Triaxial Deformation Research Articles

True Triaxial Crack Stress Thresholds and Deformation Characteristics of Cement Stone Subjected to Sulfuric Acid Corrosion

True Triaxial Crack Stress Thresholds and Deformation Characteristics of Cement Stone Subjected to Sulfuric Acid Corrosion

Triaxial deformation, shell structure, shell corrections and the connection to alpha-clustering in nuclei

Abstract We explore the connection between the appearance of quasi-stable structures in mean-field type calculations, which arise as a result of the evolution of the underlying shell structure as a function of deformation, and $\alpha$-clustering in light even-even nuclei. The Nilsson-Strutinsky mean-field approach employs a macroscopic liquid-drop whose energy is modified by a shell correction term derived using the Strutinsky method. This method reflects the variations in the energies of the single-particle states with deformation. As such, there is no obvious connection to clustering. 

Here we use the changing level scheme of the deformed harmonic oscillator as a function of triaxial deformation to fully explore the variation in stability of $\alpha$-cluster structures in light even-even nuclei. The energies of the harmonic oscillator levels are used to deduce the energy required to disrupt the $\alpha$-cluster as a function of the triaxial deformation. We find that there is good agreement between variations in the shell correction energy in the mean-field method and the energy required to disrupt the $\alpha$-cluster. This provides a necessary link between understanding of the appearance of quasi-stable $\alpha$-cluster structures and quasi-stable shapes appearing in mean-field calculations.

Survival probabilities of compound superheavy nuclei towards element 119

To synthesize superheavy element 119 is becoming a highly concerned issue as several experimental projects in major laboratories are being pursued. This work studied the survival probabilities of compound superheavy nuclei after multiple neutron emissions based on microscopic energy dependent fission barriers, demonstrating a significant role of triaxial deformation in decreasing the first fission barriers in the heaviest region. Together with the fusion cross sections by the dinuclear system model, the optimal energy and the residual cross section of 243Am(48Ca, 3n)288Mc are reproduced. Finally the cross sections and optimal beam energies of 54Cr+243Am and 50Ti+249Bk reactions are estimated, providing clues for the synthesis of new elements.

Relativistic mean field analysis of triaxial deformation for nuclei near the neutron drip line

The present study focuses on the deformation of neutron-rich nuclei near the neutron drip line. The nuclei of interest include 28O, 42Si, 58Ca, 80Ni, 100Kr, 122Ru, 152Ba, 166Sm, and 176Er. The relativistic Hartree - Bogoliubov (RHB) approach with effective density-dependent point coupling is utilized to investigate the triaxial deformation, and Skyrme - Hartree - Fock + Bardeen - Cooper - Schrieffer is used to analyze the axial deformation. The study aimed to understand the interplay between nuclear forces, particle interactions, and shell structure to gain insights into the unique behavior of neutron-rich nuclei. Despite these nuclei containing magic numbers, their shapes are still affected by the nucleons' collective behavior and energy levels. As the number of neutrons increases, the shape smoothly transitions from spherical to triaxial and then to prolate. The axial deformation analysis confirmed the results of the triaxial deformation analysis using the RHB method. An imbalance in the number of protons and neutrons can affect pairing energy, where extra neutrons can reduce overall pairing energy, and protons can disrupt the nucleon pairing due to stronger Coulomb repulsion between them.

Experiment and prediction of the strain-range dependent ultra-low-cycle fatigue based on micromechanical cyclic void growth model

