rapid convergence to optimal machining parameters in an industrial production environment.

Active learning↗

Radon Kinetics in a Basement Space Measured with Different Devices

Although indoor monitoring of radon and benchmarking of radon measurement devices remain important research topics, few intercomparisons of active radon measurement devices have been performed under realistic conditions, let alone dynamic ones enabling comparison of their transient behavior. Five different radon monitors were therefore placed in a poorly ventilated basement space under three different conditions: 24 h under a steady, elevated radon level, 24 h with fans turned on to produce a radon washout transient, and 9 d with fans turned off for a radon buildup transient. Resulting radon concentrations varied between ~200 and ~2,000 Bq m -3 . Accuracy of the devices were evaluated using root-mean-square error, and ventilation data were fit to first order linear compartmental models. To more accurately model behaviors such as cyclic diurnal variations, the source term corresponding to entry of radon from soil into the basement was considered to be non-constant, as it is likely to vary drastically with both the indoor-outdoor pressure differential and soil concentration variations. Here, the improved radon washout model fit very well with the measurements. Despite a wide variety in list prices, all devices performed similarly during transients and at different radon concentrations.

60 APPLIED LIFE SCIENCES↗

3D CFD Model Validation Using Benchmark Data of 1/16th Scaled VHTR Upper Plenum and Development of Wall Heat-Transfer Correlation For Laminar Flow

With support from the U.S. Department of Energy-Office of Nuclear Energy’s (DOE-NE’s) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, an effort has been pursued to support high-temperature gas-cooled reactor (HTGR) technology development and its modeling and simulation needs. There is a particular need for advanced modeling and simulation tools to predict thermal-fluid behavior in the nuclear reactor primary system, especially in the core and the lower and upper plena, during safety-related transients. In this report, two main such activities are presented relevant to the HTGRs: (1) three-dimensional (3D) computational fluid dynamics (CFD) validation using benchmark data from the upper plenum of Texas A&M University’s 1/16th scaled very-high-temperature gas-cooled reactor (VHTR), and (2) development of wall heat-transfer correlation for laminar flow in a wall-heated pipe. The CFD tool validation exercises can be helpful to choose the models and CFD tools to simulate and design specific components of the HTRGs such as upper plenum where jet mixing is a complex phenomenon. In a loss of forced circulation event, the laminar flow can be observed during the development of natural circulation flow. This work includes the development and validation of heat transfer correlations for laminar flow using the Nek5000 CFD code due to limited available experimental data for laminar flow conditions to guide low-order models (1D). In this report, the flow characteristics of a single isothermal jet discharging into the upper plenum was investigated using the Nek5000 Large-Eddy Simulation (LES) CFD tool. Several numerical simulations were performed for various jet-discharged Reynolds numbers ranging from 3,413 to 12,819. A grid-independent study was performed. The numerical results of mean velocity, root-mean-square fluctuating velocity, and Reynolds stress were compared against the benchmark data. Good agreement was obtained between simulated and measured data for axial mean velocities, except near the upper plenum hemisphere. The maximum predicted errors for axial mean velocities at various normalized coolant channel diameter heights of 1, 5, and 10 are 1.56%, 1.88%, and 3.82%, respectively. In addition, the predicted root-mean-square fluctuating velocity and Reynolds stress are qualitatively in agreement with the experimental data. The Nek5000 code was used to develop wall-heat transfer correlation for laminar flow in a cylindrical tube. Several simulations were performed for various Reynolds flow and wall-heat fluxes. A new heat transfer correlation was developed using data from Nek5000 simulation results and regression functions in Matlab. The developed heat transfer correlation is valid for various Reynolds flows from 200 to 2000. The predicted R² value for model fit was 0.875, which ensures that 87.5% of the model data lies on the Nek5000 data. Moreover, a machine learning (ML) tool was used to train and test the Nek5000 data. A good fit of the ML-based model was observed with the test data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Local models for scatter estimation and descattering in polyenergetic X-ray tomography

