Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Laboratory insights into the effects of methane hydrate on the anisotropic joint elastic-electrical properties in fractured sandstones

Fractured hydrate-bearing reservoirs show significantly anisotropic geophysical properties. The joint application of seismic and electromagnetic explorations is expected to accurately assess hydrate resources in the fractured reservoirs. However, the anisotropic joint elastic-electrical properties in such reservoirs that are the key to the successful application of the joint explorations, remain poorly understood. To obtain such knowledge, we designed and implemented dedicated laboratory experiments to study the anisotropic joint elastic-electrical properties in fractured artificial silica sandstones (with fracture density of about 6.2%, porosity of approximately 25.7%, and mean grainsize of 0.089 mm) with evolving methane hydrate. The experimental results showed that the anisotropic compressional wave velocities respectively increased and decreased with the forming and dissociating hydrate, and the variation in the increasing trend and the decreasing extent of the velocity perpendicular to the fractures were more significant than that parallel to the fractures, respectively. The experimental results also showed that the overall decreasing trend of the electrical conductivity parallel to the fractures was steeper than that perpendicular to the fractures during hydrate formation, and the general variations of the two conductivities with complex trend were similar during hydrate dissociation. The variations in the elastic and electrical anisotropic parameters with forming and dissociating hydrate were also found to be distinct. Interpretation of the experimental results suggested that the hydrate binding to the grains evolved to bridge the surfaces of fractures when saturation exceeded 10% during hydrate formation, and the bridging hydrate gradually evolved to floating in fractures during dissociation. The experimental results further showed that the anisotropic velocities and electrical conductivities were correlated with approximately consistent trends of different slopes during hydrate formation, and the joint elastic-electrical anisotropic parameters exhibited a sharp peak at the hydrate saturation of about 10%. The results suggested that the anisotropic joint properties can be employed not only to accurately estimate hydrate saturation but also possibly to identify hydrate distribution in the fractures.

Low-frequency laboratory measurements of the elastic properties of solids using a distributed acoustic sensing system

In recent decades,low-frequency(LF)experiments based on the forced-oscillation(FO)method have become common practice in many rock physics laboratories for measuring the elastic and anelastic properties of rocks.However,the use of the electronic displacement sensors in traditional acquisition systems of FO devices such as conventional capacitive transducers or strain gauges seriously limits both the efficiency and productivity of LF measurements,and,due to the limited contact area of the displacement sensors with a sample under test,increases the requirements for sample homogeneity.In this paper,we present the first results obtained in the development of a new laboratory method elaborated to measure the elastic properties of solids.The method is a further development of the FO method where traditional data acquisition is replaced by acquisition based on fiber-optic distributed acoustic sensing(DAS)technology.The new method was tested in a laboratory study using two FO setups designed for measurements under uniaxial and confining pressures.The study was carried out on a sample made from polymethyl methacrylate(PMMA)and an aluminium standard,first under uniaxial pressure at FO frequencies of 1,10,30,60 and 100 Hz,and then under confining pressure at an FO frequency of 1 Hz.Both uniaxial and confining pressures were equal to 10 MPa,and the strain in the PMMA sample in all measurements did not exceed 4×10^(-8).The performance of DAS acquisition was compared with the measurements conducted at a strain of 1×10^(-6) using the traditional FO method based on the use of semiconductor strain gauges and the ultrasonic method.The results of the DAS measurements are in good agreement with the FO measurements carried out using semiconductor strain gauges and with the literature data.