Under severe seismic action, the local stress concentration region in steel structures is prone to the ultra-low-cycle fatigue (ULCF) under high triaxiality and irregular cyclic deformation with intensively varying strain amplitudes. It emphasizes the necessity of the jointed effects of the stress triaxiality and strain range incorporated in the ULCF life prediction. Given the limited relevant studies in terms of the underlying micro-mechanisms, this paper focuses on experimental and modeling studies of the combined effects of stress triaxiality and strain range on the ULCF failure, based on Gurson-Tvergaard-Needleman (GTN) microvoid evolution theories. Monotonic tensile tests on three types of notched round bars suggest that fracture strain decreases with increasing triaxiality. Cyclic tests on two types of notched bars under various strain ranges confirm the combined effects of stress triaxiality and strain range. Given a specific triaxiality, the ULCF damage accumulation rate increases linearly as the tensile plastic strain range ramps up. For the same tensile plastic strain range, higher triaxiality results in a greater damage accumulation rate. In the modeling studies, the consistency of the GTN and uncoupled damage models has been proven in terms of ULCF failure of structural steel. Based on GTN theories, a new micromechanical cyclic void growth model (GCVGM) is proposed, considering the detailed processes of void nucleation, growth, and coalescence under monotonic and cyclic loadings. Moreover, the joint effects of stress triaxiality and strain range can be explicitly described within a unified framework, without additional empirical assumptions. Based on experimental and simulation results, the proposed GCVGM shows significant advantages over conventional models in accurately predicting ULCF failure under various loading protocols, with low average errors of 2.73 % and −0.91 % for two types of notched bar specimens, respectively.

Compaction and Permeability Evolution of Tuffs From Krafla Volcano (Iceland)

AbstractPressure and stress perturbations associated with volcanic activity and geothermal production can modify the porosity and permeability of volcanic rock, influencing hydrothermal convection, the distribution of pore fluids and pressures, and the ease of magma outgassing. However, porosity and permeability data for volcanic rock as a function of pressure and stress are rare. We focus here on three porous tuffs from Krafla volcano (Iceland). Triaxial deformation experiments showed that, despite their very similar porosities, the mechanical behavior of the three tuffs differs. Tuffs with a greater abundance of phyllosilicates and zeolites require lower stresses for inelastic behavior. Under hydrostatic conditions, porosity and permeability decrease as a function of increasing effective pressure, with larger decreases measured at pressures above that required for cataclastic pore collapse. During differential loading in the ductile regime, permeability evolution depends on initial microstructure, particularly the initial void space tortuosity. Cataclastic pore collapse can disrupt the low‐tortuosity porosity structure of high‐permeability tuffs, reducing permeability, but does not particularly influence the already tortuous porosity structure of low‐permeability tuffs, for which permeability can even increase. Increases in permeability during compaction, not observed for other porous rocks, are interpreted as a result of a decrease in void space tortuosity as microcracks surrounding collapsed pores connect adjacent pores. Our data underscore the importance of initial microstructure on permeability evolution in volcanic rock. Our data can be used to better understand and model fluid flow at geothermal reservoirs and volcanoes, important to optimize geothermal exploitation and understand and mitigate volcanic hazards.

Mean-field-derived IBM-1 Hamiltonian with intrinsic triaxial deformation

Mean-field-derived IBM-1 Hamiltonian with intrinsic triaxial deformation

Mechanical Properties of LL6 Chondrites Under Pressures Relevant to Rocky Interiors of Icy Moons

AbstractIcy moons in the outer Solar System likely contain rocky, chondritic interiors, but this material is rarely studied under confining pressure. The contribution of rocky interiors to deformation and heat generation is therefore poorly constrained. We deformed LL6 chondrites at confining pressures ≤100 MPa and quasistatic strain rates. We defined a failure envelope, recorded acoustic emissions (AEs), measured ultrasonic velocities, and retrieved static and dynamic elastic moduli for the experimental conditions. The Young's modulus, which quantifies stiffness, of the chondritic material increased with increasing confining pressure. The material reached its peak strength, which is the maximum supported differential stress (σ1 − σ3), between 40 and 50 MPa confining pressure. Above this 40–50 MPa range of confining pressure, the stiffness increased significantly, while the peak strength dropped. Acoustic emission events associated with brittle deformation mechanisms occurred both during isotropic pressurization (σ1 = σ2 = σ3) as well as at low differential stresses during triaxial deformation (σ1 > σ2 = σ3), during nominally “elastic” deformation, indicating that dissipative processes are likely possible in the rocky interiors of icy moons. These events also occurred less frequently at higher confining pressures. We therefore suggest that the chondritic interiors of icy moons could become less compliant, and possibly less dissipative, as a function of the moons' pressure and size.

