Hydrostatic Stress Conditions Research Articles

On the stress-dependent tight-rock permeability under anisotropic stress conditions

Permeability is a key parameter for characterizing an unconventional tight-rock reservoir and predicting hydrocarbon production from the reservoir. Because of the technical difficulty in accurately measuring extremely low tight-rock permeability, the permeability measurements have been commonly made in laboratory under hydrostatic (or isotropic stress) conditions. For unconventional reservoirs, stress distributions, however, are generally anisotropic. This paper presents a theoretical and experimental study on stress-dependent tight-rock permeability under anisotropic stress conditions. The theoretical development is based on the concept of effective stress and expresses rock permeability as an exponential function of the effective stress defined in this paper. The laboratory permeability data obtained under anisotropic stress conditions support the usefulness of the theoretical model for the stress-dependent permeability and demonstrate the importance of stress anisotropy in determining rock permeability. Considering that the effective stress is the only independent variable for determining the relationship between rock permeability and stress, we further propose a workflow to convert tight-rock permeability data collected under hydrostatic stress conditions to those for anisotropic stress conditions that are more realistic for field applications. A theoretical relation for upscaling a parameter characterizing the impact of stress anisotropy on local-scale permeability is also discussed as the first step to address this important upscaling issue.

Fluid-mineral Equilibrium Under Nonhydrostatic Stress: Insight From Molecular Dynamics

The interpretation of phase equilibria and reactions in geological materials is based on standard thermodynamics that assumes hydrostatic and homogeneous stress conditions. However, rocks and minerals in the lithosphere can support stress gradients and nonhydrostatic stresses. Currently, there is still not an accepted macroscopic thermodynamic theory to include the effect of nonhydrostatic stress on mineral reactions, and the use of several thermodynamic potentials in stressed geological system remains under debate. In experiments under nonhydrostatic stress, it is often difficult to resolve the direct effect of differential stress on phase equilibria because pressure gradients may be developed. Such gradients can affect the metamorphic equilibria at the local scale. Here, we investigate the direct effect of a homogeneous, nonhydrostatic stress field on the solid-fluid equilibrium using molecular dynamics simulations at non-zero pressure and elevated temperature conditions. Our results show that, for simple single-component systems at constant temperature, the equilibrium fluid pressure of a stressed system is always larger than the value of fluid pressure at hydrostatic stress conditions. The displacement of the equilibrium value of the fluid pressure is about an order of magnitude smaller compared to the level of differential stress in the solid crystal. Thus, phase equilibria can be accurately predicted by taking the fluid pressure as a proxy of the equilibration pressure. On the contrary, the mean stress of the solid can deviate substantially from the pressure of the fluid in stressed systems at thermodynamic equilibrium. This has implications on the use of thermodynamic pressure in geodynamic models since the fluid pressure is a more accurate proxy for predicting the location of metamorphic reactions, while the equilibrium density of the solid has to be determined from its mean stress.

Failure characterization of fully grouted rock bolts under triaxial testing

Confining stresses serve as a pivotal determinant in shaping the behavior of grouted rock bolts. Nonetheless, prior investigations have oversimplified the three-dimensional stress state, primarily assuming hydrostatic stress conditions. Under these conditions, it is assumed that the intermediate principal stress (σ2) equals the minimum principal stress (σ3). This assumption overlooks the potential variations in magnitudes of in situ stress conditions along all three directions near an underground opening where a rock bolt is installed. In this study, a series of push tests was meticulously conducted under triaxial conditions. These tests involved applying non-uniform confining stresses (σ2 ≠ σ3) to cubic specimens, aiming to unveil the previously overlooked influence of intermediate principal stresses on the strength properties of rock bolts. The results show that as the confining stresses increase from zero to higher levels, the pre-failure behavior changes from linear to nonlinear forms, resulting in an increase in initial stiffness from 2.08 kN/mm to 32.51 kN/mm. The load-displacement curves further illuminate distinct post-failure behavior at elevated levels of confining stresses, characterized by enhanced stiffness. Notably, the peak load capacity ranged from 27.9 kN to 46.5 kN as confining stresses advanced from σ2 = σ3 = 0 to σ2 = 20 MPa and σ3 = 10 MPa. Additionally, the outcomes highlight an influence of confining stress on the lateral deformation of samples. Lower levels of confinement prompt overall dilation in lateral deformation, while higher confinements maintain a state of shrinkage. Furthermore, diverse failure modes have been identified, intricately tied to the arrangement of confining stresses. Lower confinements tend to induce a splitting mode of failure, whereas higher loads bring about a shift towards a pure interfacial shear-off and shear-crushed failure mechanism.