Investigation of Electronic, Elastic and Dynamic Properties of AgNbO3 and AgTaO3 under Pressure: Ab Initio Calculation

Based on the density functional theory within the local density approximation (LDA), we studied the electronic, elastic, and dynamic properties of AgNbO3 and AgTaO3 compounds under pressure. The elastic constants, optic and static dielectric constants, born effective charges, and dynamic properties of AgNbO3 and AgTaO3 in cubic phase were studied as pressure dependences with the ab initio method. For these compounds, we have also calculated the bulk modulus, Young’s modulus, shear modulus, Vickers hardness, Poisson’s ratio, anisotropy factor, sound velocities, and Debye temperature from the obtained elastic constants. In addition, the brittleness and ductility properties of these compounds were estimated from Poisson’s ratio and Pugh’s rule (G/B). Our calculated values also show that AgNbO3 (0.37) and AgTaO3 (0.39) behave as ductile materials and steer away from brittleness by increasing pressure. The calculated values of Vicker hardness for both compounds indicate that they are soft materials. The results show that band gaps, elastic constants, elastic modules, and dynamic properties for both compounds are sensitive to pressure changes. We have also made some comparisons with related experimental and theoretical data that is available in the literature.

First principles investigation of binary intermetallics in Mg-Al-Ca-Sn alloy:Stability,electronic structures,elastic properties and thermodynamic properties

The structural stability, electronic structures, elastic properties and thermodynamic properties of the main binary phases Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca in Mg-Al-Ca-Sn alloy were determined from the first-principles calculation. The calculated lattice parameters are in good agreement with the experimental and literature values. The calculated heats of formation and cohesive energies show that Al_2Ca has the strongest alloying ability and structural stability. The densities of states（DOS）, Mulliken electron occupation number, metallicity and charge density difference of these compounds are given. The elastic constants of Mg_（17）Al_（12）, Al_2Ca, Mg_2 Sn and Mg_2 Ca phases are calculated, and the bulk moduli, shear moduli, elastic moduli and Poisson ratio are derived. The calculations of thermodynamic properties show that the Gibbs free energies of Al_2Ca and Mg_2 Sn are lower than that of Mg_（17）Al_（12）, which indicates that Al_2Ca and Mg_2 Sn are more stable than Mg_（17）Al_（12） phase. Hence, the heat resistance of Mg-Al-based alloys can be improved by adding Ca and Sn additions.

Computation of elastic properties of 3D digital cores from the Longmaxi shale

The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Longmaxi black shale samples using X-ray CT, we built detailed 3D digital images of cores with porosity properties and mineral contents. Next, we used finite-element （FE） methods to derive the elastic properties of the samples. The FE method can accurately model the shale mineralogy. Particular attention is paid to the derived elastic properties and their dependence on porosity and kerogen. The elastic moduli generally decrease with increasing porosity and kerogen, and there is a critical porosity （0.75） and kerogen content （ca. ≤3%） over which the elastic moduli decrease rapidly and slowly, respectively. The derived elastic moduli of gas- and oil-saturated digital cores differ little probably because of the low porosity （4.5%） of the Longmaxi black shale. Clearly, the numerical experiments demonstrated the feasibility of combining microstructure images of shale samples with elastic moduli calculations to predict shale properties.

A first-principles study on elastic properties and stability of Ti_xV_(1-x)C multiple carbide

The structure,stability and elastic properties of di-transition-metal carbides TixV1-xC were investigated by using the first-principles with a pseudopotential plane-waves method.The results show that the equilibrium lattice constants of TixV1-xC show a nearly linear reduction with increasing addition of V.The elastic properties of TixV1-xC are varied by doping with V.The bulk modulus of Ti0.5V0.5C is larger than that of pure TiC,as well as Ti0.5V0.5C has the largest C44 among TixV1-xC（0≤x≤1）,indicating that Ti0.5V0.5C has higher hardness than pure TiC.However,Ti0.5V0.5C presents brittleness based on the analysis of ductile/brittle behavior.The Ti0.5V0.5C carbide has the lowest formation energy,indicating that Ti0.5V0.5C is more stable than all other alloys.

