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At least 109 records · Page 6

Effective field theory for deformed odd-mass nuclei

We develop an effective field theory (EFT) for deformed odd-mass nuclei. These are described as an axially symmetric core to which a nucleon is coupled. In the coordinate system fixed to the core the nucleon is subject to an axially symmetric potential. Power counting is based on the separation of scales between low-lying rotations and higher-lying states of the core. In leading order, core and nucleon are coupled by universal derivative terms. These comprise a covariant derivative and gauge potentials which account for Coriolis forces and relate to Berry-phase phenomena. At leading order, the EFT combines the particle-rotor and Nilsson models. Here, we work out the EFT up to next-to-leading order and illustrate the results in 239 Pu and 187 Os . At leading order, odd-mass nuclei with rotational bandheads that are close in energy and differ by one unit of angular momentum are triaxially deformed. For bandheads that are well separated in energy, triaxiality becomes a subleading effect. The EFT developed in this paper presents a model-independent approach to the particle-rotor system that is capable of systematic improvement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Signature splitting of the g 7 / 2 [ 404 ] 7 / 2 + bands in Ba 131 and Ce 133

Excited states in Ba 131 and Ce 133 were studied using in-beam γ -ray spectroscopy through the Sn 122 ( C 13 , 4 n ) Ba 131 and Te 125 ( C 12 , 4 n ) Ce 133 reactions, respectively. A strongly coupled band, associated with the ν g 7 / 2 [ 404 ] 7 / 2 + configuration, was identified in Ba 131 and Ce 133 . It is the first time to observe the ν g 7 / 2 [ 404 ] 7 / 2 + bands in the N = 75 isotones. The signature partners exhibit considerable energy splitting in comparison with those in the π g 7 / 2 [ 404 ] 7 / 2 + bands in the odd- A Ta and Re isotopes. Here, extensive cranked shell model and quasiparticle-plus-triaxial-rotor model calculations reveal the origin of the signature splitting, which depends not only on the triaxiality, but also on the configuration mixing with nearby low- j orbitals.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions

In heavy ion collisions, elliptic flow v2 and radial flow, characterized by eventwise average transverse momentum [p T ], are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between v 2 and [p T ], ρ 2 , was found to be particularly sensitive to the quadrupole deformation parameter β that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation β>0 reduces the ρ 2 in ultracentral collisions (UCC), we show that the prolate deformation β<0 enhances the value of ρ 2 . As β>0 and β<0 are the two extremes of triaxiality, the strength and sign of v 2 2 -[pT] correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short timescale (<10 -24 s).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2

Large-scale models of nuclear structure are currently the only way to provide consistent datasets for the many properties of thousands of exotic nuclei that are required by nucleosynthesis simulations. In [W. Ryssens et al., Eur. Phys. J. A 58, 246 (2022)], we recently presented the new BSkG2 model based on an energy density functional of the Skyrme type. Relying on a flexible three-dimensional coordinate representation of the nucleus, the model takes into account both triaxial deformation and time-reversal symmetry breaking. BSkG2 achieves a state-of-the-art global description of nuclear ground state (g.s.) properties and reproduces in particular the known masses with a root-mean-square (rms) deviation of 678 keV. Moving beyond g.s. properties, the model also reproduces all empirical values for the primary and secondary barriers as well as isomer excitation energies of actinide nuclei with rms deviations below 500 keV, i.e. with unprecedented accuracy. Here we discuss in detail the extension of our framework to the calculation of the fission barriers of 45 actinide nuclei, including odd-mass and odd-odd systems. We focus in particular on the impact of symmetry breaking which is key to the accuracy of the model: we allow systematically for axial, reflection and time-reversal symmetry breaking. The effect of the latter on the fission properties of odd-mass and odd-odd nuclei is small, but we find that allowing for shapes with triaxial or octupole deformation, as well as shapes with both, is crucial to achieving this accuracy. Here, the numerical accuracy of our coordinate space approach, the variety of nuclear configurations explored and the simultaneous successful description of fission properties and known masses makes BSkG2 the tool of choice for the large-scale study of nuclear structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Atomistic Simulations of the Elastic Compression of Platinum Nanoparticles