Effects of triaxial deformation on the fission barrier in the Z = 118 − 120 nuclei* *Supported by the National Natural Science Foundation of China (Grant Nos. 12205076 and 12047504), the China Postdoctoral Science Foundation (Grant No. 2020M670012), and the Launching Fund of Henan University of Technology (Grant No. 2021BS047).

By using potential energy surface (PES) calculations in the three-dimensional space (β 2, γ, β 4) within the framework of the macroscopic-microscopic model, the fission trajectory and fission barrier for Z = 118(Og), 119, 120 nuclei has been systematically investigated. The calculated PES includes macroscopic liquid-drop energy, microscopic shell correction and pairing correction. Taking the 294Og176 nucleus as an example, we discuss the next closed shell after Z = 82 and N = 126 with the calculated Woods–Saxon single-particle levels. Then, the results of PES in 294Og is illustrated from the (X, Y) scale to the (β 2, γ) scale. The γ degree of freedom reveals the shape evolution clearly during the fission process. The structure near the minimum and saddle point of the PES in the Z = 118, 119, 120 nuclei is demonstrated simultaneously. Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths are also studied. The triaxial deformation in these superheavy mass regions plays a vital role in the first fission barrier, showing a significant reduction in both triaxial paths. In addition, the model-dependent fission barriers of proton-rich nuclei 295Og, 296119, and 297120 are analyzed briefly. Our studies could be valuable for synthesizing the superheavy new elements in the forthcoming HIAF and other facilities.

Fault Networks in Triaxial Tectonic Settings: Analog Modeling of Distributed Continental Extension With Lateral Shortening

AbstractTriaxial deformation is a general feature of continental tectonics, but its controls and the systematics of associated fault networks remain poorly understood. We present triaxial analog experiments mimicking crustal thinning resulting from distributed longitudinal extension and lateral shortening. Contemporary longitudinal extension and lateral shortening are related by the principal horizontal strain ratio (PHSR). We investigate the effect of crustal geometry, rheology and strain rate on deformation localization, faulting regime and pattern, and PHSR in brittle and brittle‐viscous crustal‐scale models. We find that in brittle models the fault networks reflect the basal boundary condition and fault‐density scales inversely with brittle layer thickness. In brittle‐viscous models, as strain rate (ė) decreases, (a) Three fault patterns emerge: conjugate sets of strike‐slip faults (ė > 3 × 10−4 s−1, PHSR > 0.31), sets of parallel oblique normal faults (ė = 0.3–3 × 10−4 s−1, PHSR = 0.15–0.25), horst‐and‐graben system (ė < 0.3 × 10−4 s−1, PHSR < 0.1). (b) The strain localization increases systematically and gradually. We interpret the strain rate dependent of faulting regimes to be controlled by vertical coupling between the model upper mantle and model upper crust resulting in spontaneous permutation of principal stress axes. Rate‐dependency of strain localization can be related to mechanical coupling between the upper and lower crust. We identify the following parameters controlling triaxial tectonic deformation: upper crustal thickness and friction coefficient, lower crustal thickness and viscosity, as well as strain rate. We test our models and predictions against natural prototypes (Tibet, Anatolia, Apennines, and Basin and Range Province) thus providing new perspectives on triaxial deformation.

Brittle Deformation of Damaged Mafic and Ultramafic Rocks and Their Implications on Plate Bending

AbstractThe effect of damage on the brittle deformation of mafic and ultramafic rocks has been investigated by performing triaxial deformation experiments on thermally cracked and intact rock samples. The investigation was performed by recording the axial and lateral strains during deformation while simultaneously capturing the ultrasonic velocity, and electrical resistivity. While the peak strength is presumably controlled by the stiff intrinsic fractures, the crack opening mode also showed critical effects on the attained peak strength. The pore pressure distribution showed an apparent control over the dynamic Young's modulus as the ratio between the dynamic and static modulus of thermally cracked rocks is significantly higher than that of intact rocks. The compliant nature and the higher inelastic volumetric strain of the thermally cracked samples further indicated a possible explanation to the steep dipping plates and the taller topographic heights at the trench outer rise systems of old subduction zones.

