The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials

The behavior of granular materials is very complex in nature and depends on particle shape, stress path, fabric, density, particle size distribution, amongst others. This paper presents a study of the effect of particle geometry (aspect ratio) on the mechanical behaviour of granular materials using the discrete element method (DEM). This study discusses 3D DEM simulations of conventional triaxial and true triaxial tests. The numerical experiments employ samples with different particle aspect ratios and a unique particle size distribution (PSD). Test results show that both particle aspect ratio (AR) and intermediate stress ratio \((b=({\upsigma }_{2}'-{\upsigma }_{3}')/({\upsigma }_{1}'-{\upsigma }_{3}'))\) affect the macro- and micro-scale responses. At the macro-scale, the shear strength decreases with an increase in both aspect ratio and intermediate stress ratio b values. At the micro-scale level, the fabric evolution is also affected by both AR and b. The results from DEM analyses qualitatively agree with available experimental data. The critical state behaviour and failure states are also discussed. It is observed that the position of the critical state loci in the compression \((e-p')\) space is only slightly affected by aspect ratio (AR) while the critical stress ratio is dependent on both AR and b. It is also demonstrated that the influence of the aspect ratio and the intermediate stress can be captured by micro-scale fabric evolutions that can be well understood within the framework of existing critical state theories. It is also found that for a given stress path, a unique critical state fabric norm is dependent on the particle shape but is independent of critical state void ratio.     

The influence of particle-size distribution on critical state behavior of spherical and non-spherical particle assemblies

This paper presents an investigation into the effects of particle-size distribution on the critical state behavior of granular materials using discrete element method (DEM) simulations on both spherical and non-spherical particle assemblies. A series of triaxial test DEM simulations examine the influence of particle-size distribution (PSD) and particle shape, which were independently assessed in the analyses presented. Samples were composed of particles with varying shapes characterized by overall regularity (OR) and different PSDs. The samples were subjected to the axial compression through different loading schemes: constant volume, constant mean effective stress, and constant lateral stress. All samples were sheared to large strains to ensure that a critical state was reached. Both the macroscopic and microscopic behaviors in these tests are discussed here within the framework of the anisotropic critical state theory. It is shown that both OR and PSD may affect the response of the granular assemblies in terms of the stress–strain relations, dilatancy, and critical state behaviors. For a given PSD, both the shear strength and fabric norm decrease with an increase in OR. The critical state angle of shearing resistance is highly dependent on particle shape. In terms of PSD, uniformly distributed assemblies mobilize higher shear strength and experience more dilative responses than specimens with a greater variation of particle sizes. The position of the critical state line in the e–p′ space is also affected by PSD. However, the effects of PSD on critical strength and evolution of fabric are negligible. These findings highlight the importance of particle shape and PSD that should be included in the development of constitutive models for granular materials.     

A fracture locus for a 50 volume-percent Al/SiC metal matrix composite at high temperature

The effect of the stress state on the fracture locus function of the 50 vol.% Al/SiC metal matrix composite at high temperature is studied. The value of fracture locus function is quantitatively characterized by the amount of shear strain accumulated prior to the moment of failure. Nondimensional invariant parameters are used as characteristics of the stress state, namely, the stress triaxiality k and the Lode-Nadai coefficient μ _σ showing the form of the stress state. Besides conventional testing for tension, compression and torsion of smooth cylindrical specimens, the complex of mechanical tests includes a new type of testing, namely, that for bell-shaped specimens. These kinds of testing enable one to study fracture strain under monotonic deformation in the ranges μ _σ ?=?0?…?+?1 and k?=???1.08...0 without using high-pressure technologies. The stress–strain state during specimen testing is here evaluated from the finite element simulation of testing in ANSYS. The tests were performed at a temperature of 300 °C and shear strain rate intensity Η?=?0.1;?0.3;?0.5 1/s. The test results have offered a fracture locus, which can be used in models of damage mechanics to predict fracture of the material in die forging processes.     

Photoelastic strain measurement in GaP (100) wafers under external stresses

The sign of the absolute value of residual strain measured in LEC-grown GaP wafers with scanning infrared polariscope (SIRP) has been determined by measuring the residual strain in the round-shape wafer with and without compressive load to the diametric edges. Since the external stress induced by the compressive load is additive to the residual strain in wafer, the residual strain measured in the wafer with the compressive load is increased if the sign is negative while it is decreased if the sign is positive. The measurement of residual strain was successively performed in various LEC-grown GaP (100) wafers clamped their diametric edges in a specially-made vise, in which a movable jaw is pulled by a coil spring to slide parallel toward a fixed jaw with a compressive load. It is found from their results that the residual strain component of (S _r ? S _t), where S _r is the radial strain component and S _t is the tangential strain component defined in the cylindrical coordinate system matching to the round-shape wafer, is negative; that is, radially compressive in most wafers.     