Abstract The elastic behavior of nanoparticles depends strongly on particle shape, size, and crystallographic orientation. Many prior investigations have characterized the elastic modulus of nanoscale particles using experiments or simulations; however their reported values vary widely depending on the methods for measurement and calculation. To understand these discrepancies, we used classical molecular dynamics simulation to model the compression of platinum nanoparticles with two different polyhedral shapes and a range of sizes from 4 to 20 nm, loaded in two different crystal orientations. Multiple standard methods were used to calculate the elastic modulus from stress-vs-strain data for each nanoparticle. The magnitudes and particle-size dependence of the resulting moduli varied with calculation method and, even for larger nanoparticles where bulk-like behavior may be expected, the effective elastic modulus depended strongly on shape and orientation. Analysis of per-atom stress distributions indicated that the shape- and orientation-dependence arise due to stress triaxiality and inhomogeneity across the particle. When the effective elastic modulus was recalculated using a representative volume element in the center of a large nanoparticle, the elastic modulus had the expected value for each orientation and was shape independent. It is only for single-digit nanoparticles that meaningful differences emerged, where even the very center of the particle had a lower modulus due to the effect of the surface. These findings provide better understanding of the elastic properties of nanoparticles and disentangle geometric contributions (such as stress triaxiality and spatial inhomogeneity) from true changes in elastic properties of the nanoscale material.

36 MATERIALS SCIENCE↗

Integrating Experiments and Well Logs to Predict Caney Shale Static Mechanical Properties During Production with Supervised Machine Learning

Caney shale is one of the emerging oil reservoirs in Oklahoma. Understanding the impact of effective stress on its mechanical properties is critical for predicting hydraulic fracture geometry and overall hydrocarbon production. The objective of our study is to evaluate the impact of effective stress on the dynamic Young’s modulus using ultrasonic velocity measurements for Caney shale samples. A triaxial cell was utilized to measure ultrasonic (P-wave and S-wave) velocities for ten downhole Caney shale samples under various effective stresses to indirectly assess the impact of pore pressure change. The dynamic Young’s moduli estimated from these measurements were integrated with available conventional well logs (excluding sonic logs) and triaxial test results from Benge et al. (2021) to predict the static Young’s modulus using Random Forest (RF) and Extreme Gradient Boosting (XGBoost) models. The results showed that the estimated dynamic Young’s moduli from ultrasonic measurements were higher than the corresponding static Young’s modulus of cores from the same vertical well at similar depths. With increasing effective stress, the dynamic Young’s modulus increased for all samples. The estimated dynamic-to-static correction factor tended to be higher in zones of high neutron porosity (PHIN) and low density compared to other zones. Finally, SHapley Additive exPlanations (SHAP) for RF and XGBoost models identified depth, gamma ray (GR), and PHIN as key features for predicting the static Young’s modulus. This study enhances our understanding of the dynamic and static Young’s moduli for the Caney shale interval, as a function of effective stress and conventional well logs. The findings from this study can improve predictions of production throughout the well's lifespan by offering insights into the mechanical property degradation resulting from pore pressure depletion.

Kholy, Sherif M.↗

Geodyn Material Library: Pseudocap models for dry porous tocks

This report describes the second edition of the Pseudocap Strength models for porous rocks implemented in GEODYN material library. The first model was developed in 2007 and calibrated for concrete. Then, the model parameters were calibrated based on triaxial tests reported for limestones and sandstones of various porosities. In these models some key parameters were chosen as functions of the reference porosity,Φ. Since then multiple modifications were implemented in the model, therefore, it has been recalibrated for some common porous materials such as limestones, sandstones, alluvium, tuffs and granite. Two types of models are described in this repot. The first type (called Pseudocap Model or PM) is for rocks from a specific location. Parameters were calibrated for several specific geologic materials. The second type (called Generic Pseudocap Model or GPM) is useful for the sites where only basic information (rock type, porosity) is available. Generic models include built-in correlations between porosities and other mechanical properties observed for certain rock types. The models of both types were validated by comparing not only to quasi-static triaxial tests for these materials but also to shock Hugoniot data and spherical explosion data for some materials. All models were derived in the frame of isotropic plasticity. They are designed to be used in explicit finite element/difference codes. Tangent stiffness tensor is not provided but can be calculated numerically for the model to be used in implicit finite element codes. For an isotropic material the stress can be decomposed into volumetric and deviatoric parts. The volumetric part is modeled using an Equation of state (EOS) which calculates the pressure and the bulk sound speed as functions of the internal specific energy and density. Here a simple, Mie-Gruneisen EOS is presented, but tabulated EOS (LEOS) provided by the library can be used as well. The stress is limited by the yield surface which depends on three invariants of the stress tensor and specific internal energy. In addition, to capture the strain-rate dependence a simple multiplier is used for the yield surface which depends on the equivalent plastic strain rate. The failure surface (the ultimate yield, Y f , defined later) is chosen in the Hoek-Brown form, commonly used in rock mechanics. It includes measurable parameters such as Unconfined Compressive Strength (UCS) as well as scale parameters characterizing the quality of the rock such as GSI (Geologic Strength Index). Thus, even though the model is calibrated for small samples it offers a way to extrapolate the strength to the field scale using geological characterization of the rock mass. The model captures effects of brittle-ductile transition in rocks by introducing a cap multiplier to the yield function. The rate of dilatancy (bulking) is proportional to the slope of the yield surface affected by the cap. Therefore, it takes place only at low confinements when the pressure is less than the brittle-ductile transition pressure, P BD . On the contrary, the porous compaction takes place at pressures higher than P BD . The cap moves as the porosity is compacted or new porosity is generated due to dilatancy. The porous compaction is modeled using an evolution equation which includes deviatoric stress so that the onset of compaction corresponds to the cap surface. The model captures effects of shear-enhanced compaction which is an important for porous rocks. Section 2 describes the modeling framework and Section 3 presents the model calibration procedure. Section 4 compares experimental data for various rocks versus model predictions. The model parameters used for this comparison are given in Appendix. The files with material constants are available with the latest GEODYN material library distribution.