Shape evolution of thorium isotopes in between the drip-lines

Commonly encountered shapes in nuclei are spherical, prolate and oblate. The shape of a nucleus is decided by the residual interactions among its nucleons. In our current investigation, we incorporate both axial and triaxial degrees of freedom to study how the shape of thorium nuclei changes within the boundaries of the drip lines. We employed the relativistic mean-field theory and utilized density-dependent meson-exchange as the functional throughout our calculations. We calculated the total binding energy as it varies with the deformation parameter [Formula: see text] and subsequently depicted the resulting binding energy curves. Furthermore, we examined the self-consistent energy surface for thorium isotopes with triaxial quadrupole deformations. The emergence of potential energy minima can be attributed to the presence of gaps or regions with reduced density of single-particle energy levels around the Fermi surface, as the nucleus undergoes deformation. The nuclear shape evolution of thorium isotopes ranging from [Formula: see text] to [Formula: see text] was investigated, [Formula: see text] and [Formula: see text] are spherical in shape and the nearby isotopes are less deformed and nearly spherical. Isotopes ranging from [Formula: see text] to [Formula: see text] exhibit a higher level of deformation. The most deformed nucleus is [Formula: see text] and is prolate. The weak triaxial behavior is observed within the region associated with shape phase transition.

Integration of triaxial ultrasonic velocity and deformation rate analysis for core-based estimation of stresses at the Utah FORGE geothermal site

Core-based methods for in-situ stress estimation were applied using samples from 4 intervals within the Utah FORGE 16A(78)-32 well. At three of these locations, Triaxial Ultrasonic Velocity (TUV) tests were performed, resulting in experimentally-determined relationships between wave velocities and stresses. Non-monotonic increases in the velocity-stress relationships provide evidence of stress history and are therefore used to estimate in-situ stress magnitudes. Additionally, Deformation Rate Analysis (DRA) tests were run on core plugs from various orientations at each of the sampling locations. Results indicate the minimum stress gradient to be ∼0.61–0.74 psi/ft (14–17 kPa/m) and consistent with uniform tectonic strain of 150 microstrain in the Granitoid and tectonic strain that is around 50 % higher in the Gneiss than in the Granitoid. The vertical stress gradient is ∼ 1.09–1.12 psi/ft (24.7–25.3 kPa/m) for the two zones in which it could be inferred from data. The maximum stress gradient ∼ 0.90–1.01 psi/ft (20–23 kPa/m) in the granitoid and 1.32 psi/ft (30 kPa/m) in the Gneiss and consistent with tectonic strain around 300 microstrain through the Granitoid and over 900 microstrain in the Gneiss. The stress regime thus appears to be between normal faulting and strike-slip faulting, potentially becoming more strike-slip in nature with depth and/or flipping back and forth between the two regimes in the region penetrated by the well due to variability of rock properties, structures such as faults, and/or thermal anomalies. These are broadly consistent with other recently published stress models, and therefore provide valuable evidence to the stress state at the Utah FORGE geothermal site and a promising step in the direction of using TUV and DRA together as core-based stress estimation methods.