Elastic and thermodynamic properties of Re_2N at high pressure and high temperature

First principles calculations are preformed to systematically investigate the elastic and thermodynamic properties of Re2N at high pressure and high temperature. The Re2N exhibits a clear elastic anisotropy and the elastic constants C11 and C33 vary rapidly in comparison with the variations in C12, C13 and C44 at high pressure. In addition, bulk modulus B, elastic modulus E, and shear modulus Gas a function of crystal orientations for Re2N are also investigated for the first time. The tensile directional dependences of the elastic modulus obey the following trend： [0001] [1211] [1010] [1011]EEEE〉〉〉 . The shear moduli of Re2N within the （0001） basal plane are the smallest and greatly reduce the resistance of against large shear deformations. Based on the quasi-harmonic Debye model, the dependences of Debye temperature, Grüneisen parameter, heat capacity and thermal expansion coefficient on the temperature and pressure are explored in the whole pressure range from 0 to 50 GPa and temperature range from 0 to 1600 K.

A first-principles study on electronic structure and elastic properties of Al_4Sr, Mg_2Sr and Mg_(23)Sr_6 phases

The electronic structures and mechanical properties of Al4Sr, Mg2Sr and Mg23Sr6 phases were determined by the use of first-principles calculations. The calculated heat of formation and cohesive energy indicate that Al4Sr has the strongest alloying ability as well as the highest structural stability. The elastic parameters were calculated, and then the bulk modulus, shear modulus, elastic modulus and Poisson ratio were derived. The ductility and plasticity were discussed. The results show that Al4Sr and Mg2Sr phases both are ductile, on the contrary, Mg23Sr6 is brittle, and among the three phases, Mg2Sr is a phase with the best plasticity.

Biaxial tensile properties and elastic constants evaluation of envelope material for airship

This paper presents an experimental study to determine the tensile properties of the envelope fabric Uretek3216L under biaxial cyclic loading.First the biaxial cyclic tests were carefully carried out on the envelope material to obtain the stress-strain data and the corresponding nonlinearity and orthotropy of the material were analyzed. Then for some determination options with different stress ratios the least squares method minimizing the strain terms was used to calculate the elastic constants from the experimental data.Finally the influences of the determination options with different stress ratios and the reciprocal relationship on the elastic constants were discussed.Results show that the orthotropy of the envelope material can be attributed to the unbalanced crimp of their constitutive yarns in warp and weft directions and the elastic constants vary noticeably with the determination options as well as the normalized stress ratios.In real design practice it is more reasonable to use constants determined for specific stress states in particular stress ratios depending on the project＆#39;s needs.Also calculating the structures with two limitative sets of elastic constants instead of using only one set is recommendable in light of the great variety of the constant＆#39;s values.

Elastic Tensor and Thermodynamic Property of Magnesium Silicate Perovskite from First-principles Calculations

The thermodynamic and elastic properties of magnesium silicate （MgSiO3） perovskite at high pressure are investigated with the quasi-harmonic Debye model and the first-principles method based on the density functional theory. The obtained equation of state is consistent with the available experimental data. The heat capacity and the thermal expansion coefficient agree with the observed values and other calculations at high pressures and temperatures. The elastic constants are calculated using the finite strain method. A complete elastic tensor of MgSiO3 perovskite is determined in the wide pressure range. The geologically important quantities： Young＇s modulus, Poisson＇s ratio, Debye temperature, and crystal anisotropy, are derived from the calculated data.

First principles study of electronic structure, chemical bonding and elastic properties of BiOCuS

The electronic structures, chemical bonding and elastic properties of the tetragonal phase BiOCuS were investigated by using density-functional theory （DFT） within generalized gradient approximation （GGA）. The calculated energy band structures show that the tetragonal phase BiOCuS is an indirect semiconductor with the calculated band gap of about 0.503 eV. The density of states （DOS） and the partial density of states （PDOS） calculations show that the DOS near the Fermi level is mainly from the Cu-3d state. Population analysis suggests that the chemical bonding in BiOCuS has predominantly ionic character with mixed covalent-ionic character. Basic physical properties, such as lattice constant, bulk modulus, shear modulus, elastic constants, were calculated. The elastic modulus and Poisson ratio were also predicted. The results show that tetragonal phase BiOCuS is mechanically stable and behaves in a ductile manner.