Multi‐scale characterization of granular media by in situ laboratory X‐ray computed tomography

AbstractInvestigations of biphasic monodisperse soft (rubber) and stiff (glass) particle mixtures under hydrostatic conditions show an interesting behavior with regard to the effective stiffness. P‐wave modulus measured by acoustic wave propagation at ultrasonic frequencies showed a significant decline while more soft particles are added, that is, higher rubber volume fractions, due to a change in the microstructure of the granular medium. However, for small volume fractions of soft particles, it could be observed that the P‐wave modulus is increasing. This result cannot be explained by classical mixture rules or effective medium theories. For the understanding of those effects, a detailed insight into the microstructure of the granular medium is necessary. To gain this information and link it later back to the measured effective mechanical properties, high‐resolution micro X‐ray computed tomography (XRCT) imaging is a well‐established tool. With XRCT imaging, the granular microstructure can be visualized in 3D and characterized subsequently. Combining classical effective characterization methods with XRCT imaging can help to solve a variety of multi‐scale problems. Performing the characterization step in situ, meaning inside the laboratory‐based XRCT scanner, has the advantage that exactly the same samples are mechanically characterized and visualized. To address the mentioned observation above, we designed a low X‐ray absorbing oedometer cell with integrated broadband piezoelectric P‐wave transducers which enables this kind of investigation inside a laboratory‐based XRCT scanner. The focus of this contribution is on the general experimental methodology which can be transferred to other multi‐scale problems. It starts with a description of the image acquisition and ends with the post‐processing of the in situ acquired image data. To demonstrate this, cylindrical samples consisting of the same monodisperse rubber and glass particle mixtures that were studied before under hydrostatic stress conditions are considered. Selected results are presented to explain the single steps.

Static and Dynamic Bulk Moduli of Deepwater Reservoir Sands: Influence of Pressure and Fluid Saturation

AbstractThe static bulk modulus of unconsolidated sands is essential for predicting the in situ effective pressure to reduce drilling risks in deepwater reservoirs; however, the dynamic bulk modulus is often more broadly available from seismic or well logging data. Therefore, it is tempting to investigate the relationship between static and dynamic bulk moduli. We perform a series of ultrasonic velocity measurements on 21 deepwater reservoir sands from the Gulf of Mexico (GoM) to study the static and dynamic bulk moduli simultaneously. Both room-dry and brine-saturated ultrasonic velocities are measured under hydrostatic stress conditions to derive the dynamic bulk moduli. Under brine-saturated conditions, if the pore pressure is kept constant, the pore volume change with the confining pressure can be monitored accurately by a digital pump, which is subsequently used to estimate the static bulk modulus. The experimental results suggest that both the static and dynamic bulk moduli decrease upon pressure unloading. The pressure-dependent bulk moduli are modeled using the Hertz-Mindlin contact theory at the critical porosity and combined with the modified Hashin-Shtrikman lower bound for other porosities. The results suggest that the theoretical estimates can serve as the lower bound for the dynamic bulk modulus and the upper bound for the static bulk modulus. Under room-dry conditions, the static-to-dynamic modulus ratio decreases from a value approaching 0.8 to approximately 0.25 with decreasing differential pressure. Moreover, the effects of brine saturation on the relationship between the static and dynamic moduli are investigated using Gassmann’s equation. The brine saturation substantially reduces the difference between the static and dynamic bulk moduli, making the static-to-dynamic modulus ratio approach unity, which may be relevant to the in situ reservoir rock properties.