We propose a new modeling approach for scatter estimation and descattering in polyenergetic X-ray computed tomography (CT) based on fitting models to local neighborhoods of a training set. X-ray CT is widely used in medical and industrial applications. X-ray scatter, if not accounted for during reconstruction, creates a loss of contrast in CT reconstructions and introduces severe artifacts including cupping, shading, and streaks. Even when these qualitative artifacts are not apparent, scatter can pose a major obstacle in obtaining quantitatively accurate reconstructions. Our approach to estimating scatter is, first, to generate a training set of 2D radiographs with and without scatter using particle transport simulation software. To estimate scatter for a new radiograph, we adaptively fit a scatter model to a small subset of the training data containing the radiographs most similar to it. We compared local and global (fit on full data sets) versions of several X-ray scatter models, including two from the recent literature, as well as a recent deep learning-based scatter model, in the context of descattering and quantitative density reconstruction of simulated, spherically symmetrical, single-material objects comprising shells of various densities. Our results show that, when applied locally, even simple models provide state-of-the-art descattering, reducing the error in density reconstruction due to scatter by more than half.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Response of CR-39 nuclear track detectors to protons with non-normal incidence

This paper presents data from experiments with protons at non-normal incidence to CR-39 nuclear track detectors, analyzing the properties of detection efficiency, proton track diameter, track contrast, and track eccentricity. Understanding the CR-39 response to protons incident at an angle is important for designing charged particle detectors for inertial confinement fusion (ICF) applications. This study considers protons with incident energies less than 3 MeV. In this regime, an incident angle of 10° has no effect on CR-39 detection efficiency, and >85% detection efficiency is preserved up through 25° in the range of 1.0 MeV–2.1 MeV. For ICF applications, incident angles above 30° are deemed impractical for detector design due to significant drops in proton detection at all energies. We observe significant reductions in detection efficiency compared to theoretical predictions, particularly at low energies where proton tracks are etched away. The proton track diameter measured by the scan system is observed to decrease with higher incident angles. The track diameters are analyzed with two fitting models, and it is shown that the diameter–energy relation can be fit with the existing models at angles up to 30° . The optical contrast of the tracks tends to increase with the angle, meaning that the tracks are fainter, and a larger increase is observed for higher energies. Eccentricity, a measure of how elongated proton tracks are, increases with the incident angle and drops after the critical angle. The lowest energy tracks remain nearly circular even at higher angles.

47 OTHER INSTRUMENTATION↗

Response of CR-39 nuclear track detectors to protons with non-normal incidence

This paper presents data from experiments with protons at non-normal incidence to CR-39 nuclear track detectors, analyzing the properties of detection efficiency, proton track diameter, track contrast, and track eccentricity. Understanding the CR-39 response to protons incident at an angle is important for designing charged particle detectors for inertial confinement fusion (ICF) applications. This study considers protons with incident energies less than 3 MeV. In this regime, an incident angle of 10° has no effect on CR-39 detection efficiency, and >85% detection efficiency is preserved up through 25° in the range of 1.0 MeV–2.1 MeV. For ICF applications, incident angles above 30° are deemed impractical for detector design due to significant drops in proton detection at all energies. We observe significant reductions in detection efficiency compared to theoretical predictions, particularly at low energies where proton tracks are etched away. The proton track diameter measured by the scan system is observed to decrease with higher incident angles. The track diameters are analyzed with two fitting models, and it is shown that the diameter–energy relation can be fit with the existing models at angles up to 30°. The optical contrast of the tracks tends to increase with the angle, meaning that the tracks are fainter, and a larger increase is observed for higher energies. Eccentricity, a measure of how elongated proton tracks are, increases with the incident angle and drops after the critical angle. The lowest energy tracks remain nearly circular even at higher angles.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Missing components in ΛCDM from DESI Y1 baryonic acoustic oscillation measurements: Insights from redshift remapping

