Young's Modulus Ratio Research Articles

Recognition of the Stress-Strain Curve Based on the Local Deformation Measurement of Soil Specimens in the Triaxial Test

Abstract A digital image technique was developed and used to measure the deformation distribution over the entire surface of soil specimens in triaxial tests. The measured deformation process shows that the specimen apparently exhibits three states during the test, i.e., pre-failure, in-failure, and post-failure, in correspondence to the different features of its deformation. The deformation feature in each state is then analyzed by the displacement and strain contours. Additionally, the stress level, S, is calculated to determine whether the soil is in failure at a point (representative element volume (REV)) on the surface of the specimen. Next, the failure zone, namely the shear band, was considered to be enveloped by the curve defined by S = 1 on the stress-level contour map. The stress level is calculated based on the strain, Young's modulus and Poisson's ratio. According to analysis of the deformation feature and the failure process, we recognized the following properties: (i) the deformation of the specimen was approximately uniform in the pre-failure state; (ii) failure occurred from a point and developed gradually until the shear band cleaves the specimen; (iii) in the post-failure state, deformation was exclusively due to the blocks of the specimen sliding along the shear band; (iv) the deformation feature in the shear band was quite different from that outside the shear band. In conclusion, the stress-strain curve of the specimen revealed a structural response, not an elementary response, especially in the in-failure and post-failure states, in which the deformation features of different corner points were different, and the observed deformation for the entire specimen may be the combination of local deformations. Therefore, it is not appropriate to build the constitutive model for soil according to the stress-strain curves of the entire deformation process and to take the specimen as a uniform element in the entire process.

A new laboratory apparatus for the measurement of seismic dispersion under deviatoric stress conditions

ABSTRACTA better understanding of seismic dispersion and attenuation of acoustic waves in rocks is important for quantitative interpretation of seismic data, as well as for relating seismic data, sonic‐log data, and ultrasonic laboratory data. In the present work, a new laboratory setup is described, allowing for combined measurements of quasistatic deformations of rocks under triaxial stress, ultrasonic velocities, and dynamic elastic stiffness (Young's modulus and Poisson's ratio) at seismic frequencies. The setup has been used mainly for the study of shales. For such rocks, it is crucial that the saturation of the samples is preserved, which requires fast sample mounting. The design of our setup, together with a technique that was developed for rapid mounting of strain gauges onto the sample and subsequent sealing of the sample, allows for sample preservation, which is of particular importance for shales. The performance of the new experimental setup and sample mounting procedure is demonstrated with test materials (aluminium and polyetheretherketone) and two different shale types (Mancos shale and Pierre shale). Furthermore, experimental results are presented that demonstrate the capability of measuring the impact of saturation, stress, and stress path on seismic dispersion. For the tests with Mancos shale and Pierre shale, large dispersion (up to 50% in Young's modulus normal to bedding) was observed. Increased water saturation of Mancos shale results in strong softening of the rock at seismic frequencies, whereas hardening is observed at ultrasonic frequencies due to an increase in dispersion, counteracting the rock softening. The Poisson's ratio of Mancos shale strongly increases with the level of saturation but appears to be nearly frequency independent. We have found that the different types of shale exhibit different stress sensitivities during hydrostatic loading and that the stress sensitivity is different at seismic and ultrasonic frequencies.

Studies on determining the bending strength of thin glass

In architecture, the term ‘thin glass’ is normally used for glass less than 3 mm thick. The present study aimed to address the lack of reported research concerning appropriate testing configurations and derivation of analytical equations for calculating the bending strength of thin glass to enable its use in architectural applications. Two testing methods (a modified four-point bending test and a buckling test) for determining the bending strength of thin glass are presented, supplemented with analytical approaches for calculating the relative tensile bending stresses. These methods take the geometrical non-linearity into consideration. Experimental and numerical investigations showed that both methods are suitable and satisfactorily represent the tensile bending stress in the centre of the specimen. It is, however, believed that the modified four-point bending test is preferable since the test equipment according to EN 1288-3 can be used. Use of this equipment is widespread and the test setup and execution are simple. To identify influencing and limiting parameters on the bending strength, a numerical sensitivity analysis was performed. This showed that small variations of the parameters glass thickness, Young's modulus or Poisson's ratio have an influence on the value of the tensile bending stress.