Accessibility of Pores to Methane in New Albany Shale Samples of Varying Maturity Determined Using SANS and USANS

The accessibility of pores to methane has been investigated in Devonian New Albany Shale Formation early-mature (Ro = 0.50%) to post-mature (Ro = 1.40%) samples. A Marcellus Shale Formation sample was included to expand the maturation range to Ro 2.50%. These are organic matter-rich rocks with total organic carbon (TOC) values of 3.4 to 14.4% and porosity values of 2.19 to 6.88%. Contrast matching small-angle neutron scattering (SANS) and ultra-small angle neutron scattering (USANS) techniques were used to generate porosity-related data before and after pressure cycling under hydrostatic (in a vacuum and at 500 bar of deuterated methane) and uniaxial stress (0 to ca. 350 bar) conditions. Our results showed that the accessible porosity was small for the samples studied, ranging from zero to 2.9%. No correlation between the accessible porosity and TOC or mineralogical composition was revealed, and the most likely explanation for porosity variation was related to the thermal transformation of organic matter and hydrocarbon generation. Pressure caused improvements in accessible porosity for most samples, except the oil window sample (Ro = 0.84%). Our data show that densification of methane occurs in nanopores, generally starting at diameters smaller than 20 nm, and that the distribution of methane density is affected by pressure cycling.

Stress sensitivity of porosity and permeability under varying hydrostatic stress conditions for different carbonate rock types of the geothermal Malm reservoir in Southern Germany

In geothermal reservoir systems, changes in pore pressure due to production (depletion), injection or temperature changes result in a displacement of the effective stresses acting on the rock matrix of the aquifer. To compensate for these intrinsic stress changes, the rock matrix is subjected to poroelastic deformation through changes in rock and pore volume. This in turn may induce changes in the effective pore network and thus in the hydraulic properties of the aquifer. Therefore, for the conception of precise reservoir models and for long-term simulations, stress sensitivity of porosity and permeability is required for parametrization. Stress sensitivity was measured in hydrostatic compression tests on 14 samples of rock cores stemming from two boreholes of the Upper Jurassic Malm aquifer of the Bavarian Molasse Basin. To account for the heterogeneity of this carbonate sequence, typical rock and facies types representing the productive zones within the thermal reservoir were used. Prior to hydrostatic investigations, the hydraulic (effective porosity, permeability) and geomechanical (rock strength, dynamic, and static moduli) parameters as well as the microstructure (pore and pore throat size) of each rock sample were studied for thorough sample characterization. Subsequently, the samples were tested in a triaxial test setup with effective stresses of up to 28 MPa (hydrostatic) to simulate in-situ stress conditions for depths up to 2000 m. It was shown that stress sensitivity of the porosity was comparably low, resulting in a relative reduction of 0.7–2.1% at maximum effective stress. In contrast, relative permeability losses were observed in the range of 17.3–56.7% compared to the initial permeability at low effective stresses. Stress sensitivity coefficients for porosity and permeability were derived for characterization of each sample and the different rock types. For the stress sensitivity of porosity, a negative correlation with rock strength and a positive correlation with initial porosity was observed. The stress sensitivity of permeability is probably controlled by more complex processes than that of porosity, where the latter is mainly controlled by the compressibility of the pore space. It may depend more on the compaction of precedented flow paths and the geometry of pores and pore throats controlling the connectivity within the rock matrix. In general, limestone samples showed a higher stress sensitivity than dolomitic limestone or dolostones, because dolomitization of the rock matrix may lead to an increasing stiffness of the rock. Furthermore, the stress sensitivity is related to the history of burial diagenesis, during which changes in the pore network (dissolution, precipitation, and replacement of minerals and cements) as well as compaction and microcrack formation may occur. This study, in addition to improving the quality of input parameters for hydraulic–mechanical modeling, shows that hydraulic properties in flow zones largely characterized by less stiff, porous limestones can deteriorate significantly with increasing effective stress.