Effect of restricted geometry and external pressure on the phase transitions in ammonium hydrogen sulfate confined in a nanoporous glass matrix

A study of heat capacity, thermal dilatation, susceptibility to hydrostatic pressure, permittivity and polarization loops was carried out on NH₄HSO₄–porous glass nanocomposites (AHS?+?PG) as well as empty glass matrices. The formation of dendrite clusters of AHS with a size, d_cryst, exceeding the pore size was found. An insignificant anisotropy of thermal expansion of AHS?+?PG showing statistically uniform distribution of AHS with random orientations of nanocrystallites over the matrix was observed. The effect of internal and external pressures on thermal properties and permittivity was studied. At the phase transition P-1???Pc, a strongly nonlinear decrease in the entropy ΔS₂ and volume strain (ΔV/V)_T2 was observed with decreasing d_cryst. The linear change in temperatures of both phase transitions P-1???Pc???P2₁/c under hydrostatic pressure is accompanied by the expansion of the temperature range of existence of the ferroelectric phase Pc, while this interval narrows as d_cryst decreases.     

Critical state behaviors of a coarse granular soil under generalized stress conditions

Critical state line (CSL) is the central concept in soil mechanics. A series of true triaxial compression tests under the constant-\({p}'\) and constant-b loading condition were carried out to investigate the CSL of a coarse granular soil. It was observed that the intermediate principal stress ratio (i.e., the b-value) greatly influenced the CSLs in both \(q{-}{p}'\) and \(e{-}{p}'\) spaces. The CSL slope in the \(q{-}{p}'\) space decreased with an increase in b-value. The intercept and gradient of the CSL in the \(e{-}{p}'\) space decreased with increasing b-value. CSLs incorporating the effects of the b-value in \(q{-}{p}'\) and \(e{-}{p}'\) spaces were extended to three-dimensional critical state surfaces (TCSSs) in \(q{-}{p}'{-}b\) and \(e{-}{p}'{-}b\) spaces. Two empirical equations were proposed for the two TCSSs in \(q{-}{p}'{-}b\) and \(e{-}{p}'{-}b\) spaces, respectively. The predictions by the two equations were in good agreement with the corresponding experimental data. The relationship between the excess friction angle (the difference between the peak state and critical state friction angles) and initial state parameter was influenced by the b-value. However, the relationship between the maximum dilatancy and initial state parameter was independent of the b-value.     

Vacancies in as-grown CZ silicon crystals observed by low-temperature ultrasonic measurements

By means of the low-temperature ultrasonic measurement, we try to observe the elastic softening due to the vacancies in as-grown silicon crystals grown by the Czochralski (CZ) method. We prepared a high-resistivity CZ silicon crystal ingot comprising the following defect-regions: the void region, the region of ring-like oxidation stacking fault, the Pv-region, the Pi-region, and the region of the dislocation clusters. Both of the elastic constants C ₄₄(T) and [C ₁₁(T) ? C ₁₂(T)]/2 measured for the samples taken from the Pv-region exhibit the softening of the type C _Γ(T) = C _Γ ⁽⁰⁾ [1 ? Δ_JT/(T ? Θ)] which was also found in our previous study for the non-doped FZ silicon and attributed to the neutral vacancy. No response of the softening to the applied magnetic field is found, as in our previous case of the non-doped FZ silicon. The observed softenings are attributed to the triply degenerate T ₂ states of the vacancy accommodating two electrons with anti parallel spins. The samples in the Pi-region exhibit no such softening, confirming that the origin of the softening is the vacancies. A qualitative explanation is given to the measured distribution of the vacancy concentration.     