Investigations on structural, elastic, thermodynamic and electronic properties of TiN, Ti2N and Ti3N2 under high pressure by first-principles

The lattice parameters, cell volume, elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio are calculated at zero pressure, and their values are in excellent agreement with the available data, for TiN, Ti2N and Ti3N2. By using the elastic stability criteria, it is shown that the three structures are all stable. The brittle/ductile behaviors are assessed in the pressures from 0GPa to 50GPa. Our calculations present that the performances for TiN, Ti2N and Ti3N2 become from brittle to ductile with pressure rise. The Debye temperature rises as pressure increase. With increasing N content, the enhancement of covalent interactions and decline of metallicity lead to the increase of the micro-hardness. Their constant volume heat capacities increase rapidly in the lower temperature, at a given pressure. At higher temperature, the heat capacities are close to the Dulong–Petit limit, and the heat capacities of TiN and Ti2N are larger than that of c-BN. The thermal expansion coefficients of titanium nitrides are slightly larger than that of c-BN. The band structure and the total Density of States (DOS) are calculated at 0GPa and 50GPa. The results show that TiN and Ti2N present metallic character. Ti3N2 present semiconducting character. The band structures have some discrepancies between 0GPa and 50GPa. The extent of energy dispersion increases slightly at 50GPa, which means that the itinerant character of electrons becomes stronger at 50GPa. The main bonding peaks of TiN, Ti2N and Ti3N2 locate in the range from −10 to 10eV, which originate from the contribution of valance electron numbers of Ti s, Ti p, Ti d, N s and N p orbits. We can also find that the pressure makes that the total DOS decrease at the Fermi level for Ti2N. The bonding behavior of N–Ti compounds is a combination of covalent and ionic nature. As N content increases, valence band broadens, valence electron concentration increases, and covalent interactions become stronger. This is reflected in shortening of Ti–N bonds.

First-principles study of thermal expansion and thermomechanics of single-layer black and blue phosphorus

The linear thermal expansion coefficients (LTEC) and thermomechanics of single-layer black and blue phosphorus are systematically studied using first-principles based on quasiharmonic approximation. We find the thermal expansion of black phosphorus is very anisotropic. The LTEC along zigzag direction has a turning from negative to positive at around 138 K, while the LTEC along armchair direction is positive (except below 8 K) and about 2.5 times larger than that along zigzag direction at 300 K. For blue phosphorus, the LTEC is negative in the temperature range from 0 to 350 K. In addition, we find that the Young's modulus and Poisson's ratio of black phosphorus along zigzag direction are 4 to 5 times larger than those along armchair direction within considered temperature range, showing a remarkable anisotropic in-plane thermomechanics property. The mechanisms of these peculiar thermal properties are also explored. This work provides a theoretical understanding of the thermal expansion and thermomechanics of this single layer phosphorus family, which will be useful in nanodevices.

Finite Element Analysis on Nanomechanical Detection of Small Particles: Toward Virus Detection.

Detection of small particles, including viruses and particulate matter (PM), has been attracting much attention in light of increasing need for environmental monitoring. Owing to their high versatility, a nanomechanical sensor is one of the most promising sensors which can be adapted to various monitoring systems. In this study, we present an optimization strategy to efficiently detect small particles with nanomechanical sensors. Adsorption of particles on the receptor layer of nanomechanical sensors and the resultant signal are analyzed using finite element analysis (FEA). We investigate the effect of structural parameters (e.g., adsorption position and embedded depth of a particle and thickness of the receptor layer) and elastic properties of the receptor layer (e.g., Young's modulus and Poisson's ratio) on the sensitivity. It is found that a membrane-type surface stress sensors (MSS) has the potential for robust detection of small particles.