First principles calculation of electronic structure, chemical bonding and elastic properties of ultra-incompressible Re_2P

The electronic structures, chemical bonding and elastic properties of the Co2P-type structure phase ultra-incompressible Re2P （orthorhombic phase） were investigated by density-functional theory （DFT） within generalized gradient approximation （GGA）. The calculated energy band structures show that the orthorhombic structure phase Re2P is metallic material. The density of state （DOS） and the partial density of state （PDOS） calculations show that the DOS near the Fermi level is mainly from the Re-5d state. Population analysis suggests that the chemical bonding in Re2P has predominantly covalent character with mixed covalent-ionic character. Basic physical properties, such as lattice constant, bulk modulus, shear modulus, and elastic constants Cij, were calculated. The elastic modulus and Poisson ratio were also predicted. The results show that the Co2P-type structure phase Re2P is mechanically stable and behaves in a brittle manner.

Study on structural stability,elastic and electronic properties for β-Ti under pressure based on first principles

The structural stability, elastic and electronic properties under pressure at 0 K for β-Ti have been investigated by per-forming first-principles calculations. With the increase of pressure, the structure of β-Ti becomes stabler, which is further con-firmed by the calculation for density of state （DOS）. The phase transition pressure of is about 64. 3 GPa, which is consist-ent with other theoretical predictions （63. 7 GPa） and the experimental result （50 GPa）. The pressure dependence of elastic constants shows that the low-pressure limit for a mechanically stable β-Ti is about 50 GPa with low Young？s modulus value of about 30. 01 GPa, which approaches the value of a human bone （30 GPa）. In addition, the pressure dependence of bulk modu-lus B, shear modulus G, Young’s modulus E,Poisson’s ratio σ,aggregate sound velocities,and ductility/brittleness under different pressures were also discussed. B, G and E ascend monotonously with increasing pressure, while a descends. β-Ti re-mains ductile by analysis of B/G under considered pressures.

Chemical bonding and elastic properties of quaternary arsenide oxides YZnAsO and LaZnAsO investigated by first principles

The structural parameters, chemical bonding and elastic properties of the tetragonal phase quaternary arsenide oxides YZnAsO and LaZnAsO were investigated by using density-functional theory （DFT） within generalized gradient approximation （GGA）. The GGA calculated structural parameters are in agreement with the experimental results. Population analysis suggests that the chemical bonding in YZnAsO and LaZnAsO can be classified as a mixture of ionic and covalent characteristic. Single-crystal elastic constants were calculated and the polycrystalline elastic modules were estimated according to Voigt, Reuss and Hill＇s approximations （VRH）. The result shows that both YZnAsO and LaZnAsO are relatively soft materials exhibiting ductile behavior. The calculated polycrystalline elastic anisotropy result shows that LaZnAsO is more anisotropy in compressibility and YZnAsO is more anisotropy in shear.

First-principles calculation of structural and elastic properties of Pd_(3-x)Rh_xV alloys

The structural stability, electronic and elastic properties of Pd3-xRhxV alloys with L12 and D022 structures were investigated theoretically by the first-principles calculations. The results reveal that with the increase of Rh content, the unit cell volume of Pd3-xRhxV alloys with L12 and D022 structures decreases, and the structure of Pd3-xRhxV alloys tends to transform from D022 to L12. The elastic parameters such as elastic constants, bulk modulus, shear modulus, elastic modulus, and Poisson ratio, were calculated and discussed in details. Electronic structures were also computed to reveal the underlying mechanism for the stability and elastic properties.