We explore transformations of the Friedman-Lemaître-Robertson-Walker (FLRW) metric and cosmological parameters that align with observational data while aiming to gain insights into potential extensions of standard cosmological models. We modified the FLRW metric by introducing a scaling factor, e 2Θ(a) –the cosmological scaling function (CSF), which alters the standard relationship between cosmological redshift and the cosmic scale factor without affecting angular measurements or cosmic microwave background (CMB) anisotropies. Using data from DESI Year 1, Pantheon+ supernovae, and the Planck CMB temperature power spectrum, we constrained both the CSF and cosmological parameters through a Markov chain Monte Carlo approach. Our results indicate that the CSF model fits observational data with a lower Hubble constant (although it is compatible with the value given by Planck 2018 within 1σ) and is predominantly dark matter dominated. Additionally, the CSF model produces temperature and lensing power spectra similar to those predicted by the standard model, though with lower values in the CSF model at large scales. We also checked that when fitting a CSF model without dark energy to the data, we obtain a more negative conformal function. This suggests that the CSF model may offer hints about missing elements and opens up a new avenue for exploring physical interpretations of cosmic acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗

Similarity Metric for Data Optimization and Efficient Training of Reactive Machine Learning Force Fields for Hydrocarbon Radiolysis

Radiolysis is a common approach to sterilize polymers, chemically modify them for upcycling, and accelerate their decomposition for recycling purposes. Reactive molecular dynamics (MD) simulations provide a powerful tool to generate atomic-level trajectories of the reactive processes and quantify radiolytic chemical degradation pathways. For this, machine learning (ML) surrogate models for reactive force fields with quantum mechanical accuracy are now widely used, which require ML training data sets that can provide information on atomic environments for target chemical systems. However, radiolysis chemistry can be highly complex and diverse, which poses significant challenges for generating training data to parametrize ML models. In this regard, we developed a method for optimizing the training data set using a cosine similarity metric to help guide training set selection for radiolysis of polyethylene, a model hydrocarbon polymer, as well as to enhance the transferability of our reactive ML force field (MLFF) to a variety of molecular and polymeric systems. Our approach performs atom-by-atom comparisons between local atomic environments to pinpoint important data points associated with rare and localized events, such as radiolysis damage within structures. We apply this approach to train the Chebyshev Interaction Model for Efficient Simulation (ChIMES) MLFF model, which expresses the atomic interaction potentials in terms of linear combinations of many-body Chebyshev polynomials. We first show that our method can reduce our training set size by ∼70% while improving overall accuracy compared to more standard MD model fitting approaches. We then validate our optimum model against diverse hydrocarbon simulation data, including simple alkanes and systems with unsaturated carbon bonds, over a wide range of thermodynamic conditions. Finally, we use our ChIMES model to perform MD simulations of radiolytic damage with large-scale systems that help avoid system size effects. Overall, our approach yields an MD force field that retains most of the accuracy of the underlying quantum method while yielding many orders of improvement in computational efficiency. In conclusion, our efforts will have impact on future hydrocarbon polymer radiolysis studies, where the chemical details of the polymer–radiation interactions can have a strong effect on the resulting products observed in experiments.

Hydrocarbons↗

Verification Testing of OLI Systems Mixed Solvent Electrolyte Model for the Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 ) System to High Ionic Strength at 25°C

