Showing papers on "Hydrostatic stress published in 2019"

Inelastic Deformation of the Slochteren Sandstone: Stress-Strain Relations and Implications for Induced Seismicity in the Groningen Gas Field

Abstract: Pore pressure reduction in sandstone reservoirs generally leads to small elastic plus inelastic strains. These small strains (0.1%–1.0% in total) may lead to surface subsidence and induced seismicity. In current geomechanical models, the inelastic component is usually neglected, though its contribution to stress-strain behavior is poorly constrained. To help bridge this gap, we performed deviatoric and hydrostatic stress cycling experiments on Slochteren sandstone samples from the seismogenic Groningen gas field in the Netherlands. We explored in situ conditions of temperature (T = 100 °C) and pore fluid chemistry, porosities of 13% to 26% and effective confining pressures (≤320 MPa) and differential stresses (≤135 MPa) covering and exceeding those relevant to producing fields. We show that at all stages of deformation, including those relevant to producing reservoirs, 30%–50% of the total strain measured is inelastic. Microstructural observations suggest that inelastic deformation is largely accommodated by intergranular displacements at small strains of 0.5%–1.0%, with intragranular cracking becoming increasingly important toward higher strains. The small inelastic strains relevant for reservoir compaction can be described by an isotropic, Cam-clay plasticity model. Applying this model to the depleting Groningen gas field, we show that the in situ horizontal stress evolution is better represented by taking into account combined elastic and inelastic deformation than it is by representing the total deformation behavior using poroelasticity (up to 40% difference). Therefore, inclusion of the inelastic contribution to reservoir compaction has a key role to play in future geomechanical modelling of induced subsidence and seismicity.

Scanning 3DXRD Measurement of Grain Growth, Stress, and Formation of Cu6Sn5 around a Tin Whisker during Heat Treatment.

Abstract: The 3D microstructure around a tin whisker, and its evolution during heat treatment were studied using scanning 3DXRD. The shape of each grain in the sample was reconstructed using a filtered-back-projection algorithm. The local lattice parameters and grain orientations could then be refined, using forward modelling of the diffraction data, with a spatial resolution of 250 n m . It was found that the tin coating had a texture where grains were oriented such that their c-axes were predominantly parallel to the sample surface. Grains with other orientations were consumed by grain growth during the heat treatment. Most of the grain boundaries were found to have misorientations larger than 15 ∘ , and many coincidence site lattice (CSL) or other types of low-energy grain boundaries were identified. None of the grains with CSL grain boundaries were consumed by grain growth. During the heat treatment, growth of preexisting Cu6Sn5 occurred; these grains were indexed as a hexagonal η phase, which is usually documented to be stable only at temperatures exceeding 186 ∘ C . This indicates that the η phase can exist in a metastable state for long periods. The tin coating was found to be under compressive hydrostatic stress, with a negative gradient in hydrostatic stress extending outwards from the root of the whisker. Negative stress gradients are generally believed to play an essential role in providing the driving force for diffusion of material to the whisker root.

Molecular dynamics simulation of subsurface damage mechanism during nanoscratching of single crystal silicon

Abstract: Three-dimension molecular dynamics (MD) simulation is employed to investigate the nanoscratching process of monocrystalline silicon with diamond tools. The effects of tool geometry on subsurface damage and scratching surface integrity are investigated by analyzing phase transformation, chip, defect atoms, hydrostatic stress, von Mises stress and workpiece deformation. In addition, a theoretical analytical model to study the subsurface damage mechanism by analyzing the zone size of phase transformation and normal force with diamond tools at different half-apex angles on silicon surfaces is established. The results show that a bigger half apex angle causes a higher hydrostatic stress, a larger chip volume, a higher temperature and a higher potential energy, and increases subsurface damage. The results also reveal that the evolution of crystalline phases is consistent with the distribution of hydrostatic stress and temperature. In addition, tip scratching with a bigger half-apex angle would result in a large...