Phase transition, elastic and electronic properties of topological insulator Sb_2Te_3 under pressure: First principle study

The phase transition, elastic and electronic properties of three phases（phase Ⅰ,Ⅱ, and Ⅲ） of Sb_2Te_3 are investigated by using the generalized gradient approximation（GGA） with the PBESOL exchange–correlation functional in the framework of density-functional theory. Some basic physical parameters, such as lattice constants, bulk modulus, shear modulus,Young＇s modulus, Poisson＇s ratio, acoustic velocity, and Debye temperature Θ are calculated. The obtained lattice parameters under various pressures are consistent with experimental data. Phase transition pressures are 9.4 GPa（Ⅰ→Ⅱ） and 14.1 GPa（Ⅱ→Ⅲ）, which are in agreement with the experimental results. According to calculated elastic constants, we also discuss the ductile or brittle characters and elastic anisotropies of three phases. Phases Ⅰ and Ⅲ are brittle, while phaseⅡ is ductile. Of the three phases, phaseⅡ has the most serious degree of elastic anisotropy and phase Ⅲ has the slightest one.Finally, we investigate the partial densities of states（PDOSs） of three phases and find that the three phases possess some covalent features.

Electronic structures and elastic properties of monolayer and bilayer transition metal dichalcogenides MX_2(M= Mo,W;X= O,S,Se,Te):A comparative first-principles study

First-principle calculations with different exchange-correlation functionals, including LDA, PBE, and vd W-DF functional in the form of opt B88-vd W, have been performed to investigate the electronic and elastic properties of twodimensional transition metal dichalcogenides（TMDCs） with the formula of MX2（M = Mo, W; X = O, S, Se, Te） in both monolayer and bilayer structures. The calculated band structures show a direct band gap for monolayer TMDCs at the K point except for MoO2 and WO2. When the monolayers are stacked into a bilayer, the reduced indirect band gaps are found except for bilayer WTe2, in which the direct gap is still present at the K point. The calculated in-plane Young moduli are comparable to that of graphene, which promises possible application of TMDCs in future flexible and stretchable electronic devices. We also evaluated the performance of different functionals including LDA, PBE, and opt B88-vd W in describing elastic moduli of TMDCs and found that LDA seems to be the most qualified method. Moreover, our calculations suggest that the Young moduli for bilayers are insensitive to stacking orders and the mechanical coupling between monolayers seems to be negligible.

Thermodynamics and elastic properties of Ta from first-principles calculations

Within the framework of the quasiharmonic approximation, the thermodynamics and elastic properties of Ta, including phonon density of states （DOS）, equation of state, linear thermal expansion coefficient, entropy, enthalpy, heat capacity, elastic constants, bulk modulus, shear modulus, Young＇s modulus, microhardness, and sound velocity, are studied using the first-principles projector-augmented wave method. The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon DOS and the Debye model. The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic DOS. By comparing the experimental results with the calculation results from the first-principles and the Debye model, it is found that the thermodynamic properties of Ta are depicted well by the first-principles. The elastic properties of Ta from the first-principles are consistent with the available experimental data.

Phase stability,elastic properties and electronic structures of Mg-Y intermetallics from first-principles calculations

The phase stability,elastic properties and electronic structures of three typical Mg-Y intermetallics including Mg_(24)Y_(5),Mg_(2)Y and MgY are systematically investigated using first-principles calculations based on density functional theory.The optimized structural parameters including lattice constants and atomic coordinates are in good agreement with experimental values.The calculated cohesive energies and formation enthalpies show that either phase stability or alloying ability of the three intermetallics is gradually enhanced with increasing Y content.The single-crystal elastic constants C_(ij) of Mg-Y intermetallics are also calculated,and the bulk modulus B,shear modulus G,Young's modulus E,Poisson ratio v and anisotropy factor A of polycrystalline materials are derived.It is suggested that the resistances to volume and shear deformation as well as the stiffness of the three intermetallics are raised with increasing Y content.Besides,these intermetallics all exhibit ductile characteristics,and they are isotropic in compression but anisotropic to a certain degree in shear and stiffness.Comparatively,Mg_(24)Y_(5) presents a relatively higher ductility,while MgY has a relatively stronger anisotropy in shear and stiffness.Further analysis of electronic structures indicates that the phase stability of Mg-Y intermetallics is closely related with their bonding electrons numbers below Fermi level.Namely,the more bonding electrons number below Fermi level corresponds to the higher structural stability of Mg-Y intermetallics.