This technical report summarizes model verification results and summary statistics for 41 evaporite mineral solubility cases evaluated by Savannah River National Laboratory using OLI Systems’ aqueous electrolyte thermodynamic modeling software. The 41 verification cases containing a total of 60 solubility curves comprise mineral solubility data from low to high ionic strength at 25°C for the eight-component system Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 O as reported by Harvie et al. (1984). Thermodynamic calculations were executed using OLI Systems’ Stream Analyzer computation module within the OLI Studio software platform (Ver. 11.0, Rev. 11.0.1.9). The Mixed Solvent Electrolyte (MSE) thermodynamic framework was chosen for this investigation because of its superiority in modeling high ionic-strength inorganic salt solutions and actinide redox chemistry and solubility, both of which are relevant to the geological repository conditions at the Waste Isolation Pilot Plant in Carlsbad, New Mexico. Mineral solubility data in various inorganic salt solutions were digitized and extracted from figures generated by Harvie et al. (1984). For each of the 60 solubility curves, a case-specific chemistry model and input file were generated in OLI Studio using OLI Stream Analyzer and the MSE (H 3 O + ion) public databank provided by OLI Systems. Model simulation results were exported to Microsoft Excel to calculate summary statistics and to generate graphs comparing the OLI model predictions to the solubility data. Summary statistics include residuals (model – data) and concordance (accuracy × precision, where precision is indicated by the Pearson correlation coefficient and accuracy accounts for bias and scale differential). Private databanks were not developed, and activity coefficient model regressions were not performed to improve OLI model fits to the data. Of the 41 model verification plots, 83% have a mean of the percent residuals less than or equal to 25%. Similarly, 75% display a concordance greater than or equal to 0.75. Only seven of the 41 verification plots fail to show good agreement between the model and data. Of these seven, three are relevant to the WIPP repository because they involve the Mg-OH-Cl-SO 4 -CO 3 aqueous system. The remaining four address salt solubilities at the pH extremes (strong acid and strong base). It should be noted that in two of the three Mg-OH-Cl-SO 4 -CO 3 system cases, the regressed Harvie et al. (1984) solubility curve also deviated from the data. Lack of agreement between the OLI model-predicted solubility curves and the data is attributable to one or more of the following: specific solid species are not included in the OLI MSE databank; there is significant variation among the different solubility datasets chosen by Harvie et al. (1984); the OLI MSE model’s thermodynamic parameters were determined using different solubility datasets; and the activity coefficient parameters for certain relevant ion-ion and ion-molecule pairs have not been optimized via data regression. Two recommendations for future work are to (1) evaluate solubility data for the Mg-OH-Cl-SO 4 -CO 3 system at high ionic strength and, if necessary, develop a private OLI MSE database that includes missing species and, where necessary, regressed standard state properties and interaction parameters; (2) perform similar verification testing of the OLI model for actinide solubility data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Glass Property-Composition Models Update for use in Direct Feed High-Level Waste Flowsheet Development

A set of preliminary glass property models and constraints were developed and augmented by models from literature for use in design of direct-feed high-level waste (DFHLW) glasses for flowsheet evaluation, testing, and design of the Tank Waste Treatment and Immobilization Plant (WTP) high-level waste (HLW) Facility. These models and constraints are meant to be used as a place-holder while glass property-composition data gaps are filled and final plant operating models are developed. This report describes the motivation and intended use of the models, the compilation of data, model fitting and selection, methods to apply the models and constraints in glass design and offers example calculations demonstrating their intended use.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Glass Property-Composition Models Update for use in Direct Feed High-Level Waste Flowsheet Development: EWG2.6

A set of preliminary glass property models and constraints were developed and augmented by models from literature for use in design of direct-feed high-level waste (DFHLW) glasses for flowsheet evaluation, testing, and design of the Waste Treatment and Immobilization Plant (WTP) high-level waste (HLW) Facility. These models and constraints are meant to be used as a place-holder while glass property-composition data gaps are filled and final plant operating models are developed. This report describes the motivation and intended use of the models, the compilation of data, model fitting and selection, methods to apply the models and constraints in glass design and offers example calculations demonstrating their intended use.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Hydrothermal but Not Mechanical Pretreatment of Wastewater Algae Enhanced Anaerobic Digestion Energy Balance due to Improved Biomass Disintegration and Methane Production Kinetics