Stress-strain state of fibrin-blood clot and periosteum in the area of diaphyseal fracture under different conditions of fracture fragments fixation and its impact on the structural organization of regenerate

The goal: using mathematical finite-element modeling to calculate the stress-strain state (SSS) of fibrin-blood clot and periosteum around the fracture zone in the conditions of fixation of femur fragments with on-bone plate, intramedullary locking nail and ExFix. The methods: the model represents two fragments of femur with transverse fracture plane joined with spindly fibrin-blood clot enclosed in periosteum and devices mentioned above. The existing data on the Young's modulus and Poisson's ratio of all components of the model were used. The calculations of SSS of clot and periosteum were performed under axial load of 800 N on femur and transverse load of 200 N on the distal femur. The control points on the horizontal section of clot and periosteum were selected for a quantitative comparison of the voltage in various conditions of fragments fixation. Moreover, the area covered by the maximum stress level was compared. The results: The following patterns were revealed. At the same axial load of model the lowest level of stress in periosteal-fibrin spindle was observed when fragments were fixed with intra­medullary locking nail, a little more — with plate, and the biggest one — with ExFix. The ratio of the stress values was 1: 2: 3–4.At the same transverse load of model the lowest level of stress in periosteal-fibrin spindle was observed when fragments were fixed with plate, a little more – with intramedullary locking nail, and the biggest one — with ExFix. The ratio of the stress values was 1: 6: 10–12.The greatest difference in stress levels was noticed in the conditions of transverse load on the segment. Conclusion: The presented data on SSS in tissues around the fracture zone explain the origin of sizes, shapes and structures of periosteal bone regenerate in the treatment of diaphyseal fractures with devices with different modes of mobility of bone fragments.

Unloading Elastic Behavior of Sand in Cyclic Triaxial Tests

In this paper, digital image technology was used in the surface-deformation measurement of soil, making it possible to monitor the axial, radial, and volumetric deformations and the deformation distribution over the entire surface of specimens in triaxial tests. A series of cyclic triaxial tests on silica powder and Fujian sand were conducted to investigate the stress-strain behavior of sand in pre-failure deformation, particularly in the unloading elastic behavior. The sand gradually tended toward the stable state of deformation after it was subjected to a certain number of cyclic loadings. The sand appeared to be entirely nonlinear elastic, with unchanged and closed hysteresis loops of the stress-strain curve. In addition, the elastic parameters—Young's modulus and Poisson's ratio—of the specimens during the unloading process of the stable state of deformation were carefully studied. The test results suggested that the unloading tangent Young's modulus of sand was determined by the stress state and void ratio but was not affected by the stress amplitude of cyclic loading. However, Young's modulus depended more definitely on the axial stress than on the lateral stress when the deviatoric stress increment was applied in the triaxial stress condition. Moreover, the unloading average Poisson's ratio was dependent on the stress state and void ratio.

Structural, half-metallic magnetism and elastic properties of the KMnQ2 (Q=O, S, Se, Te) chalcogenides from first-principles calculations

The structural, electronic, magnetic and elastic properties of the ternary chalcogenides KMnQ2 (Q=O, S, Se, Te) crystals were investigated by means of spin-polarized density functional theory calculations. The 3d orbitals of the Mn atoms were treated using the GGA+U approach. The calculated equilibrium structural parameters agree well with the experimental data. Based on the analysis of the spin-polarized band structures and density of states, we predict the half-metallic character of the studied compounds, with a half-metallic gap of 1.38eV, 0.53eV, 0.37eV and 0.14eV for KMnO2, KMnS2, KMnSe2 and KMnTe2, respectively, and a total magnetic moment of 4.00μB per unit-cell for all considered structures. The examined properties for the title compounds include also the single-crystal elastic constants, bulk modulus, shear modulus, Young's modulus and Poisson's ratio.