Unexpected liquefaction under isotropic consolidation of idealized granular materials

The drained isotropic compression behaviour of very loose and fully saturated monodisperse glass beads in triaxial compression is investigated in this paper. Short cylindrical samples were prepared by moist-tamping technique and isotropically compressed in a classical axisymmetric triaxial machine. Very loose glass bead samples exhibit numerous local collapses with sudden volumetric compaction and axial contraction of very large amplitude and experience ultimately global collapse with spontaneous liquefaction under undetermined external isotropic stress. Excess pore pressure instantaneously generated at the beginning of the collapse phenomenon, and rapidly dissipated with the usual drainage system, shows a global complex system with local dynamic instability. The dynamic time evolution of the excess pore pressure \(\varDelta U\) consists in a first and fast transient phase I at constant volume and constant axial strain with large spikes \(\varDelta U^{peak}\), followed by an intermediate second phase II of large increase of volumetric compaction and axial contraction at stabilizing \(\varDelta U_{stable}\) or constant effective stress \(\sigma ^{\prime }\) and finally a third and longest phase III of excess pore water pressure dissipation at nearly constant axial strain toward the initial back-pressure. For local collapses, the second phase is totally missing. Upon ignoring the local collapses, very loose idealized granular materials have a unique and global isotropic compressibility behaviour, independently of the void ratio at the end of the fabrication stage; and liquefaction-free for dense state below a threshold void ratio at fabrication \(e_{30}^{liq}\), representing the transition from global instability with total failure to local instability with partial collapse. This paper provides the first reported spontaneous liquefaction instability under isotropic consolidation. It gives the necessarily conditions for an isotropic liquefaction and emphases some usually hidden or partially developed mechanisms underlying the diffuse instability phenomenon and adds a new intriguing layer to the complex behaviour of idealized granular materials in classical drained triaxial isotropic compression.     

Multiscale structural characterization of methyltriethoxysilane-based silica aerogels

A series of methyltriethoxysilane-based silica aerogel monoliths were prepared by ambient pressure drying with various volume ratios of water to ethanol (R). The pore volumes and average pore sizes of silica aerogels were obtained by Barrett–Joyner–Halenda (BJH) method from nitrogen adsorption–desorption isotherms. The stress–strain curves of the cylindrical aerogel specimens were measured by performing uniaxial compressive tests. The particle size distributions and the average particle sizes of silica aerogels were also evaluated based on scanning electron microscopic observations. The experimental data revealed that the average particles size increased from 0.115 to 3.08 μm as R varied from 0.7 to 1.5, and that the silica aerogels exhibited two characteristic types of the compressive stress–strain responses. By proposing a multiscale structural model to describe microstructures of silica aerogels, a structural parameter, defined as the slenderness L/D of the cube column length L and the average particle diameter D, was related to the specific volume and the BJH volume of the silica aerogel monoliths, as well as the specific volume of silica. Accordingly, the two types of the compressive stress–strain responses may be distinguished by the critical value (L/D)_c.     

The H-T and P-T Phase Diagram of the Superconducting Phase in Pd:Bi<Subscript>2</Subscript>Te<Subscript>3</Subscript>

We study the magnetic field vs. temperature (H – T) and pressure vs. temperature (P – T) phase diagrams of the T _c ≈ 5.5 K superconducting phase in Pd _x Bi₂Te₃ (x ≈ 1) using electrical resistivity versus temperature measurements at various applied magnetic fields (H) and magnetic susceptibility versus temperature measurements at various applied magnetic fields (H) and pressure (P). The H – T phase diagram has an initial upward curvature as observed in some unconventional superconductors. The critical field extrapolated to T = 0 K is H _c (0) ≈ 6–10 kOe. The T _c is suppressed approximately linearly with pressure at a rate d T _c /d P ≈ ?0.28 K/GPa.     

The motion induced by the orthogonal stretching and shearing of a membrane beneath a quiescent fluid

The flow induced above an impermeable membrane undergoing orthogonal linear stretching and orthogonal linear shearing is investigated. For an exact solution of the Navier–Stokes equations, the orthogonal shearing motions must be related through the constant σ = γ δ, where γ and δ are the dimensionless streamwise and transverse shear rates, respectively. The resulting similarity reduction leads to three nonlinearly coupled ordinary differential equations governed by σ and the ratio of membrane stretch rates β. All possible solutions of these equations are found either numerically or, in special cases, analytically. Features of the σ = 0 solutions at β = 0 and asymptotically as β → ∞ are found to be in excellent agreement with numerical calculations. An aside calculation shows that orthogonal shearing in the absence of any plate stretching cannot exist. However, shearing in one coordinate direction is possible as long as the membrane stretches in at least one direction with the caveat that there exists uniform suction through a porous membrane.     