Permeability of Coking Coals and Patterns of Its Change in Leninsky Area, Kuznetsk Coal Basin, Russia

A prediction of the permeability of gas-bearing coking coals in the Leninsky area, Kuznetsk coal basin (Kuzbass), which is promising for the production of coal methane, was performed. The results of laboratory studies of coal permeability and cleat compressibility under hydrostatic stress conditions are presented. As the confining pressure increased by 8 times (from 1 MPa to 8 MPa), the coal permeability perpendicular to the butt cleat direction decreased by 6.7 times (from 60 mD to 9 mD). The coal cleat compressibility was 0.085 MPa−1. On the basis of the results of filtration tests and microstructural analysis of the coking coals, we provide the estimation of the permeability anisotropy along the bedding planes (perpendicular to the face and butt cleat directions). The predicted dependences of gas-bearing coking coal permeability perpendicular to the butt and face cleat directions on depth and on features of coal seam bedding were determined under uniaxial strain conditions. It was found that in the coking coal depth intervals, as the depth increased, their permeability decreased by 61–82%. The obtained results can be used to select facilities and to design industrial works for the extraction of coal methane in the region.

Time Dependent Mechanical Crack Closure as a Potential Rapid Source of Post‐Seismic Wave Speed Recovery: Insights From Experiments in Carrara Marble

AbstractSeismological observations indicate strong variations in wave velocities around faults both co‐seismically during earthquakes, and post‐seismically. Recovery is commonly associated with a reduction in crack damage. Here, we explore the recovery associated with time‐dependent mechanical closure of cracks. We report results from laboratory experiments conducted on dry cores of Carrara marble at room temperature. We deformed cylindrical samples in the semi‐brittle regime to induce crack damage before subjecting them to hydrostatic and triaxial stress conditions for extended periods of time while recording dilatancy and wave speeds repeatedly. We report wave speed increases of up to 40% of the damage‐induced wave speed drop in samples subject to hydrostatic loading. Moreover, we report the occurrence of significant wave speed increases contemporaneously with time‐dependent creep in triaxially loaded samples. Wave speed recovery during creep is only observed below a threshold creep strain rate, a result we interpret as a transition from brittle to plastic creep with decreasing strain rate. We interpret the wave speed increase in terms of reduced crack density and increased contact area within the crack array, and show that around 40% of the total crack surface has to be closed to justify the observed wave speed recoveries. We propose that mechanical crack closure is driven by the viscous relaxation of the bulk rock under the influence of locked‐in stresses at low confining pressure, and of the external stresses at higher confining pressure. Our study shows that mechanical crack closure is a significant source of time‐dependent wave speed recovery.

Hydrostaticity in high pressure experiments: some general observations and guidelines for high pressure experimenters

ABSTRACT The characteristics of hydrostatic stress conditions are discussed and compared with real experimental observations made under high pressure with a diamond-anvil cell. While fluid pressure-transmitting media give a well-defined single stress condition, solid pressure-transmitting media give a variety of stress conditions within the limit of their shear strength under high pressure. Owing to its low shear strength, solid helium would be the best choice for a pressure-transmitting medium to at least 100 GPa. However, helium is so compressible that care should be taken on minimizing irregular deformation of a gasket hole, which often causes complicated stress states. A review is given on the quasi-hydrostatic limits of solidified pressure-transmitting media, and some ways to reduce nonhydrostaticity are discussed including the case of low-temperature experiments.

Improved predictions of thermal fluid pressurization in hydro-thermal models based on consistent incorporation of thermo-mechanical effects in anisotropic porous media

