Average Elastic Constants Research Articles

Effect of Grain Level Anisotropy on Numerical Rock Fracture Behaviour under Dynamic Loading

The effect of rock crystal anisotropy is tested in numerical simulation of rock fracture at the laboratory sample level of scale. For this end, a numerical model based on the embedded discontinuity finite element method is applied here in simulations of uniaxial tension test on granitic rock. The rock material, consisting of Quartz (trigonal), Feldspar (triclinic) and Biotite (taken hexagonal here), is described as a linear elastic (up to fracture) heterogeneous and anisotropic material, which fails upon reaching the tensile strength of the individual constituent minerals. In the simulations of uniaxial tension test at two different levels of strain rate, the effect of averaged versus anisotropic elastic constants is tested. The results demonstrate that the effect of anisotropy is stronger at low strain rates (0.25 s-1 here), resulting in macrocrack planes at different locations for the isotropic and anisotropic material descriptions, while at higher rates (25 s-1 here) its notable effects disappear in the details of multiple macrocracks.

Флексоэлектрические домены в бинарной смеси нематиков

Flexoelectric domains formation in mixture of nematic liquid crystals (NLC) MBBA and 5CB with anisotropy of dielectric permeability ε_a ~ 0 under the action of dc electric voltage is investigated. Threshold characteristics of flexoelectric domains formation (threshold voltage and spatial period) in the studied mixture are measured. The difference of flexoelectric coefficients |e1-e3| is determined. It is shown that in the mixture of nematics with ε_a ~ 0 , the threshold voltage is determined only by the ratio k/(e1-e3) (k - average elastic constant), which allows to calculate the difference in flexocoefficients |e1-e3| directly, excluding the properties of substrate surfaces. The definition method of the flexoelectric coefficients, proposed and approved in paper, can be useful for the new synthesized NLC with ε_a <- 0.5.

Measuring fibre orientation and predicting elastic properties of discontinuous long fibre thermoplastic composites

Elastic properties in critical areas of 3 D shells made from discontinuous long fibre (DLF) composites are difficult to determine via traditional methods, due to the heterogeneity of the material and the geometry of the part. In this paper, a method is proposed to predict the local modulus of DLF composites based on a micrograph of the polished edge of a specimen. The position and orientation of each fibre are extracted from the micrograph and used in conjunction with classical lamination theory to predict the elastic modulus. Fibre discontinuity is accounted for by including a correction factor based on the Cox formula for averaged elastic constants. Model predictions successfully matched the experimental tests results. In a previous study, material flow during compression moulding of recycled DLF panels led to anisotropic behaviour, which was hypothesized to be caused by chip alignment in the flow direction. By using the proposed method, chip alignment due to flow was confirmed and the anisotropy in the elastic modulus was accurately predicted.

Upper and Lower Bounds of Average Elastic Constants of an Anisotropic Polycrystalline Medium: Calculations and A Priori Estimates

Abstract —A general procedure is suggested for calculating the upper (Voigt) and lower (Reuss) bounds of the average elastic constants of an anisotropic medium from crystallographic directions. The elastic tensors of Hooke’s law can be expanded into irreducible representations of the rotation group. The Voigt/Reuss-averaged elastic constants depend on the second and fourth moments of the distribution function rather than on the entire function used for the averaging. In this case, the distribution function depends on one angle, while the elastic constants depend on two variables. The limitations imposed by the probability theory on the moment values are investigated and used to derive general constraints on the Voigt (Reuss) bounds of elastic constants.

Effects of Si and Y co-doping on stability and oxidation resistance of <i>γ</i>-TiAl based alloys

