Stress-strain Method Research Articles

Elastic and optoelectronic properties of CaTa2O6 compounds: Cubic and orthorhombic phases

Using first principles density functional theory (DFT) simulations, the structural, electronic, optical and elastic properties of CaTa2O6 oxide for cubic and orthorhombic phases are studied by highly accurate (FP-LAPW) method within the GGA + U approximation. The calculated lattice parameters are consistent with available experimental data. The electronic band structure calculations have shown that the band gaps in CaTa2O6 are equal to 3.08 eV and 4.40 eV for the cubic and orthorhombic structures, respectively. For both the phases the main optical properties, e.g., absorption coefficient, dielectric constant, energy loss function, reflectivity are calculated and discussed in detail in the spectral range 0–14 eV. Cubic and orthorhombic phases exhibit significantly different optical characteristics. The electronic bonding characters of CaTa2O6 with different symmetries are explored via charge density distribution mapping. Strong covalent bonding character dominates in both the phases of CaTa2O6. Elastic properties of CaTa2O6 for cubic and orthorhombic phases are also investigated. The stress strain method is used for the determination of elastic constants in both the phases. The bulk modulus, shear modulus, Young's modulus, along with the important elastic anisotropy factors and Poisson's ratio are studied in detail.

First-principles study of structural, elastic, electronic, vibrational and thermodynamic properties of uranium aluminides

The structural, elastic, electronic, vibrational and thermodynamic properties of uranium aluminides UAlx (x = 2, 3, 4) were studied by density functional theory calculations. The single crystal elastic constants of UAlx were predicted using the stress-strain method, which were further used to calculate the polycrystalline aggregate properties of UAlx, including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio, etc. The calculated electronic density of states confirm that UAlx compounds are metallic phases with majority states at the Fermi level contributed by U 5f electrons. The phonon dispersion relations and density of states show that the low frequency acoustic phonon modes of UAlx are dominated by the lattice vibration of uranium atoms while high frequency optical phonon modes are from the vibration of aluminum atoms. Using quasiharmonic approximation, thermodynamic properties of UAlx, including Gibbs free energy, entropy, heat capacity, and linear thermal expansion coefficient, were predicted by including both lattice vibrational and thermal electronic contributions. The thermal electronic energy was found to be crucial for the description of the temperature dependence of the thermodynamic properties. The derived Gibbs energy functions of UAlx are expected to be useful to the thermodynamic modeling of the ternary U-Mo-Al system.

Unobvious elastic anisotropy of measured single–crystal cementite

Electron backscattered diffraction and nanoindentation measurements are used to investigate the elastic anisotropy of single–crystal cementite in cast iron. The measured orientations of single–crystal cementite are mostly low–index crystal directions, and the values of Young’s modulus are at about 210–270 GPa, with less obvious anisotropy. These findings are compared with results of first–principle calculations by using energy–strain and stress–strain methods. A deviation is found between measured and calculated Young’s moduli, and the elastic anisotropy calculated by first–principle calculations is more obvious than the measured one. The crystal defect of experimental cementite leads to reduced elastic anisotropy.

Theoretical research on structural, electronic, mechanical, lattice dynamical and thermodynamic properties of layered ternary nitrides Ti2AN (A = Si, Ge and Sn)

Abstract First-principles density functional theory (DFT) calculations within generalized gradient approximation (GGA) are carried out to investigate the structural, electronic, mechanical, lattice dynamical and thermodynamic properties of Ti 2 AN (A = Si, Ge and Sn) MAX phases. The optimized geometrical parameters such as lattice constants ( a , c ) and the internal coordinates have been calculated. Electronic band structure and corresponding density of states (DOS) have been obtained. The analysis of the band structures and density of states have shown that these compounds are electrical conductors. The elastic constants have been ascertained using the stress-strain method. The isotropic elastic moduli, known as bulk modulus ( B ), shear modulus ( G ), young's modulus ( E ), poisson's ratio ( ν ), vickers hardness ( H v ) and linear compressibility coefficients ( α ) have been studied within framework of the Voigt–Reuss–Hill approximation for ideal polycrystalline Ti 2 AN (A = Si, Ge and Sn) MAX aggregates. Furthermore, the phonon dispersion curves as well as accompanying phonon density of states have been comprehensively computed. And also raman and infrared modes at the Γ point have been obtained. Within the thermodynamic properties, specific heat capacity, entropy, helmholtz free energy and internal energy changes were analyzed depending on the temperature of Ti 2 AN (A = Si, Ge and Sn) compounds. The obtained results are presented in comparison with present theoretical data for Ti 2 SiN. This is the first quantitative theoretical study of the electronic properties and other properties for Ti 2 GeN and Ti 2 SnN compounds and therefore theoretical results for these compounds need to be verified experimentally.