58 GEOSCIENCES↗

Design and Scoping Tests on Alloy 617 Using Notched Specimen Geometry to Validate Methods for Multiaxial Stress Relaxation

In FY 2022, a development effort was initiated at the US Department of Energy’s Oak Ridge National Laboratory (ORNL) to examine the multiaxial stress-relaxation behavior and multiaxial stress-state effect on the creep-fatigue (CF) performance for Alloy 617 at elevated temperatures. This effort supported the development of the design rules in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC), Section III, Division 5. In this work, two types of the notch specimen geometries were designed. An inelastic constitutive model was used to investigate the stress triaxiality and elastic follow-up effects on the notch specimens under CF deformation in the finite element (FE) simulations. The numerical study demonstrated that the stress triaxiality and elastic follow-up caused by the notches both play significant roles in the stress-relaxation behavior. In addition, Alloy 617 CF experiments were designed, and the testing on the notch specimens is ongoing. CF test failure data will be generated on the specimens with notches under various conditions in FY 2023, and the results will be used to validate methods for accounting for the multiaxial stress relaxation effect in the design code.

36 MATERIALS SCIENCE↗

Symmetry and Shape Coexistence in 10 Be

Within the low-lying spectrum of 10 Be, multiple rotational bands are found, with strikingly different moments of inertia. A proposed interpretation has been that these bands variously represent triaxial rotation and prolate axially-deformed rotation. The bands are well-reproduced in ab initio no-core configuration interaction (NCCI) calculations. Here, we use the calculated wave functions to elucidate the nuclear shapes underlying these bands, by examining the Elliott SU(3) symmetry content of these wave functions. The ab initio results support an interpretation in which the ground-state band, along with an accompanying K = 2 side band, represent a triaxial rotor, arising from an SU(3) irreducible representation in the 0hw space. Then, the lowest excited K = 0 band represents a prolate rotor, arising from an SU(3) irreducible representation in the 2hw space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Predicting Fracture Network Development in Crystalline Rocks

The geometric properties of fractures influence whether they propagate, arrest, or coalesce with other fractures. Thus, quantifying the relationship between fracture network characteristics may help predict fracture network development, and perhaps precursors to catastrophic failure. To constrain the relationship and predictability of fracture characteristics, we deform eight one centimeter tall rock cores under triaxial compression while acquiring in situ X-ray tomograms. The tomograms reveal precise measurements of the fracture network characteristics above the spatial resolution of 6.5 µm. We develop machine learning models to predict the value of each characteristic using the other characteristics, and excluding the macroscopic stress or strain imposed on the rock. The models predict fracture development more accurately in the experiments performed on granite and monzonite, than the experiments on marble. Fracture network development may be more predictable in these igneous rocks because their microstructure is more mechanically homogeneous than the marble, producing more systematic fracture development that is not strongly impeded by grain contacts and cleavage planes. The varying performance of the models suggest that fracture volume, length, and aperture are the most predictable of the characteristics, while fracture orientation is the least predictable. Orientation does not correlate with length, as suggested by the idea that the orientation evolves with increasing differential stress and thus fracture length. This difference between the observed and expected relationship between orientation and length highlights the influence of mechanical heterogeneities and local stress perturbations on fracture growth as fractures propagate, link, and coalesce.