Deformation Behavior and Seismic Characteristics of Sandy Facies Opalinus Clay During Triaxial Deformation Under Dry and Wet Conditions

Unconsolidated, undrained triaxial deformation tests were performed on sandy facies Opalinus Clay at 50 MPa confining pressure to characterize the effect of water and microfabric orientation on the deformation behavior, mechanical properties, and P-wave velocity evolution. Dry and wet (≈ 8 and > 95% initial water saturation, respectively) samples with 12.6 ± 0.4 vol% porosity were deformed parallel and perpendicular to the bedding direction at a constant strain rate of 5 × 10–6 s−1. Dry samples revealed semi-brittle behavior and exhibited strain localization at failure, while deformation was more ductile at saturated conditions, promoting stable, slow faulting. Peak strength, Young’s modulus, and number of cumulative acoustic emissions decreased significantly for wet samples compared to dry samples; the opposite was observed for Poisson’s ratio. P-wave velocity anisotropy was significantly altered by differential stress, primarily due to the interplay between pore and fracture closure and stress-induced microcrack formation. For samples that were deformed perpendicular to bedding, we observed a reduction and reversal of P-wave velocity anisotropy with increasing differential stress, whereas anisotropy of parallel samples increased. The results suggest that water saturation reduces the pressure at the brittle-ductile transition and that the elastic properties and anisotropy of sandy facies Opalinus Clay can be significantly altered in an anisotropic stress field, e.g., adjacent to fault zones or tunnel excavations. Changes in elastic anisotropy are primarily controlled by the orientation between the pre-existing microfabric and the maximum principal stress direction, stress magnitude, and the degree of water saturation.

Evolution of the giant monopole resonance with triaxial deformation

Evolution of the giant monopole resonance with triaxial deformation

Temperature-dependent void nucleation and growth in single-crystal and nanocrystalline iron at extreme strain rates: atomistic insights

In this paper, we use molecular dynamics simulation with the embedded atomic method to perform triaxial deformation experiments on single-crystal and nanocrystalline iron at a strain rate of 5×10−9 s−1 and investigate the temperature effect on the void nucleation and growth process. We also evaluate the applicability of the Nucleation And Growth (NAG) model for single-crystal iron. The results indicate that the maximum tensile stress of both single-crystal and nanocrystalline iron decreases as temperature increases, with a reduction of 35.9% for single-crystal iron and 36.2% for nanocrystalline iron from 100 K to 1100 K. It is demonstrated that void nucleation and growth is more favored at high temperature. The void nucleation and growth process in single-crystal iron under high strain rate follows the NAG model. We analyze the sensitivity of the NAG parameters at different temperatures and find that the void nucleation and growth threshold of single-crystal iron is much higher than that of low carbon steel. The results can provide insights for developing fracture models of iron at extremely high strain rate and describing the dynamic damage at continuum length scales.

Empirical evaluation of the strength and deformation characteristics of natural and synthetic gas hydrate-bearing sediments with different ranges of porosity, hydrate saturation, effective stress, and strain rate

Evaluating the mechanical properties of gas (primarily methane) hydrate-bearing sediments is essential for commercial production as a next-generation resource and understanding the global carbon cycle. Triaxial and uniaxial compression tests have been conducted on synthetic gas hydrate and natural core samples recovered from deep-sea beds using pressure coring techniques. The results show that four factors are vital in establishing the strength of hydrate-bearing sediments: hydrate saturation, effective confining stress, porosity, and strain rate. However, no study has evaluated these factors in a unified and quantitative manner, and even if the physical properties of the reservoir are known in detail from logging, predicting the strength has been challenging. In this study, pressure cores were drilled and recovered from the Eastern Nankai Trough in April 2018 after Japan’s second offshore production test, and triaxial or uniaxial compression tests were performed on 12 pressure core samples brought back to the laboratory. The mechanical properties of the hydrate-bearing sediments were classified with previous obtained results from 53 pressure cores and 223 synthetic cores, and empirical equations for triaxial compressive strength and deformation modulus were proposed as functions of gas hydrate saturation, effective confining pressure, porosity, and strain rate. The obtained equations were found to correlate well with the experimental data and can predict the strength and deformation modulus from logging data.