Coupled thermo-hydro-mechanical models are commonly used to model the evolution of temperature, pore pressure, and stress in a wide range of geotechnologies such as geothermal applications or around canisters of high-level radioactive waste in deep underground storage facilities. Their numerical modeling is often computationally highly demanding, especially if parameter identification, sensitivity analyses or uncertainty quantification require many model evaluations. Often, the thermally driven pore pressure evolution and the subsequently altered flow processes are the primary targets of an analysis. To benefit from the computational efficiency of hydro-thermal (HT) models while maintaining the accuracy of the thermo-hydro-mechanical (THM) model, we derived two cases of a simplified representation of mechanical deformations in a coupled hydro-thermal model. Deformations induced by pressure as well as temperature changes are consistently incorporated into the mass balance storage terms. We demonstrate the exact coincidence of THM and modified TH formulations in isotropic and orthotropic materials as long as the basic assumptions like constant hydrostatic stress conditions or uniaxial strain hold. By modeling of a point heat source in isotropic or anisotropic porous media it is shown that a good agreement between TH and THM models can be maintained even though the assumptions underlying the simplification are no longer valid exactly. On our test-machine, a significant speed-up could be achieved by the reduction of the problem size when transitioning from a THM to a TH model. The highest speed-ups were achieved when Taylor-Hood elements were employed in order to avoid the problem of spurious pressure oscillations in the fully coupled THM model.

Simultaneous static and dynamic bulk modulus measurements under hydrostatic stress conditions and without applying strain gauge

The static properties of subsurface rocks are needed for geomechanical applications, but the dynamic properties are usually more extensively available and can be acquired with much less effort. Therefore, it is important to know the relationships between the static and dynamic properties. Studying these relationships based on traditional triaxial testing yields confusing results, partly due to intrinsic deficiencies of the experimental setup and testing procedures. We have developed a new approach to study the relationship under hydrostatic stress conditions. The traditional ultrasonic velocity measurement system is sufficient for all of the testing, and it requires no application of the traditional strain gauge. During the pressure-dependent ultrasonic velocity measurements, the rock sample experiences static deformation when the pressure changes are in the order of megapascals. If the pore pressure is kept constant, the pore volume will vary with the confining pressure. The pore volume change can be monitored accurately by the pore pressure controlling pump, and it can be related to the volume strain of the rock for estimating the static bulk modulus of the rock sample. Based on the laboratory ultrasonic measurements available in the literature, we analyzed the effects of the differential pressure, clay content, crack density, and pore fluid on the relationship between the static and dynamic bulk moduli. From the analyses, we inferred that most of the laboratory-observed differences between the static and dynamic property may not exist for the reservoir rock under in situ conditions.

A comparative study of the stress-dependence of dynamic and static moduli for sandstones

Understanding the differences between the static and dynamic elastic moduli of reservoir rocks is essential for the successful exploration and production of hydrocarbon reservoirs. However, the controlling factors on the dynamic-static discrepancy for sandstones remain ambiguous. Consequently, we have purposely selected three outcrop sandstone samples with large porosity contrast to investigate the effects of the stress state, magnitude, and load-unload history on the dynamic and static moduli through laboratory measurements. The results suggest that the dynamic moduli are systematically larger than the static moduli at almost any hydrostatic or deviatoric stress magnitude. In contrast, the static moduli are much more sensitive to the stress variations than the dynamic ones, leading to the decreasing dynamic-static difference upon hydrostatic loading and the increasing dynamic-static difference upon deviatoric loading. When the maximum stress in a cycle is initially reversed, the dynamic-static ratio tends to approach one, whatever the bulk modulus under hydrostatic pressure condition or the Young’s modulus under triaxial stress condition. Under the subsequent unloading process, the static bulk modulus is always higher than that derived during loading. However, the unloading static Young’s modulus is larger than the loading Young’s modulus only at a relatively high deviatoric stress magnitude greater than 30 MPa, while showing an opposite trend at a low-stress condition of less than 25 MPa. From the microstructural viewpoint, it is believed that the static tests accumulate the elastic, viscoelastic, and nonelastic properties within a certain stress or strain range. In contrast to the dynamic modulus, the static modulus exhibits greater sensitivity to the pressure or stress changes under hydrostatic and deviatoric stress conditions. The strong stress dependence makes it important to consider the in situ stress conditions when establishing dynamic-static modulus relations.