Specific features of structural, electronic, optical and elastic properties of the cubic calcium pyroniobate Ca2Nb2O7 crystals

Using first principles density functional theory (DFT) calculation, the structural, electronic, optical and elastic properties of cubic Ca2Nb2O7 pyrochlore oxide is studied by highly accurate full potential augmented plane wave method with GGA+U approximation. The calculated lattice parameter is in good agreement with available experimental data. The electronic band structure calculations reveal that Ca2Nb2O7 has direct energy band. For the understanding of optical properties of Ca2Nb2O7, absorption coefficient, dielectric constant, energy loss function, reflectivity, refractive index, extension coefficient and optical conductivity are also calculated for 0–12 eV. A study of elastic properties for cubic pyrochlore oxide (Ca2Nb2O7) is also conducted within a frameowork of DFT calculations. The stress strain method is used for the determination of elastic constants (C11, C12 and C44) in cubic phase. Hence, bulk, shear and Young's modulus along with Debye temperature, elastic anisotropy factors and Poisson's ratio are calculated successfully. Furthermore, pressure dependence of transverse and longitudinal wave velocities for cubic pyrochlore oxide (Ca2Nb2O7) are also calculated for the first time.

An enhanced broad-frequency-band apparatus for dynamic measurement of elastic moduli and Poisson's ratio of rock samples.

We built a broad-frequency-band measurement system for rock elastic parameters based on the stress-strain method following Batzle et al., Geophysics 71, N1-N9 (2006). The system gives strain amplitude anomalies at some measurement frequencies. These anomalies put limitations on the range of the measurement frequency and jeopardize the credibility of the measurement results over a broad frequency band. To overcome these limitations, we investigated the cause of these anomalous strains by numerical model simulations with a finite element method based on the experimental apparatus. Through the systematic analysis of the modeling results, we conclude that the resonances caused by non-axial perturbations lead to such anomalous measurement results. Based on the analysis, we give a solution to reduce the effect of the resonances and shift the first resonance frequency beyond the frequency band of 1-2000 Hz. The enhanced measurement system can provide robust and reliable measurements on the elastic parameters of rocks between 1 and 2000 Hz, which is crucial for a quantitative study of the frequency-dependent phenomenon related to fluid effects. This in turn will provide a powerful tool for the experimental characterization of elastic properties of oil/gas reservoir rocks, thus laying a solid foundation for low-frequency rock physics analysis and quantitative seismic interpretation.

A Review of Geometry Investigations of Helicoids

This paper presents research on geometry of helicoids which occurred in different papers. The purpose of the paper is to show a variety in types of helical surfaces which are not well known, and discuss their possible application in architecture and civil engineering. This review is a first stage of a wide investigation on stress-strain analysis methods as applied to helical structures. Author’s attention is paid to the differences in terms, geometry and materials used for these shells, and future possibilities of application of five types of helicoid are also discussed. The work would be interesting for architects, civil engineers, mathematicians and designers, and could lead to a progress in material usage efficiency.

A first-principles prediction of anisotropic elasticity and thermal properties of potential superhard WB3

The first-principles calculations were used to predict the anisotropic elasticity and thermal properties of hexagonal (hP4-WB3, hP8-WB3 and hP16-WB3) and trigonal (hR24-WB3) WB3 triborides. The single-crystal and polycrystalline elastic properties were computed from the stress-strain method and Voigt-Reuss-Hill approximations, respectively. Based on the obtained elastic modulus, two theoretical models were used to theoretically calculate Vickers hardness HV of WB3. The results showed that hP16-WB3 and hR24-WB3 are potential candidates for superhard materials. The elastic anisotropies of WB3 were characterized by elastic anisotropic indexes (AU, Acomp and Ashear, and A1, A2 and A3), three-dimensional views and projections of bulk, shear and Young's moduli. The anisotropic elasticity is ordered as hP8-WB3 > hP4-WB3 > hR24-WB3 > hP16-WB3. Furthermore, the thermal properties such as Debye temperature and sound velocity were computed from the elastic constants and moduli. Finally, the directional sound velocities were also discussed.

Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation

In this study, nonlinear vibration and stability of a polymeric pipe reinforced by single-walled carbon naotubes (SWCNTs) conveying fluid-nanoparticles mixture flow is investigated. The Characteristics of the equivalent composite are determined using Mori-Tanaka model considering agglomeration effects. The surrounding elastic medium is simulated by orthotropic visco-Pasternak medium. Employing nonlinear strains-displacements, stress-strain energy method the governing equations were derived using Hamilton\'s principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The influence of volume percent of SWCNTs, agglomeration, geometrical parameters of pipe, viscoelastic foundation and fluid velocity are shown on the frequency and critical fluid velocity of pipe. Results showed the increasing volume percent of SWCNTs leads to higher frequency and critical fluid velocity.

Normalized Rotational Multiple Yield Surface Framework (NRMYSF) stress-strain curve prediction method based on small strain triaxial test data on undisturbed Auckland residual clay soils

Small strain triaxial test measurement is considered to be significantly accurate compared to the external strain measurement using conventional method due to systematic errors normally associated with the test. Three submersible miniature linear variable differential transducer (LVDT) mounted on yokes which clamped directly onto the soil sample at equally 120° from the others. The device setup using 0.4 N resolution load cell and 16 bit AD converter was capable of consistently resolving displacement of less than 1µm and measuring axial strains ranging from less than 0.001% to 2.5%. Further analysis of small strain local measurement data was performed using new Normalized Multiple Yield Surface Framework (NRMYSF) method and compared with existing Rotational Multiple Yield Surface Framework (RMYSF) prediction method. The prediction of shear strength based on combined intrinsic curvilinear shear strength envelope using small strain triaxial test data confirmed the significant improvement and reliability of the measurement and analysis methods. Moreover, the NRMYSF method shows an excellent data prediction and significant improvement toward more reliable prediction of soil strength that can reduce the cost and time of experimental laboratory test.

DFT study of structural, electronic and elastic properties of two polymorphs of monoclinic CsGaQ2 (Q = S, Se)

In this paper, we report an ab-initio calculations of the structural, electronic and elastic properties of monoclinic CsGaQ2 (Q = S, Se) crystals in two polymorphs CsGaQ2-mC64 and CsGaQ2-mC16 (Q = S, Se). The investigation is done using the pseudo-potential plane-wave (PP-PW) method combined to the generalized gradient approximation (GGA) within the density functional theory (DFT). The calculated equilibrium lattice constants (a, b and c), angle β are in good agreement with the available experimental data. We have calculated and analyzed the energy gap, band structure and density of states. The electronic structure calculation demonstrates that crystals are direct-gap semiconductors. The single-crystal elastic constants Cij of CsGaQ2-mC16 are predicted, for the first time, using the stress–strain method. The polycrystalline bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio ν, and elastic anisotropy AU are determined based on the predicted Cij. Our results indicate that CsGaQ2 (Q = S, Se) can be classified as brittle materials.

Fracture assessment of mismatched girth welds in oval-shaped clad pipes subjected to bending moment

This paper provides an engineering assessment of an oval-shaped clad pipes with a circumferential part-through surface crack subjected to bending moment based upon equivalent stress-strain relationship method (ESSRM) in conjunction with EPRI J-estimation procedure. Plastic limit load equations are developed specially to determine the equivalent stress-strain relationship of the welded clad pipe. Then, the conventional EPRI J-estimation procedure is extended to calculate J values of the equivalent configuration with oval cross-section converted from the welded clad pipe using the ESSRM. The validation of the ESSRM/EPRI estimation framework mentioned in the above is carried out by comparing with the results obtained from 3-D elastic-plastic finite element (FE) analysis.

The First Principles Approach to The Structural, Elastic, Electronic, Vibrational and Thermal Properties of CsCl type-ErAu Alloy

Lanthanide-gold binary alloys are very attracting attention in applications of electrical measuring technology based on resistance. Such materials are considered suitable for electrical circuits due to the large temperature stability. In this study, the structural, elastic, electronic, vibrational and thermal properties of the CsCl-type crystal structure of the ErAu binary alloy with two atoms in the unit cell are investigated in the framework of the first principles approach. The lattice parameter is found as 3.603 Å. Obtained structural parameters are consistent with the available studies. Considering of electronic properties, the electronic band structures, total and partial density of states of the ErAu alloy are determined. From these calculations, it has been decided that ErAu alloy is metallic in nature. The elastic constants are calculated using the stress-strain method. The elastic constants are also obtained for different pressure values. Elastic properties of the system present that ErAu alloy is mechanically stable at different pressure values. Phonon frequencies are calculated and the structure is determined as dynamically stable. To present the thermal properties of ErAu alloy, the free energy, entropy and heat capacity of the system are also obtained under increasing temperature values.