The brittleness indices used in rock mechanics and their application in shale hydraulic fracturing: A review

Abstract Brittleness is commonly used to characterize the possible failure features in rocks, quantified by the brittleness index (BI(26)BIs, the applicability of each BI should be well understood to enable the selection of the most suitable for each application. This study reports on a detailed review of existing BI definitions in the rock mechanics field, the transition from brittle to ductile and the application of BIs to shale fracturing. The success of shale gas recovery using hydraulic fracking is greatly dependent on the shale's brittleness, since brittle shales have many pre-existing fractures and are easy to fracture in tensile and shear modes. A combination of laboratory and geophysical approaches are recommended for shale brittleness quantification. Precise quantification of brittleness is important, both in the laboratory and the field. Brittleness indices based on the elastic moduli (Young's modulus and Poisson's ratio) and mineral composition are common in field applications, and can be derived from both laboratory tests and field log data.

Ab initio study of the parent (BCC) and martensitic (HCP) phases of nonferrous Ti, Zr, and Hf metals

We present calculations of the structural, elastic and electronic properties of nonferrous Ti, Zr, and Hf pure metals in both parent and martensitic phases in bcc and hcp structures respectively. They are based on the generalized gradient approximation (GGA) within the density functional theory. The shear modulus, Young's modulus and Poisson's ratio for Ti, Zr, and Hf metals have were calculated and compared with the corresponding experimental values. Using elastic constants obtained from calculations under the GGA, the bulk modulus along the crystallographic axes of single crystals is calculated. This is in good agreement with experiment for Ti and Zr, whereas the hcp structure for Hf is a prediction. At zero temperature and zero pressure, the bcc crystal structure is found to be mechanically unstable for Ti, Zr, and Hf. In our calculations the hcp structure is correctly found to be stable at the equilibrium volume. In the electronic density of states, the smaller n(EF) is, the more stable the compound is, in agreement with the results obtained from the total energy minimum.

Single‐Crystal Elastic Properties of Aluminum Oxynitride (AlON) from Brillouin Scattering

The Brillouin light scattering technique was used to determine experimentally the three independent elastic constants of cubic aluminum oxynitride at the ambient condition. They are , and . Its bulk modulus is 221.2 GPa. The magnitude of Zener anisotropic ratio is 2.1 similar to other spinels. The anisotropic nature of the material is shown by a large variation in the Young's modulus and Poisson's ratio with crystallographic directions. The material was found to be auxetic in certain orientations.

Effects of the granule composition on the compaction behavior of deformable dry granules

Calibration of the Drucker Prager Cap (DPC) model parameters provides a means for a deeper understanding of the impact of granule composition on the compaction properties of dry granules independent of their solid fraction. In this study, monodisperse granules of mixtures of microcrystalline cellulose and mannitol (0%, 25%, 50%, 75% and 100% mannitol) prepared as small cylindrical compacts with well-defined size, shape and solid fraction (0.58) were used as model dry granules. DPC parameters–namely, cohesion, internal friction angle, cap eccentricity, and hydrostatic yield strength of materials–were determined from the diametrical and uniaxial compression, and in-die compaction tests. Elastic properties such as Young's modulus and Poisson's ratio were also determined from the in-die compaction test. Higher level of mannitol in granules required a lower compression pressure to obtain a low solid fraction tablet but higher compression pressure to obtain a high solid fraction tablets. Properties such as cohesion and diametrical tensile strength go through a maximum as the mannitol level increases in the binary granules, and clearly do not follow a simple linear mixing rule. At an industrially-relevant tablet solid fraction of 0.88, granules with 75% mannitol exhibited the highest cohesion, and produced the strongest tablet. Other properties either approximately follow the linear mixing rule (e.g., hydrostatic yield strength, Young's modulus and Poisson's ratio) where limited interactions between the constituents are present, or not sensitive to the composition (e.g., internal angle of friction). In general, the compaction behavior of granules of a multicomponent system may not be precisely estimated from the properties of individual components, simply by using the linear mixing rule.