Deformation of Granular Aggregates: Static and Dynamic Bulk Moduli

AbstractSand and glass bead samples were monotonically loaded from 0 to 50 MPa and then monotonically unloaded, all under hydrostatic stress conditions. Sand deformed irreversibly and its porosity loss was permanent. In contrast, the glass bead deformation was almost fully reversible with the initial porosity recovered. During loading, the static bulk modulus in all sand samples increased from 0 to about 0.5 GPa between 0‐ and 15‐MPa stress and remained constant for the remainder of the loading. Such behavior, somewhat unexpected in a granular system, means that sand deforms as a linear elastic body during loading from 15 to 50 MPa. The unloading behavior was very different—the static bulk modulus almost linearly decreased from about 4 GPa at 50 MPa to zero as the stress was reduced. Once again, this behavior was very different from that observed in glass beads, where the static bulk modulus during loading was essentially the same as during unloading and appeared to be a unique function of stress, independent of the direction of its variation. Moreover, the static and dynamic bulk moduli in glass beads, the latter computed from Vp, Vs, and density measured during the loading/unloading cycle, were very close to each other. In contrast, the dynamic bulk modulus in dry sand exceeded the static modulus during unloading by a factor of 1.5 to 2.0. We used a quantitative theory based on contact mechanics and the concept of stress heterogeneity in particulates to analytically match the observed results.

Analysis of the effects of blast-induced damage zone with attenuating disturbance factor on the ground support interaction

ABSTRACT The rock mass properties are typically influenced by the excavation technique and the changes in the state of stress due to the rock excavation. The amount and extent of damage introduced in the rock mass depends on the excavation technique and practice quality. The influence of blasting in the rock mass near the tunnel periphery is far more significant due to the energy of waves and redistribution of stresses and the severity of the damage diminishes as the radial distance from the tunnel opening increases. Therefore, it is important to consider the effect of the damaged zone when analysing the stresses and deformations around a tunnel. This study aimed at providing a new numerical solution for the determination of the ground response (reaction) curve with the consideration of the non-uniform damage zone around the tunnel periphery. A deep circular tunnel subjected to hydrostatic stress condition and excavated in rock materials obeying the Hoek-Brown failure criterion is considered. A solution for the determination of stresses, strains, and deformations around the circular deep tunnel is presented in order to correctly assess the attenuation of damaged rock as the distance from the tunnel perimeter increases considering the loads applied to the supporting structure.

The Stress Sensitivity and Porosity Sensitivity of Coal Permeability at Different Depths: A Case Study in the Pingdingshan Mining Area

Determining the relationships among the stress, porosity and permeability of coal masses at different depths is a key problem in coalbed methane extraction and greenhouse gas storage. In this study, we successfully conducted porosity and permeability experiments under different depth-dependent hydrostatic stress conditions using coal samples collected from the same coal seam group but at five different depths in the Pingdingshan mining area. The porosity, permeability, stress sensitivity and porosity sensitivity of the coal at different depths were analyzed, and the results showed that the coal porosity at different depths (300–1050 m) ranged from 0.15 to 0.50% and that the coal permeability ranged from 5 × 10−4 to 3 × 10−3 mD. The porosities and permeabilities of the coal samples collected from different depths decreased according to negative exponential functions as the effective stress increased. The porosity, permeability, porosity sensitivity and stress sensitivity of the coal mass at depths from 300 to 1050 m initially increased with depth and then decreased at depths greater than 600–700 m; this behavior is different from the conventional understanding in which the porosity and permeability of a coal mass decrease continuously with the depth. The stress sensitivity of the coal is also stress-dependent and clearly increases when the effective stress in the coal mass is less than 10 MPa. The porosity and stress sensitivities of the coal are directly associated with the initial porosity and physical properties of the coal. The depth effect on the porosity and stress sensitivities of the coal permeability is closely related to specific coal fracture compression properties at different depths. A coal mass with a high porosity and a correspondingly low density typically has high porosity and stress sensitivities, as supported by the experimental results and theoretical analyses.

Review: Coefficients for Stress, Temperature, and Composition Effects in Fluorescence Measurements of Alumina.