This study used pilot-scale high-rate algae ponds to assess algal–bacteria biomass productivity and wastewater nutrient removal as well as the impact of mechanical and hydrothermal pretreatments on biomass disintegration, methane production kinetics, and anaerobic digestion (AD) energy balance. Mechanical pretreatment had a minor effect on biomass disintegration and methane production. By contrast, hydrothermal pretreatment significantly reduced particle size and increased the solubilized organic matter content by 3.5 times. The methane yield and production rate increased by 20–55% and 20–85%, respectively, with the highest values achieved after pretreatment at 121 °C for 60 min. While the 1st-order and pseudo-1st-order reaction equation models fitted methane production from untreated biomass best (R2 > 0.993), the modified Gompertz sigmoidal-type model provided a superior fit for hydrothermally pretreated algae (R2 ≥ 0.99). The AD energy balance revealed that hydrothermal pretreatment improved the total energy output by 25–40%, with the highest values for volume-specific and mass-specific total energy outputs reaching 0.23 kW per digester m3 and 2.3 MW per ton of biomass volatile solids. Additionally, net energy recovery (energy output per biomass HHV) increased from 20% for untreated algae to 32–34% for hydrothermally pretreated algae, resulting in net energy ratio and net energy efficiency of 2.14 and 68%, respectively.

09 BIOMASS FUELS↗

High-contrast Thermal Infrared Spectroscopy with ALES: The 3–4 μm Spectrum of κ Andromedae b

We present the first L-band (2.8–4.1 μm) spectroscopy of κ Andromedae b, a ~20 M Jup companion orbiting at 1" projected separation from its B9-type stellar host. We combine our Large Binocular Telescope (LBT) Arizona Lenslets for Exoplanet Spectroscopy (ALES) integral field spectrograph data with measurements from other instruments to analyze the atmosphere and physical characteristics of κ And b. We report a discrepancy of ~20% (2σ) in the L' flux of κ And b when comparing to previously published values. We add an additional L' constraint using an unpublished imaging data set collected in 2013 using the LBT Interferometer/LMIRCam, the instrument in which the ALES module has been built. The LMIRCam measurement is consistent with the ALES measurement, both suggesting a fainter L-band scaling than previous studies. The data, assuming the flux scaling measured by ALES and LMIRCam imaging, are well fit by an L3-type brown dwarf. Atmospheric model fits to measurements spanning 0.9–4.8 μm reveal some tension with the predictions of evolutionary models, but the proper choice of cloud parameters can provide some relief. In particular, models with clouds extending to very low pressures composed of grains ≤1 μm appear to be necessary. If the brighter L' photometry is accurate, there is a hint that subsolar metallicity may be required.

79 ASTRONOMY AND ASTROPHYSICS↗

CONSTRAINT-INDEPENDENT CONSTANT CTOA DETERMINATION FOR DUCTILE STABLE CRACK GROWTH

Crack tip opening angle (CTOA) has been used as a reliable fracture toughness parameter for decades to characterize stable ductile crack growth for thin-walled aerospace structures in the low-constraint conditions. Recently, the CTOA parameter was also applied to the pipeline industry, and a CTOA test standard ASTM E3039 was thus developed for testing a critical constant CTOA. Research showed that the constant CTOA can reasonably describe fracture toughness required to arrest a dynamic crack propagation for a modern gas pipeline. However, the CTOA fracture criterion requires constraint-independent CTOA toughness against stable ductile crack growth. ASTM E3039 recommends a drop weight tearing test (DWTT) specimen for CTOA testing. Since a shallow crack is used, DWTT measured CTOA may depend on constraint level at the crack tip. To understand if it is the case, this paper evaluates the critical CTOA for a set of fracture toughness tests on single edge notched bend (SENB) specimens with shallow and deep cracks based on four CTOA estimation models. In which, the Ln(P)-LLD linear fit model is similar to that used by ASTM E3039 in the CTOA calculation. Fracture test data for X80 pipeline steel and HY80 structural steel are considered in the CTOA evaluation. The results show that the four CTOA models can determine a crack size-independent constant CTOA over stable ductile crack growth for the SENB specimens. As a result, CTOA determined by ASTM E3039 is constraintindependent and transferable to use for an actual crack propagating in a gas pipeline.

Zhu, Xian-Kui↗