Young's modulus and Poisson's ratio for TiO2-based nanotubes and nanowires: modelling of temperature dependence

The temperature dependence of the Young's modulus and Poisson's ratio of a number of TiO2-based four-facetted nanotubes and nanowires are predicted through the calculation of the Helmholtz free energy.

Mechanical characterization of aerogel materials with digital image correlation

Silica aerogels are ultralow density materials with nano-sized skeleton network of pores. Their high brittle nature presents a major challenge for mechanical testing and a need exists for novel testing methods. Two new mechanical setups and testing techniques are proposed for measuring the aerogel elastic mechanical properties. Both techniques employ full-field Digital Image Correlation (DIC) for surface deformation measurements. The first setup uses disk compression experiment, known as diametral compression test (Brazilian disk). However, the elastic properties of the material cannot be obtained directly. Instead, an inverse mechanics computational scheme, using both a finite element (FE) model and analytical solution, is proposed. The second direct testing setup is uniaxial compression of rectangular-shaped blocks. The Young's modulus and Poisson's ratio are extracted directly from the experimental stress–strain curves. Our results of tested samples show the relation between the density and the Young's modulus to coincide with previously published trends. The direct and iterative inverse-mechanics solution methods agree well with each other. The Poisson's ratio is found to be independent of the material apparent density. Comparisons between the two methods and recommendations for expanding the disk testing approach to fracture toughness are discussed.

Physical properties of La2B2O7(B[dbnd]Zr, Sn, Hf and Ge) pyrochlore: First-principles calculations

Using first-principles theory and further verified by the experimental results, we have studied the electronic structure, mechanical and thermal properties of La2B2O7(BZr, Sn, Hf and Ge) pyrochlore. It is shown that the La2B2O7 pyrochlore are charge-transfer-type insulators with the strong ionic bonding. The calculated band gap of La2Zr2O7, La2Sn2O7, La2Hf2O7, and La2Ge2O7 are 4.01, 3.05, 3.13 and 2.42 eV, respectively. The elastic constants, hardness, shear modulus, bulk modulus, Young's modulus and Poisson's ratio of La2B2O7 compounds were investigated systematically. Anisotropic elastic and thermal properties of La2B2O7 compounds were discussed by using Zener's indexes (AZ) and universal elastic anisotropic index (AU). The sound velocities along [100], [110] and [111] directions were calculated for each La2B2O7 compounds. Both Clark's model and Cahill's model were used to evaluate the minimum thermal conductivity of all compounds. According to the Clark's model, when the temperature is much higher than Debye temperature, the minimum thermal conductivity of La2Zr2O7, La2Sn2O7,La2Hf2O7, and La2Ge2O7 are 1.27, 1.24, 1.09 and 1.41 W/m K, respectively. According to the calculated results of these crystals, the La2B2O7 compounds exhibit an extraordinary low thermal conductivity which can be used as thermal insulating materials.

Compaction mechanics of plastically deformable dry granules

To improve the understanding of how dry granulation and in particular, granule solid fraction (SF) impact the compaction behavior of plastically deformable microcrystalline cellulose (MCC), in this study, the Drucker Prager Cap (DPC) model parameters were calibrated using monodisperse MCC dry granules as model granules. Dry granules were produced as directly compressed small cylindrical compacts of MCC with SF in the range of 0.40 to 0.70 which were monodisperse in both size and SF. Virgin MCC powder and granules were compressed into tablets with SF in the range of 0.70 to 0.90. The DPC parameters (cohesion, internal friction angle, cap eccentricity, and hydrostatic yield stress), Young's modulus and Poisson's ratio were experimentally determined from diametrical and uniaxial compression, and in-die compaction tests. Results showed that calibration of the shear failure surface only may be adequate for MCC granules when the DPC model is completely calibrated for virgin MCC. Increasing granule SF significantly decreased the cohesion only. All other parameters were impacted by the tablet SF only. In the 2D yield surface, only the shear failure surface expanded as the granule SF increased. MCC of any granulation status requires the same in-die compaction stress state for densification to a given tablet solid fraction.