Effects of LiNbO<Subscript>3</Subscript> doping on the microstructures and electrical properties of BiScO<Subscript>3</Subscript>–PbTiO<Subscript>3</Subscript> piezoelectric system

Piezoelectric ceramics xLiNbO₃–yBiScO₃–(1?x?y)PbTiO₃ (LN–BS–PT, 0.00?≤?x?≤?0.10, 0.30?≤?y?≤?0.36) were synthesized and their phase diagram and morphotropic phase boundary between rhombohedral and tetragonal phases have been confirmed. The optimal properties were found at the composition of 0.03LN–0.36BS–0.61PT with piezoelectric coefficient d₃₃^* value of 702 pm/V, d₃₃ of 551 pC/N, planar electromechanical coupling factor k_p of 0.51, remnant polarization P_r of 46.5 µC/cm², Curie temperature T_c of 337 °C, and a large strain of 0.351% at an electric field of 50 kV/cm and frequency of 2 Hz with a low strain hysteresis of 5.9%. The Curie temperature of the ternary system presents a linear relationship with LiNbO₃ and BiScO₃ contents. The optimization of these electric properties was probably ascribed to the enhancement in domain walls and the improving mobility of domain switching due to LiNbO₃ doping.     

Ab Initio Study of the Electronic Structure,Elastic Properties,Magnetic Feature and Thermodynamic Properties of the Ba<Subscript>2</Subscript>NiMoO<Subscript>6</Subscript> Material

We report first-principles calculations of the elastic properties, electronic structure and magnetic behavior performed over the Ba₂NiMoO₆ double perovskite. Calculations are carried out through the full-potential linear augmented plane-wave method within the framework of the Density Functional Theory (DFT) with exchange and correlation effects in the Generalized Gradient and Local Density Approximations, including spin polarization. The elastic properties calculated are bulk modulus (B), the elastic constants (C₁₁, C₁₂ and C₄₄), the Zener anisotropy factor (A), the isotropic shear modulus (G), the Young modulus (Y) and the Poisson ratio (υ). Structural parameters, total energies and cohesive properties of the perovskite are studied by means of minimization of internal parameters with the Murnaghan equation, where the structural parameters are in good agreement with experimental data. Furthermore, we have explored different antiferromagnetic configurations in order to describe the magnetic ground state of this compound. The pressure and temperature dependence of specific heat, thermal expansion coefficient, Debye temperature and Grüneisen parameter were calculated by DFT from the state equation using the quasi-harmonic model of Debye. A specific heat behavior C_V?≈?C_P was found at temperatures below T = 400 K, with Dulong–Petit limit values, which is higher than those, reported for simple perovskites.     

Letter to the editor: Dimensionless citation indicators

Bornmann and Leydesdorff (Scientometrics, 2018.  https://doi.org/10.1007/s11192-018-2682-1) make an excellent case to use normalized citation based indicators instead of the h-index. In this Letter to the Editor we point out that h/P, p/P and i/P are all very simple and intuitive dimensionless citation indicators where h is the Hirsch h-index, p the performance index of Prathap, and i the value of impact as measured by the ratio of citations C to Publications P.     

Impact of High Pressure and High Temperature on Annealed Oxygen-deficient CoSrO<Subscript>3−<Emphasis Type="Italic">δ</Emphasis></Subscript> Perovskites: Structural and Magnetization Studies

In this brief article, structural, magnetization studies of oxygen deficient perovskite cobalt oxides CoSrO_3?δ synthesized in two different ways are reported. The structural refinements (JANA2006) of X-ray powder diffraction data indicate that the sample prepared under ambient pressure (stage-1) shows a hexagonal structure with P6₃/mmc (194) as a possible space group. The stage-1 sample subsequently sintered at 1450?°C for 1–2 h under high-pressure 6 GPa conditions (stage-2) crystallizes in tetragonal symmetry with I4/mcm (140) space group having a=5.444(7) Å and c=7.68(2) Å. While the stage-1 sample exhibits a paramagnetic nature in the magnetic susceptibility, M(T), measurements, interestingly the sample annealed under high-pressure conditions shows ferromagnetism in the magnetic susceptibility, M(T) and field dependence magnetization, M(H) measurements. The high-pressure annealed sample shows hysteresis opening with a quite large coercive field of 7.3 kOe at 1.8 K. The temperature dependence of the inverse molar susceptibility curves exhibits linear behavior in the high-temperature regime and could be fitted to the Curie–Weiss expression, χ(T)=C/(T?θ _W). The experimental values of θ _W and p _eff obtained from the linear region of the inverse molar magnetic susceptibility curves are found to be: ?210.7(5) K and 2.38(2) μ _B/Co for stage-1 and 260.2(7) K and 1.87(3) μ _B/Co for stage-2 samples, respectively. A negative sign of θ _W indicates rather strong antiferromagnetic correlations in the stage-1 sample. Apart from these results, the structural parameters reported by various groups for the strontium-based perovskite cobalt oxides are also presented in the form of literature collections.     