58 GEOSCIENCES↗

Microseismic Monitoring of Laboratory Hydraulic Fracturing Experiments in Granitic Rocks for Different Fracture Propagation Regimes

While hydraulic fracturing (HF) is a widely employed process, the underlying fracturing processes are still heavily contested. The attributes of the HF generated fracture network can exhibit substantial variation when dealing with specific HF propagation regimes encountered in the field. In this study, HF experiments were performed on true-triaxially loaded Barre granite cubes, with microseismic monitoring, to identify and characterize the fracturing mechanisms associated with different viscosity injection fluids. Utilizing fluids with high (oil/1450 cP) and low (water/1 cP) viscosity represented two key HF propagation regimes: viscosity- and toughness-dominated. The experiments conducted with oil involved higher breakdown pressures, larger fluid volumes, and slower fracture propagation speeds. Furthermore, the frequency–magnitude distribution (b value) for all experiments (1.9–2.3) was similar to those encountered for large-scale operations. Slightly larger b values were encountered during the initiation phase (2.4–2.7) relative to the fracture propagation and post-fracturing phases (1.9–2.2). Techniques such as polarity and moment-tensor inversion were utilized to characterize the source mechanisms. For the HF experiments with oil, tensile fractures were most dominant (92%) in the initiation phase compared to fracture propagation and post-fracturing phases (70–75%). Similar tensile fracturing dominancy was not observed with water, attributable to fluid permeation and leak-off. Regardless of the injection fluid or classification criteria employed, tensile fractures were the dominant type consistently, with fewer occurring in water experiments but the specific ratio of crack types varied with different source mechanism criteria employed.

58 GEOSCIENCES↗

A thermodynamically consistent finite strain phase field approach to ductile fracture considering multi-axial stress states

Phase field models for ductile fracture have gained significant attention in the last two decades due to their ability in implicitly tracking the nucleation and propagation of cracks. However, most crack phase field formulations for elastoplastic solids focus only on the effects of plastic deformation, and do not consider the different multi-axial stress states that may arise in practical designs. In this work, a thermodynamically consistent phase field approach coupled with finite strain plasticity, considering multi-axial stress states is presented. In order to account for the coupling between plasticity and stress states, the Stress-Weighted Ductile Fracture Model (SWDFM) is utilized. The SWDFM represents a criterion for predicting ductile crack initiation under both monotonic and cyclic loadings based on histories of an internal plastic variable, stress triaxiality, and the Lode angle parameter. The excellent performance of the SWDFM for predicting ductile crack initiation motivates for its incorporation into a phase field approach for predicting both crack initiation and propagation through degradation of the fracture toughness. Moreover, based on the second law of thermodynamics, exact requirements are imposed on the rate at which the fracture toughness can evolve. Here, a novel function for degrading the plastic yield surface during the evolution of damage is introduced. This function, in line with experimental observations, leads to an accumulation of plastic deformation in damaged regions of a solid, and avoids numerical instabilities arising from concentrations of large plastic deformations in severely damaged regions. For validating the proposed model, results of computational simulations are compared to data from selected tests considering different multi-axial stress states. Comparisons of the numerical results with data from laboratory experiments demonstrate the capabilities of the proposed framework.

42 ENGINEERING↗

Influence of gradation on shear behavior and pore water response of sand

Here, this paper examines the influence of particle size distribution (PSD) on the shearing behavior of sand using axisymmetric triaxial compression (ATC) testing in conjunction with 3D imaging using synchrotron micro-computed tomography (SMT). Angular sand was sieved to obtain a narrow gradation (uniform) and a wide gradation (non-uniform) with uniformity coefficients (C u ) of 1.2 and 3.0, respectively. Experiments were conducted under drained conditions and a constant effective cell pressure (σ$^{'}_3$) of 50 kPa at low and high back pressures (BP). Results of paired ATC-SMT were analyzed in terms of global constitutive behavior, strain localization, and localized flow characteristics. A new particle tracking algorithm is developed to expose strain localization. Relative particle translation gradient (RPTG) results revealed that gradation affects how early the shear band develops and a tendency for narrow gradation to exhibit varying degrees of diffused shear band at high axial strain (ε 1 ) even though a clear single shear band was observed at the peak strength. Geometric tortuosity (τ) is used as a quantitative parameter to assess flow changes and the efficiency of the flow path. Representative elementary volumes (REVs) inside and outside the shear band were analyzed and the results showed a variation in flow path characteristics where wide gradation specimens had preferential flow paths.

Computed tomography↗

In situ measurement of three-dimensional intergranular stress localizations and grain yielding under elastoplastic axial-torsional loading

The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σ θZ ) and axial (σ ZZ ) stress tensor components, stress and stress deviator tensor invariants (I 1 , J 2 , and J 3 ), von Mises equivalent stress (σ$^{grain}_{VM}$), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter ($\barθ$) values were tracked for ~300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σ θZ , σ$^{grain}_{VM}$, and J 2 ; by comparison, I 1 , J 3 , η, and $\barθ$ metrics did not show discernible trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I 1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.