Quantitative analysis of impact measurements using dynamic load cells

A mathematical model is used to estimate material properties from a short duration transient impact force measured by dropping spheres onto rectangular coupons fixed to a dynamic load cell. The contact stress between the dynamic load cell surface and the projectile are modeled using Hertzian contact mechanics. Due to the short impact time relative to the load cell dynamics, an additional Kelvin–Voigt element is included in the model to account for the finite response time of the piezoelectric crystal. Calculations with and without the Kelvin–Voigt element are compared to experimental data collected from combinations of polymeric spheres and polymeric and metallic surfaces. The results illustrate that the inclusion of the Kelvin–Voigt element qualitatively captures the post impact resonance and non-linear behavior of the load cell signal and quantitatively improves the estimation of the Young's elastic modulus and Poisson's ratio. Mathematically, the additional KV element couples one additional differential equation to the Hertzian spring-dashpot equation. The model can be numerically integrated in seconds using standard numerical techniques allowing for its use as a rapid technique for the estimation of material properties.

Friction Reduction in Lubricated Rough Contacts: Numerical and Experimental Studies

Combining the contact model of elastic-layered solid with the concept of asperity contact in elastohydrodynamic lubrication (EHL), a mixed-lubrication model is presented to predict friction coefficient over rough surfaces with/without an elastic-layered medium under entire lubrication regimes. Solution of contact problems for elastic-layered solids is presented based upon the classical model of Greenwood and Williamson (GW) in conjunction with Chen and Engel's analysis. The effects of the Young's modulus ratio of the layer to substrate and the thickness of the layer on the elastic real area of contact and contact load for a fixed dimensionless separation are studied using the proposed method, which is used for the asperities having contact with an elastic coating. Coefficient of friction with elastic-layered solids in boundary lubrication is calculated in terms of Rabinowicz's findings and elastic-layered solutions of Gupta and Walowit. The effect of rough contacts with an elastic layer on friction coefficient in lubrication regimes has been analyzed. Variations in plasticity index ψ significantly affect friction coefficients in boundary and mixed lubrications. For a large value of ψ, the degree of plastic contact exhibits a stronger dependence of the mean separation or film thickness than the roughness, and for a small value of ψ, the opposite result is true. The effect of governing parameters, such as inlet oil viscosity at ambient pressure, pressure–viscosity coefficient, combined surface roughness, and El/E2 on friction coefficient, has been investigated. Simulations are shown to be in good agreement with the experimental friction data.

Control of the Microhardness to Young Modulus Ratio by Mechanical Processing of a Ti-10Mo-20Nb Alloy

β-metastable titanium alloys with high strength to Young’s modulus ratio have been developed by different authors aiming their use as biomaterials for hard tissue replacement. However, it is not easy to combine low elastic modulus with high mechanical strength. In this work, a β-Ti alloy (Ti-10Mo-20Nb) was produced by arc-melting, then homogenized, cold swaged and aged in order to obtain fine α-Ti precipitates in a β-Ti matrix. The microstructures were characterized by transmission electron microscopy and X-ray diffraction. Mechanical properties characterization was based on Vickers microhardness tests and Young’s modulus measurements. The cold swaged material subjected to an ageing treatment at 500 °C for 4 h showed the highest hardness/ Young’s modulus ratio, associated to very fine α phase precipitates in a β-Ti matrix.