Pairing effect on critical spin in chiral rotation

The critical spin Ic (or critical frequency ħωc) represents the minimum spin (or rotational frequency) required for stable chiral solutions in nuclear systems. The effect of pairing on the critical spin has been examined for the particle-hole configuration π(1h11/2)⊗ν(1h11/2)−1 with a triaxial deformation parameter of γ=30∘ using the particle rotor model, which treats the total angular momentum as a good quantum number. Increasing pairing interaction keeps the critical spin Ic constant, but decreases the critical rotational frequency ħωc. This is due to that the enhanced pairing interaction causes valence nucleons angular momenta to align preferentially along the medium axis, resulting in a larger effective collective moment of inertia and facilitating the emergence of chiral rotation at a lower frequency. However, even with an increase in pairing gap from 0.0 to 2.0MeV, the resulting increase in medium axis alignment is less than 1ħ, which is insufficient to change the value of the critical spin Ic. This study suggests that the critical spin remains robust against the influence of pairing interaction.

Linking sand permeability anisotropy to fabric anisotropy via numerical simulation

Characterisation of the permeability of soils is of practical importance and, for cohesionless or granular soils, it can be predicted from the void ratio and the particle size distribution (PSD). However, the effect of fabric anisotropy on the permeability is rarely discussed. Restricting consideration to granular (cohesionless) soil, this study combines a variety of numerical methods to investigate (1) how the anisotropy of the permeability evolves as the soil fabric anisotropy evolves in triaxial deformation and (2) establish a link between the anisotropy of the permeability and the fabric anisotropy. The Discrete Element Method (DEM) was employed to create linearly graded virtual samples of spheres (Cu of 1 to 2). Initially isotropic sphere packings were subjected to triaxial compression or triaxial extension up to 30% of absolute axial strain to induce an anisotropic fabric. Pore Network Models (PNMs) present a computationally efficient option for simulation of flow through the pore space. A PNM models fluid flow between pores (nodes) connected by pipes (edges) whose geometry is defined by the topology of the connected pores and the mass balance equation is solved at each pore. After demonstrating the accuracy of the PNM framework adopted here, this contribution presents data from PNM simulations that used the positions of individual particles in the sheared spherical packings as input data. The fabric and permeability anisotropies during triaxial shear deformation were compared at axial strain intervals of 1%. Detailed microscale analyses suggest that the anisotropy in the permeability can be attributed to an increase in the local conductance of fluid pipes in the direction of the major principal stress, which is related to the evolution of the pore topologies during the shear deformation.

Analysis of the structural, electronic, optical and mechanical properties of CsGeI2Br under tensile and compressive strain for optoelectronic applications: A DFT computational perspective

In this work, the impact of triaxial strain on the structural, optoelectronic and mechanical properties of CsGeI₂Br is thoroughly investigated, with a particular emphasis on its applicability in optical technologies spanning the visible and ultraviolet spectra. This research fills a notable gap in the literature, highlighting the intriguing properties of this material under external strain. First, the unstrained CsGeI₂Br is identified as a direct band gap semiconductor, revealing an energy gap of 0.714 eV. Moreover, the obtained results show a remarkable sensitivity of CsGeI₂Br's band gap to triaxial strain. Under a triaxial deformation ranging from −6% to 6 %, the energy of the bandgap undergoes a remarkable transformation, varying from 1.81 eV under tensile stress to 0.101 eV under compressive strain; The material approaches the metallic state under compressive strain and exhibits increased bandgap energy under tensile stress. Furthermore, the investigation delves into the optical coefficients in both x = y, z directions, revealing that triaxial strain can significantly enhance absorbance, particularly within the visible and ultraviolet energy spectra. Additionally, triaxial strain introduces significant anisotropy and influences the optical band gap. This results in increased absorption capacity and optical conductivity under tensile stress, making it more effective and better suited for various optical applications, including surgical tools, integrated circuits, QLED, OLED, solar cells, waveguides, and materials for solar heat reduction. The mechanical stability of CsGeI₂Br across the entire range of applied strain is validated by the elastic constants, which impeccably adhere to stability criteria. The negative cohesive energy values determined for unconstrained and constrained CsGeI₂Br signify their thermodynamic stability, establishing their experimental feasibility. Compression strain significantly influences the mechanical properties, enhancing the ductility of this compound.