The numerical coefficients linearly relating the effects of stress (including pressure), temperature, and composition to shifts in the energies of the Cr-related fluorescence in alumina (Al2O3) are reviewed. The primary focus is the shift of the R1 and R2 "ruby" fluorescence lines under conditions typical for stress determination in polycrystalline Al2O3. No significant experimental difference in the R1 and R2 responses is observed for hydrostatic stress (or pressure) conditions (average shift coefficient of about 7.6 cm-1/GPa), changes in temperature (about 0.140 cm-1/K), or variations in composition (about 120 cm-1/mass fraction of Cr). There are significant differences in the R1 and R2 responses for nonhydrostatic stress conditions. In particular, for uniaxial stress along the a and c directions in the Al2O3 crystal, the R1 piezospectroscopic tensor coefficients (about 3.0 cm-1/GPa and 1.6 GPa cm-1/GPa, respectively) differ considerably, whereas the R2 coefficients (about 2.6 cm-1/GPa and 2.3 GPa cm-1/GPa, respectively) do not. Measurements of the piezospectroscopic tensor coefficients are shown to have interlaboratory relative consistency of about 4 % extending over 30 years, and are consistent with the scalar high-pressure measurements. Measurements of the temperature coefficients are shown to have interlaboratory relative consistency less than 1 % extending over 60 years. Fluorescence-based measurements of stress in polycrystalline Al2O3, although requiring temperature adjustment, are shown to have a relative uncertainty of about 2.5 %.

Discrete element modeling of shielding and size effects during single particle crushing

In granular assemblies such as soil, ballast, cementitious aggregates, food and medical products, particle fragmentation and crushing alter material properties. The goal of this research work is to better understand the microstructure parameters that control the triggering of fragmentation, and to predict how microstructure evolution consequent to crushing can actually enhance or reduce material properties. We focused on size and shielding effects, which respectively refer to the decrease of particle strength with increasing particle size, and to the increase of particle strength with the redistribution of stress towards hydrostatic stress conditions upon crushing of neighboring particles. We calibrated the parameters of a Distinct Element Method (DEM) cluster model of crushable particle so as to match the displacement and axial force obtained experimentally at the first particle fragmentation. In order to study the influence of the coordination number on particle crushing, we modeled the mechanical confinement effect of neighboring particles by placing rigid walls around the DEM cluster. In order to understand why larger particles have lower tensile strength, we studied size effects on the crushing process of clusters with and without internal flaws. We found that for clusters with a porosity ranging between 0% and 30%, tensile strength only depends on porosity and not on flaw size. Overall results show that particle strength depends: (1) linearly on particle coordination number; (2) quadratically on particle porosity. Theoretical and DEM modeling of particle crushing will advance the fundamental understanding of energy transfer in particulate media.

Residual stresses in steel rod with collar formed by partial diameter-enlarging technique

Residual stress distribution in a carbon steel component with collar manufactured by partial diameter-enlarging (PDE) process was evaluated using the angular dispersion and time-of-flight neutron diffraction methods in the interior and X-ray diffraction method at the surface of the collar. The residual stresses in the PDE specimen were smaller compared with those of a specimen with the similar shape and dimension made by a simple compression (SC) process. The hoop residual stress varied from −98 to 2 MPa around the circumference at the surface of the collar in the PDE specimen, whereas it was nearly constant in the SC one. The residual stresses in the central region of the both specimens were nearly in a hydrostatic compressive stress condition.

Modeling graphite under stress: Equations of state, vibrational modes, and interlayer friction

Extensive two- and three-dimensional periodic first-principles simulations have been carried out to investigate the mechanical response of graphite to hydrostatic and nonhydrostatic stress conditions. Our results show a clear analogy between uniaxial $({\ensuremath{\sigma}}_{z})$ stress and hydrostatic pressure as far as structural changes in the unit cell are concerned. For intralayer C-C distances and in-plane graphite vibrational frequencies, the similarity with hydrostatic conditions is however found under biaxial $({\ensuremath{\sigma}}_{x}={\ensuremath{\sigma}}_{y})$ stresses. The calculated uniaxial equation of state is further used to investigate sliding mechanisms of a graphite layer in graphite at different interlayer separations, thus providing insight at an atomic level on the origin of the low static friction coefficient of graphite.