36 MATERIALS SCIENCE↗

Deformation Precursors to Catastrophic Failure in Rocks

Forecasting the timing of catastrophic failure, such as crustal earthquakes, has been a central concern for centuries. Such forecasting requires identifying signals that evolve or accelerate in the precursory phase leading to failure, and the subset of signals that may be detected in the crust. We develop machine learning models to predict the proximity of catastrophic failure in synchrotron X-ray tomography triaxial compression experiments on rocks using characteristics of evolving fracture networks. We then examine the characteristics that most strongly influence the model results, and thus may be considered the best predictors of the proximity of macroscopic failure. Finally, the resulting suite of predictive parameters underscores the importance of dilation in the precursory phase leading to catastrophic failure. The results indicate that the evolution of the strain energy density field may provide more robust predictions of the proximity of failure than other existing metrics of rock deformation.

58 GEOSCIENCES↗

Hydro-Mechanical Measurements of Sheared Crystalline Rock Fractures With Applications for EGS Collab Experiments 1 and 2

We present hydro-mechanical measurements that characterize shear on natural fractures in schist, amphibolite, and rhyolite specimens from the enhanced geothermal system (EGS) Collab Project's Experiment 1 and 2 sites (E1 and E2) at the Sanford Underground Research Facility. We employed a triaxial direct shear method augmented with X-ray imaging to perform hydroshearing (injection-induced shearing) and mechanical shearing on naturally fractured specimens at in situ stress conditions. Measurements included fracture permeability, strength, stress-dependent aperture, shear dilation, and frictional strength. Results reveal that in situ natural fractures must be permeable, weak, and shear-oriented to be hydrosheared, and only a subset of the observable in situ fractures were suitable. When sheared, the fracture permeability typically increased by a factor of 10 or more and this increase was retained over time. However, shear slip did not always result in permeability increase. High phyllosilicate content associated with exceptionally weak fractures exhibited poor or even decreased permeability after stimulation. These measurements in combination with site data were used to conduct a slip-tendency analysis for different fracture sets, and we selected the top candidate natural fractures for hydroshearing at the EGS Collab sites. We also found that the lower in situ shear stress and stronger fractures at the E2 site make hydroshearing more challenging than at the E1 site. Overall, the methods and analysis used in our work can be applied to any geothermal project to identify in situ joint sets that are best suited for hydroshearing, which in turn can help to optimize well placement and energy production.

58 GEOSCIENCES↗

Complex Fluid‐Driven Fractures Caused by Crack‐Parallel Stress

Abstract Managing fluid‐driven fracture networks is crucial for subsurface resource utilization, yet the current understanding of the key controlling factors remains insufficient. While geologic discontinuities have been shown to significantly influence fracture network complexity, this study identifies another major contributor. We conducted a new set of experiments using a transparent true triaxial cell, which enabled video recording of the temporal evolution of fluid‐driven fracture paths. Using pseudo‐2D samples without macroscale structural discontinuities, we observed multiple occurrences of hydraulic fracture curving and branching under anisotropic boundary stresses. We proposed a theoretical model demonstrating that the stress parallel to the crack line in the solid matrix near the crack tip (i.e., the T ‐stress) accounts for the observed fracture curving behavior. This finding suggests that T ‐stress is an additional mechanism contributing to the complexity of fluid‐driven fracture networks in the subsurface, besides the geologic discontinuities.

58 GEOSCIENCES↗

Utah FORGE 2-2446: Closing the Loop Between In-situ Stress Complexity and EGS Fracture Complexity - Workshop Presentation

This is a presentation on the Closing the Loop Between In-situ Stress Complexity and EGS Fracture Complexity project by Lawrence Livermore National Laboratory, presented by Dr. Matteo Cusini. The project's objective was to employ a combination of high-fidelity simulations and true-triaxial block fracturing tests at high temperature to explore the intricate relationship between in-situ stress and hydraulic fracture patterns and better characterize the in-situ stress at Utah FORGE. This presentation was featured in the Utah FORGE R&D Annual Workshop on September 7, 2023. The workshop provided a valuable opportunity to explore the progress made in each of the 17 Research and Development projects funded under Solicitation 2020-1 which aim to enhance our understanding of the crucial factors influencing the development of Enhanced Geothermal Systems (EGS) reservoirs and resources.

15 GEOTHERMAL ENERGY↗