The pressure dependence of physical properties of (W2/3Ti1/3)3AlC2 and its counterpart W3AlC2 by first-principles calculations

First-principles calculations based on density functional theory (DFT) were used to investigate the mechanical properties, elastic anisotropy, electronic structure, optical properties and thermodynamic properties of a new quaternary MAX phase (W[Formula: see text]Ti[Formula: see text])[Formula: see text]AlC[Formula: see text] and its counterpart W[Formula: see text]AlC[Formula: see text] under hydrostatic pressure. The results indicate that the volumetric shrinkage of (W[Formula: see text]Ti[Formula: see text])[Formula: see text]AlC[Formula: see text] is faster than that of axial shrinkage under hydrostatic pressure. The stress–strain method and Voigt–Reuss–Hill approximation were used to calculate elastic constants and moduli, respectively. These compounds are mechanically stable under hydrostatic pressure. Moreover, the moduli of (W[Formula: see text]Ti[Formula: see text])[Formula: see text]AlC[Formula: see text] and W[Formula: see text]AlC[Formula: see text] increase with an increase in pressure. The anisotropic indexes and surface constructions of bulk and Young’s moduli were used to illustrate the mechanical anisotropy under hydrostatic pressure. Electronic structure and optical property of (W[Formula: see text]Ti[Formula: see text])[Formula: see text]AlC[Formula: see text] and W[Formula: see text]AlC[Formula: see text] have also been discussed. The results of Debye temperature reveal that the covalent bonds among atoms in (W[Formula: see text]Ti[Formula: see text])[Formula: see text]AlC[Formula: see text] may be stronger than that of W3AlC[Formula: see text]. The heat capacity, [Formula: see text]–[Formula: see text], and thermal expansion coefficient of (W[Formula: see text]Ti[Formula: see text])[Formula: see text]AlC[Formula: see text] and W[Formula: see text]AlC[Formula: see text] were discussed in the ranges of 0–30 GPa and 0–2000 K using quasi-harmonic Debye model considering the phonon effects.

Laboratory Study of Acoustic Velocity in Different Types of Rocks at Seismic Frequency Band

In order to understand the characteristics of acoustic wave propagation in rocks within seismic frequency band (<100 Hz), the velocities of longitudinal and transverse waves of four different types of rocks were tested using low-frequency stress-strain method by means of the physical testing system of rock at low frequency and the experimental data of acoustic velocities of four different types of rocks at this frequency band were obtained. The experimental results showed that the acoustic velocities of four different types of rocks increased with the increase of temperature and pressure within the temperature and pressure ranges set by the experiment. The acoustic velocity of fine sandstone at 50% water saturation was smaller than that of dry sample. The acoustic velocities of four different types of rocks were different and the velocities of longitudinal waves of gritstone, fine sandstone, argillaceous siltstone and mudstone increased in turn under similar conditions and were smaller than those at ultrasonic frequency. Few of existing studies focus on the acoustic velocity at seismic frequency band, thus, further understanding of the acoustic characteristics at this seismic frequency band still requires more experimental data.

A new modified ECM approach on the identification of plastic anisotropic properties by spherical indentation

This paper proposes a new approach on the identification of plastic anisotropic properties (σY, n, m), which is based on new modified expanding cavity model (ECM). The new ECM incorporates Hill's an anisotropic yield criterion in 1948 by equivalent transformation of stress expression form from spherical polar coordinate system to space rectangular coordinate system, and considers piling-up or sinking-in effect by introducing volume correction factor t as a semi-theoretical function. Through the indentation analysis for new ECM, the representative stress-strain method can characterize indentation mean pressure and uniaxial flow properties. Meanwhile, nonlinear functional relations between indentation response and plastic anisotropic properties are established. The effectiveness and reliability of new developed ECM approach are verified by the comparisons between identified properties and input properties in spherical indentation simulations, the comparisons between plastic anisotropic properties identified from instrumented indentation experiments and uniaxial compression experiments, and the comparisons between representative flow stress-strain points and compression experimental curves. The identified results are obtained by iterative calculations using the trust-region techniques based on the nonlinear least-square method. Excellent agreement is achieved. Finally, it is demonstrated that the proposed approach is reliable and useful for identification of plastic anisotropic properties of various anisotropic materials.

Effects of alloying element on stabilities, electronic structures, and mechanical properties of Pd–based superalloys**Project supported by the Young-Talent Support Programs of Kunming University of Science and Technology, China (Grant No. 11504146) and the National Natural Science Foundation of China (Grant No. 51762028).