Stress and strain mapping of micro-domain bundles in barium titanate using electron backscatter diffraction

Cross-correlation of electron backscatter diffraction patterns has been used to generate stress and strain maps of a single crystal of tetragonal barium titanate (BaTiO₃) containing bundles of small, (0.2–5) μm, a- and c-domains separated by 90° domain boundaries. The strains peaked at the domain boundaries, and approximately equal, but opposite, values were observed in the a- and c-domains; the peak strain magnitudes were slightly less than half the tetragonal distortion of BaTiO₃, about 0.004, consistent with a tendency to a cubic structure at domain boundaries. The strain state was dominated by two normal strains: in-plane, perpendicular to domain wall intersections with the surface, and out-of-plane, perpendicular to the surface. In distinction to larger, lamellar domains, significant shear strains were also observed. Stress maps were constructed from strain maps using a method that does not require zero stress at reference locations. Peak in-plane normal stresses of approximately 700 MPa were observed. The variation of the stress component parallel to the domain walls was used to determine numerically a microstructurally based stress intensity factor for crack propagation perpendicular to the domain walls. The conditions for stable micro-crack formation in the microstructural stress field and unstable crack propagation under the action of a superposed applied stress were considered in the context of multi-layer ceramic capacitor reliability.     

Dual relaxation behaviors and large electrostrictive properties of Bi<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>–Sr<Subscript>0.85</Subscript>Bi<Subscript>0.1</Subscript>TiO<Subscript>3</Subscript> ceramics

Lead-free ceramics (1???x)Bi_0.5Na_0.5TiO₃–xSr_0.85Bi_0.1TiO₃ (BNT–xSBT, x?=?0.4, 0.5, 0.6 and 0.7) were prepared by a solid-state reaction process. Coexistence of ferroelectric relaxation at low temperature and Maxwell–Wagner dielectric relaxation at high temperature was revealed for the first time in this system. Meanwhile, hysteresis-free P–E loops combined with a very high piezoelectric strain coefficient (d₃₃) of 1658 pC/N concurrently with large electrostrictive coefficient Q?=?0.287 m⁴C^?2 were achieved. The ferroelectric relaxor behavior and large electrostrictive strain might be linked to easy reorientation and reversal of ergodic PNRs and the combined effect of Bi off-center position and lone pair electrons.     

Crystal Structure of Nb<Subscript>5</Subscript>Si<Subscript>3 − <Emphasis Type="Italic">x</Emphasis></Subscript>P<Subscript>0.5 + <Emphasis Type="Italic">x</Emphasis></Subscript> (<Emphasis Type="Italic">x</Emphasis> = 0–0.5)

The structure of the ternary compound Nb₅Si_{3 ? x}P_{0.5 + x} (x = 0–0.5) is determined by single-crystal x-ray diffraction: sp. gr. P6₃mc, a = 1.32350(5) nm, c = 0.52954(1) nm; R _F = 0.028, R_w = 0.081 for 547 reflections with F _hkl > 4.0σ(F _hkl ). Relations between the structure of Nb₅Si_{3 ? x}P_{5 + x}, the Mn₅Si₃ structure type, and its derivatives are discussed.     

Variation of the yield stress and latent strain energy in the course of plastic deformation of a neutron-irradiated chromium-nickel steel

The laws of variation of the flow stress (σ) and latent strain energy (E_s) in the course of plastic deformation have been studied in the samples of a titanium-doped chromium-nickel steel (12Kh18N10T grade) before and after neutron irradiation to a dose of 5×10²²m^?2 (neutron energy E>0.1 MeV). The E_s versus σ curve can be divided into several characteristic regions, the first of which is described by a relation of the type E_s～E₀+kσ² (E₀ and k being certain coefficients). It is established that neutron irradiation shifts the E_s versus σ curve toward smaller latent energies.