Influence of the Intermediate Principal Stress on Sandstone Failure

Abstract: This paper reports the results of fracture testing of sandstone under constant minor principal stress (20 MPa) and various intermediate principal stresses. The results show that when the minor principal stress is constant, as the intermediate principal stress increases, the ratio of the octahedral shear stress (τoct) to the octahedral normal stress (σoct) decreases. The strength criterion of τoct/σoct = f(σ2) is obtained. This criterion reflects not only the hydrostatic stress and intermediate principal stress effects but also the Lode angle effect. This criterion reveals the reason why the rock strength increases and then decreases with increasing intermediate principal stress. The decreasing trend is fitted by linear, logarithmic and Boltzmann equations. The applicability of the three fitting equations for strength prediction and the π plane strength envelopes is analysed, and the results of the Boltzmann fitting equation are the best. The deformation characteristics of rock during the failure process are analysed. The changing process of the tangential deformation modulus of the rock is found to be divided into three stages during the loading process: an increasing stage, an initial decreasing stage and a rapidly decreasing stage. Based on an analysis of computed tomography (CT) images of the internal fractures of rock and photographs of the fracture surfaces, the internal fractures are found to be clear and smooth, and the shear stresses in the fracture surfaces are strengthened with increasing intermediate principal stress. The dominant shear stress in the process of failure is considered to cause these phenomena.

A numerical study on subsurface quality and material removal during ultrasonic vibration assisted cutting of monocrystalline silicon by molecular dynamics simulation

Abstract: Molecular dynamics (MD) simulation is used to study the subsurface quality and material removal of single crystal silicon with a diamond tool during ultrasonic elliptical vibration assisted cutting (UEVAC), 1D ultrasonic vibration assisted cutting (1D UVAC) and traditional cutting (TC) process. In the simulations, a long-range analytical bond order potential is used to describe the interaction inside the silicon specimen, providing a more accurate depiction of the atomic scale mechanisms of ductile plasticity, brittle fracture, and structural changes in silicon. The results show that UEVAC and 1D UVAC in cutting brittle material silicon causes a much smaller cutting force, much lower von Mises stress at the subsurface, larger material remove rate, lower compressive normal stress and and smaller shear stress In addition, the hydrostatic stress of subsurface for TC and 1D UVAC is much higher than that for UEVAC, which results in fewer Si-II and bct5-Si formed from the original Si-I in UEVAC. Moreover, the number of other atoms for UEVAC is overall smaller than those of using TC and 1D UVAC, which confirms that UEVAC produces a better subsurface. And atomic flow field analysis shows that the UEVAC tends to cut silicon in a more ductile mode. Besides, the temperature in front of tool edge and below the tool flank face of TC is much higher. This means that 1D UVAC and UEVAC have a positive effect on the tool life. However, the temperature in subsurface zone is overall larger, which reveals that 1D UVAC and UEVAC have a negative effect on the subsurface temperature.

Experimental investigation on the stress sensitivity of permeability in naturally fractured shale

Abstract: In this paper, we present an experimental investigation regarding the stress sensitivity of permeability in naturally fractured shale. Gas permeability tests were performed on the fractured cylindrical shale samples under loading and unloading conditions. Different hydrostatic stress and gas pressure levels were chosen to investigate the dependence of permeability on stress. The permeability of the fractured shale decreases with increasing hydrostatic stress, re-increases during unloading and is irreversible during loading and unloading processes. The gas pressure exhibits a significant effect on the permeability in comparison with the hydrostatic stress. Small gas pressure changes (e.g., 2 MPa) induce a comparable change in permeability with a large hydrostatic stress change (e.g., 40 MPa). The gas pressure gradient on the permeability will be discussed. The fracture aperture was estimated by recording the volume change during loading and shows that the aperture change is consistent with the permeability evolution during loading, which is more complicated at a higher hydrostatic stress value. The roughness of the fractured surface was also analyzed and will be discussed in combination with the permeability evolution.

Dynamic Fracture Test of Laurentian Granite Subjected to Hydrostatic Pressure

Abstract: Dynamic fracture failure of rocks subjected to static hydrostatic pressure is commonly encountered in deep underground rock engineering. The static fracture behavior of rocks under hydrostatic stress has been well studied in the literature. However, it is desirable to investigate the dynamic fracture failure of rocks under various hydrostatic pressures. In this study, a triaxial split Hopkinson pressure bar (SHPB) system is used to measure the dynamic fracture toughness of rocks under five hydrostatic pressures. The results show that dynamic fracture toughness under a certain hydrostatic pressure enhances with the increase of the loading rate, and the dynamic fracture toughness at the similar loading rate increases with the hydrostatic pressure due to the closure of microcracks in rocks. An empirical formula is proposed to describe the influences of the loading rate and the hydrostatic pressure on the rock dynamic fracture toughness.