The thermodynamic stabilities, electronic structures, and mechanical properties of the Pd-based superalloys are studied by first principles calculations. In this work, we discuss the effect of Pd-based superalloys made from Al, Si, Sc, Ti, V, Cr, Mn, Fe, Cu, Zn, Y, Zr, Nb, Mo, Tc, Hf, Ta, W, Re, Os, Ir and Pt, and we also calculate a face centered cubic (fcc) structure 2×2×2 superalloy including 31 Pd atoms and one alloying element TM (Pd31TM). The mixing energies of these Pd-Based superalloys are negative, indicating that all Pd-based superalloys are thermodynamically stable. The Pd31Mn has the lowest mixing energy with a value of −0.97 eV/atom. The electronic structures of the Pd-based superalloys are also studied, the densities of states, elastic constants and moduli of the mechanical properties of the Pd-based superalloys are determined by the stress-strain method and Voigt–Reuss–Hill approximation. It is found that Pd31TM is mechanically stable, and Pd31Tc has the largest C11, with a value 279.7 GPa. The Pd31Cr has the highest bulk modulus with a value of 299.8 GPa. The Pd31Fe has the largest shear modulus and Young’s modulus with the values of 73.8 GPa and 195.2 GPa, respectively. By using the anisotropic index, the anisotropic mechanical properties of the Pd31TM are discussed, and three-dimensional (3D) surface contours and the planar projections on (001) and (110) planes are also investigated by the Young modulus.

Structural, elastic and anisotropic properties of CuZr from first-principles calculations

A systematic investigation on the structural, elastic and anisotropic properties of B19′ martensite CuZr is conducted using first principles calculations based on density-functional theory. Through geometry optimization, we observed an obvious structure change featuring a variation of the monoclinic angle β which shifts B19′ CuZr to a B33 type. In addition, the independent elastic constants of CuZr are determined by the stress-strain method, further enabling predictions of their Cauchy pressure, mechanical stability, anisotropic factor and Debye temperatures. Their anisotropic characters of linear compressibility, Young’s modulus and shear modulus are analyzed in details by constructing three-dimensional models.

Hydrostatic pressure effects on the structural, elastic and thermodynamic properties of the complex transition metal hydrides A2OsH6 (A = Mg, Ca, Sr and Ba)

ABSTRACTWe report a systematic first-principles density functional theory study on the pressure dependence of the structural parameters, elastic constants and related properties and thermodynamic properties of the complex transition metal hydrides Mg2OsH6, Ca2OsH6, Sr2OsH6 and Ba2OsH6. The calculated structural parameters are in excellent agreement with the existing data in the scientific literature. The single-crystal elastic constants and related properties were predicted using the stress–strain method. The elastic moduli of the polycrystalline aggregates were evaluated via the Voigt–Reuss–Hill approach. The dependences of the lattice parameter, bulk modulus, volume thermal expansion coefficient, isobaric and isochoric heat capacity and Debye temperature on the pressure and temperature, ranging from 0 to 15 GPa and from 0 to 1000 K, respectively, were investigated using the quasi-harmonic Debye model in combination with first-principles calculations.

Effects of alloying elements on relative phase stability and elastic properties of L12 Co3V from first-principles calculations

Nineteen transition metal elements have been taken into account to study the alloying effects on the relative phase stability, elastic properties and electronic structure of L12 Co3V compound, based on the first-principles calculations. The site preference of ternary alloying elements was primarily determined with the help of normalized transfer energy. According to the results, four groups of alloying elements were classified, namely strong/weak V site preference and strong/weak Co site preference. In view of relative phase stability, we found that the Co–V–Hf, Co–V–Ir and Co–V–Pt systems have strong potential to precipitate the stable γ’ phase, other than Co–V–Ti, Co–V–Ta systems that have been experimentally reported. The stabilizing effect of ternary alloying elements on γ’ phase has an order of Ti > Ta > Hf > Ir > Pt > Nb > Zr > Rh > Sc > W. By using stress–strain method, the elastic properties including bulk modulus, shear modulus and Young’s modulus were evaluated. Significantly, the intrinsic linear relationship between elastic properties and electron density per molar volume was revealed. It is found that the shear moduli G {110} and G {111} of L12 Co3V compound are increased by alloying Cr, Tc, Re and Pt elements, while reduced by other transition metal elements. To understand the mechanism, we employed the charge density difference to characterize the electronic structure of some typical X-substituted L12 Co3V compounds. The results successfully associate the shear moduli of these compounds with the anisotropic distribution of transfer electron density.