Influence of stress and high-temperature treatment on the permeability evolution behavior of sandstone

Abstract: Permeability is an important property of rock in gas and oil exploration engineering; environmental temperature and geo-stress have great influence on it. This paper aims to analyze the influence of thermal treatment on the permeability of sandstone under triaxial compression. Based on the gas seepage tests on a sandstone specimen after different thermal treatment temperatures with different gas pressures, hydrostatic stresses and deviatoric stresses, the thermal effect on the physical properties of sandstone is firstly analyzed. The results show that the mass of the sandstone specimen decreases with the increase of temperature; some spalling damage and tensile cracks occur on the lateral surface of the specimen at 400 °C. According to the seepage test results with various gas pressures, an exponential relationship has been found between the permeability coefficient and temperature. The permeability coefficient is approximately 100 times as large as the initial value when the temperature increases from 20 °C to 800 °C. The permeability evolution of the heated sandstone under hydrostatic and deviatoric compression has also been analyzed. A simplified double-pore texture model is proposed which can describe well the permeability evolution of sandstone under compression with hydrostatic stress and deviatoric stress, and it can be helpful to estimate the permeability of thermally treated sandstone under elastic triaxial compression.

General coupling model for electromigration and one-dimensional numerical solutions

Abstract: A three-dimensional (3D) general coupling model for electromigration has been developed with the use of the mass conservation equation. The flux terms that include concentration gradient, electron wind force, stress migration, and thermal migration are considered. The constitutive equation for the electromigration strain has been derived. Then, the governing equations for one-dimensional (1D) metal lines are obtained for both totally fixed and stress-free mechanical boundary conditions. The numerical results reveal that the hydrostatic stress is significantly lower than the predicted results in the existing literature for the totally fixed configuration. Extensive discussions are presented to provide the explanations of such difference. The vacancy concentration gradient plays an important role in formulating electromigration problems. The current-driven flux can be entirely balanced by the concentration gradient that acts as an opposing force during electromigration under a stress-free condition in steady-state. The new solutions of the critical threshold jL, the product of current density, and metal line length are obtained in terms of vacancy concentration. As electromigration is eventually determined by the void growth, the critical vacancy concentration is used to reanalyze Blech's experiment data. The theoretical predictions are consistent with the experimental observations.A three-dimensional (3D) general coupling model for electromigration has been developed with the use of the mass conservation equation. The flux terms that include concentration gradient, electron wind force, stress migration, and thermal migration are considered. The constitutive equation for the electromigration strain has been derived. Then, the governing equations for one-dimensional (1D) metal lines are obtained for both totally fixed and stress-free mechanical boundary conditions. The numerical results reveal that the hydrostatic stress is significantly lower than the predicted results in the existing literature for the totally fixed configuration. Extensive discussions are presented to provide the explanations of such difference. The vacancy concentration gradient plays an important role in formulating electromigration problems. The current-driven flux can be entirely balanced by the concentration gradient that acts as an opposing force during electromigration under a stress-free condition in stead...

On the effect of hydrostatic stress on plastic deformation in metallic glasses

Abstract: Previous experimental observations have demonstrated that large stress gradient results in high plasticity, while the underlying mechanism and constitutive laws are rarely reported. In this work, a micro-mechanics based model was proposed to account for the contribution made by hydrostatic stress. This micro-mechanics model was then incorporated into the free volume model describing the viscous softening behavior and a generalized constitutive law was established. Using a user material subroutine (UMAT) and von-Mises criterion, the new constitutive equations were implemented into a finite element code to simulate the material response and free volume evolution procedure under tensile and compressive loading when hydrostatic stress was taken into account. Furthermore, comparison was made between current simulation and previous theoretical or experimental results, good agreement was successfully obtained. Therefore, it is concluded that the current constitutive law is a good candidate for describing the deformation behavior of metallic glass under complex stress states.

Effect of dynamic adjustment of diamond tools on nano-cutting behavior of single-crystal silicon

Abstract: A new method for adjusting the tool rake and flank angles by changing the position of the tools was used to dynamic explore the nano-cutting behavior of single-crystal silicon using MD simulation. Simulations under the same cutting conditions were carried out using a tool swinging to six different rake angles of − 10°, − 15°, − 20°, − 25°, − 30°, − 35°, and − 45°. The advantages of Tersoff potential function are discussed in comparison with those of using SW potential function. The coordination number, von Mises stress, hydrostatic stress, system temperature, potential energy and cutting force during the nano-cutting process are studied. The results of a statistical study reveal that the coordination numbers of silicon atoms showed a minimum value and the highest average hydrostatic stress at − 25° adjustment angle. Besides, the maximum system potential energy and temperature is also obtained at an adjustment angle of − 25° after − 20° (it can be defined as a larger adjustment angle after − 15°). In addition, the results also point out that the highest average tangential force was observed at − 25°, which is different from the previous researches.

Chemo-thermo-mechanically Coupled Crystal Plasticity Simulation of Stress Evolution in Thermally Strained β-Sn Films

Abstract: Whisker formation in tin films is a mode of stress relaxation, but the exact conditions causing them are yet to be established. In this work, a three-dimensional full-field chemo-thermo-mechanically coupled crystal plasticity simulation of thermally strained tin films was performed to evaluate the stress evolution and connect it to the redistribution of vacancies. Spatial heterogeneity in the hydrostatic stress along the grain boundary network (that served as the primary conduit for mass transport) was observed, which became more homogeneous towards the film surface. Normal and shear tractions on the columnar grain boundaries were evaluated as they might be crucial to breaking of the oxide layer (formed on the film surface) especially when inclined grain boundaries are present. With such an advanced multi-physics framework, several crystallographic and geometrical factors influencing whisker formation can be analyzed thereby leading to a better understanding of the factors modulating the nucleation and growth of such whiskers.

Quantification of Temperature Dependence of Hydrogen Embrittlement in Pipeline Steel.

Abstract: The effects of temperature on bulk hydrogen concentration and diffusion have been tested with the Devanathan–-Stachurski method. Thus, a model based on hydrogen potential, diffusivity, loading frequency, and hydrostatic stress distribution around crack tips was applied in order to quantify the temperature’s effect. The theoretical model was verified experimentally and confirmed a temperature threshold of 320 K to maximize the crack growth. The model suggests a nanoscale embrittlement mechanism, which is generated by hydrogen atom delivery to the crack tip under fatigue loading, and rationalized the ΔK dependence of traditional models. Hence, this work could be applied to optimize operations that will prolong the life of the pipeline.

Prediction of fatigue life to crack initiation in unidirectional plies containing voids

Abstract: In the present work, a model is proposed to predict the life to crack initiation in porous unidirectional composite plies subjected to tensile fatigue loadings. The average values of the Local Maximum Principal Stress (LMPS) and Local Hydrostatic Stress (LHS) in a control volume of the matrix are proposed to be the driving forces to the initiation of fatigue cracks in off-axis plies. The experimental fatigue curves for the life to crack initiation of laminates characterised by different void contents are found to fall in the same scatter band once plotted in terms of the proposed driving forces, thus proving the capability of the proposed model to predict the life to crack initiation in porous laminates based on the behaviour of the void-free material. Finally, a parametric analysis is carried out to study the influence of the global void content and average void size on the reduction of the life to crack initiation and the applicability of the proposed model to different void distributions and shapes is discussed.

Embrittlement of an elasto-plastic medium by an inclusion

Abstract: A mathematical model for the embrittlement of a long elastic-plastic crack by a relatively small, misfitting inclusion is presented. The model makes direct contact with the Dugdale–Bilby–Cottrell–Swinden model as a limiting case. The particular case of an oxide inclusion with a triangular cross-section at the tip of an intergranular crack in the Ni-based superalloy RR1000 at $$650\,^{\circ }\hbox {C}$$ is considered. The positive misfit of the intrusion provides an additional tensile load on the crack tip and on the plastic zone, raising the local stress intensity factor $$k_I$$ and the crack tip opening displacement $${\varDelta } u$$ above those when the inclusion is replaced by a dislocation-free zone of the same length. It is shown that for a given misfit strain and inclusion shape, the enhancement of $$k_I$$ and $${\varDelta } u$$ is controlled by a dimensionless parameter $$\omega = (\sigma /\sigma _1)\sqrt{c/(2l)}$$ where $$\sigma $$ is the applied stress, $$\sigma _1$$ is the yield stress, c is the crack length and l is the length of the inclusion. The anti-shielding effect of the intrusion is significant only when $$\omega \lesssim 6$$ . As a result of the anti-shielding effect of the intrusion, the stress singularity at the crack tip always exceeds the compressive normal stress that exists within the thickest part of the intrusion when it is isolated. It is also shown that the gradient of the hydrostatic stress within the intrusion subjected to different applied stresses drives the oxygen diffusion and, hence, assists the oxidation at the grain boundary. The fracture toughness is considerably greater than that of a bulk sample of the oxide particle, which we attribute to the plastic zone.

Effect of stress-dependent activation enthalpy on electrochemical reaction and diffusion-reaction-induced stress in spherical electrodes

Abstract: Effect of chemical reaction on Li-ions diffusion and diffusion-reaction-induced stresses in a spherical electrode is studied, considering the reaction rate determined by the relation between hydrostatic stress and activation enthalpy, to derive new diffusion equation. The coupling equations of diffusion and mechanics are developed to obtain numerical simulation results of Li-ion concentration and diffusion-reaction-induced stress under galvanostatic operation during lithiation. Results indicate that chemical reaction can slow down the diffusion process and lead to the increase of radial stress and hoop stress, which is enhanced as the reaction rate constant increases. The effect of hydrostatic stress in activation enthalpy can change the reaction rate, resulting in distribution difference of the Li-ion and reaction product concentration and the decline of the radial and hoop stress.

Rock strength criterion considering the effect of hydrostatic stress on lode angle effect

Abstract: 1State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, China 2State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, China 3Deep Earth Energy Research Laboratory, Department of Civil Engineering, Monash University, Melbourne, Victoria, Australia 4Department of Civil and Mineral Engineering, University of Toronto, Toronto, Ontario, Canada

Modelling and analysis of the oxide growth coupling behaviour of thermal barrier coatings

Abstract: A chemo-transport-mechanics model is developed to study the growth of thermally grown oxide (TGO) and its impact on deformation and stress in air plasma-sprayed thermal barrier coatings (TBCs). As the driving force for oxygen transport, the chemical potential consists of contributions from both species concentration and hydrostatic pressure. The model suggests that both the concentration boundary condition and the transport process of the oxygen are affected by hydrostatic stress. Since oxygen has smaller diffusion coefficient in TGO than in BC, the retarding effect of the formed TGO on oxygen transport is considered and clarified by the coupled model. The competition between geometrical imperfection (i.e. concave morphology) and the chemo-mechanics coupling to influence the transport of oxygen is also identified numerically. The geometrical imperfection can introduce additional oxygen transport at the margin of the concave imperfection due to the horizontal component of the gradient of the chemical potential of the oxygen, which plays a dominant role in the TGO growth kinetics for the studied TBCs. Consequently, there is a limited effect of the chemo-mechanics coupling on the growth kinetics of a concaved TGO. The amplitude change of the concave portion is found to be up to 0.36 µm after 600-h exposure at 1150 °C, which leads to large tensile stress above the concave portion potentially causing micro-cracks.

Correlations among atomic mobility, microstructure and local stress of shear bands and necking regions in notched Cu50Zr50 metallic glasses

Abstract: The atomic mobility, microstructure, and local stress in the shear bands and necking regions of notched Cu50Zr50 metallic glasses are compared, and the intricate interplay among them is examined via molecular dynamics simulations. The virtual tensile tests show that the average atomic mobility inside the mature shear band is lower than that in the necked region, which is controlled by the corresponding atomic-level structure. The short-range topological orders revealed by the Voronoi tessellation of both the necked region and the shear band are, however, quite similar to each other, while the excess free volume of the former is significantly higher than that of the latter. This high free volume content contributes to the migration of atoms or clusters and, thus, expedites the local plastic deformation. Further investigations suggest that the free volume content correlates closely with the local hydrostatic stress, while the topological microstructure is rather insensitive to the hydrostatic stress, especially when the hydrostatic stress is low. In addition, it is also found that the atomic mobility of the central atom in a cluster correlates not only with the local packing environment, such as the free volume content or the hydrostatic stress, but also with the geometry of the cluster, such as its symmetry or coordination number. The findings are helpful in developing/selecting the constitutive models for the deformation of metallic glasses.

Predicting embrittlement of polymer glasses using a hydrostatic stress criterion

Abstract: In this study, the aging-induced embrittlement of three polymer glasses is investigated using a previously developed hybrid experimental–numerical method. The evolution of yield stress of unnotched tensile bars upon aging is coupled to the evolution of embrittlement of notched tensile bars using a numerical model combined with a critical hydrostatic stress criterion that determines the onset of failure. The time-to-embrittlement of notched tensile bars with a different notch geometry is predicted and in good agreement with the experimentally determined value. Next to that, the approach is extended to three polysulfone polymers, and it is shown that the value of the critical hydrostatic stress correlates well with the polymers entanglement density: : polymers with a denser entangled network display higher values, that is, a higher resistance against incipient cavitation.