Improving the oxidation resistance of TiAl-based alloys at high temperature has great significance for expanding their application fields. Adding ternary and quaternary elements is one of the effective ways to solve the oxidation problem of this kind of alloys materials. The first-principles method based on density functional theory was used to study the Si and Y substitution co-doping effects on the oxidation resistance of <i>γ</i>-TiAl based alloys from the aspects of atomic average formation energy and elastic constant of system, as well as the formation energies of interstitial O atom, Ti vacancy and Al vacancy in the system. The results indicate that the atomic average formation energies of the Si and Y dual-doped systems are all negative, which imply they possess energy stability and can be prepared by experiments. In addition, the elastic constants of most Si and Y substitution co-doping <i>γ</i>-TiAl systems satisfy the mechanical stability criterion. For the mechanical stable systems, the analysis results about the formation energies of the interstitial O atom, Ti vacancy and Al vacancy reveal that the Ti<sub>6</sub>SiYAl<sub>8</sub> series, in which both Si and Y substitute Ti, have obvious promotion effect on the improvement about oxidation resistance; system Ti<sub>7</sub>YAl<sub>7</sub>Si, in which Y substitutes Ti and Si substitutes Al, and system Ti<sub>7</sub>SiAl<sub>7</sub>Y, in which Si substitutes Ti and Y substitutes Al, have uncertain influence on improving oxidation resistance; system Ti<sub>8</sub>Al<sub>6</sub>SiY, in which both Si and Y substitute Al, is harmful to the improvement about oxidation resistance of the <i>γ</i>-TiAl based alloys. Therefore, the preparation conditions should be controlled moderately so that both Si and Y substitute Ti at the same time to form a large proportion configurations of Ti<sub>6</sub>SiYAl<sub>8</sub> series in the materials. In these configurations, the outward diffusion of Ti atoms and the inward diffusion of interstitial O atoms are suppressed, meanwhile the outward diffusion of the Al atoms is facilitated. In this way, the production of <i>α</i>-Al<sub>2</sub>O<sub>3</sub> is promoted and that of TiO<sub>2</sub> is weakened on the surface of co-doping <i>γ</i>-TiAl based alloys. Thus, a scale rich in <i>α</i>-Al<sub>2</sub>O<sub>3</sub>, i. e., a continuous, dense, and protective oxide scale can be grown on the surface of Si and Y substitution co-doping <i>γ</i>-TiAl alloys.

A new approach to rapidly generate random periodic representative volume elements for microstructural assessment of high volume fraction composites

An algorithm based on event-driven molecular dynamics theory was developed to rapidly generate periodic representative volume elements (RVEs) with nonuniform distributions for both unidirectional fibre-reinforced and spherical particle-reinforced composites. Detailed statistical analyses were conducted for assessing the ability to generate RVEs with nonuniformly dispersed microstructures and either constant or random inclusion sizes for a wide range of volume fractions. The generated microstructures were directly compared with available microstructural optical images of a composite material, showing excellent statistical correlation and providing validation for the developed RVE generation approach. For further validation, finite element analysis was conducted using the generated RVEs in order to evaluate volume averaged elastic constants. The expected isotropic characteristics of the RVEs were correctly calculated, and excellent correlations with experimental data from the literature provided additional support for the algorithm accuracy. The versatile algorithm can rapidly generate RVEs with realistic reinforcement dispersions and high volume fractions up to 80%, which is advantageous compared to other algorithms. The proposed algorithm can be used as a design tool to accurately evaluate and tailor the mechanical properties of distinct composite material systems, and for their microstructural assessment including local damage predictions.

Equilibrium Lattice Relaxation and Misfit Dislocations in Step-Graded In x Ga1−x As/GaAs (001) and In x Al1−x As/GaAs (001) Metamorphic Buffer Layers

The inclusion of metamorphic buffer layers (MBLs) in the design of lattice-mismatched semiconductor heterostructures is important in enhancing reliability and performance of optoelectronic and electronic devices through proper control of threading dislocations; threading dislocation can be reduced by allowing the distribution of the misfit dislocations throughout the MBL, rather than concentrating them at the interface where substrate defects and tangling can pin dislocations or otherwise reduce their mobility. Compositionally graded layers have been particularly used for this purpose and in this work we considered heterostructures involving a step-graded InxGa1−xAs or InxAl1−xAs epitaxial layer on a GaAs (001) substrate. For each structure type, we present minimum energy calculations including (i) the surface and (ii) average in-plane strain and (iii) the misfit dislocation density profile with various grading coefficients (thickness and indium composition variation). In both types of structures, the average in-plane strain and misfit dislocation density profile scale with the average grading coefficient, but InxAl1−xAs structures with a greater average elastic stiffness constants exhibit slightly higher average compressive in-plane strain (absolute valued) which is associated with higher misfit dislocation densities. However, the rate of change in the normalized relaxation percentage per unit thickness of each step with respect to the lattice mismatch of the step is lower in the InxAl1−xAs material system. The difference of the in-plane strain is small (<3%), however, so that these material systems are virtually interchangeable in terms of their mechanical behavior (<5.1% change in elastic constants).

Improvement of permanent memory effect in PDLC films using TX-100 as an additive

ABSTRACTA number of polymer dispersed liquid crystal (PDLC) films based on dimethacrylate monomers were synthesised by polymer-induced phase separation (PIPS) using polyethylene glycol p-(1,1,3,3-tetramethylbutyl)-phenyl ether (TX-100) as an additive up to total solution weight of 10% aiming to modify the initial anchorage force of the liquid crystal (LC) molecules to the polymeric matrix. The effects of the addition of this additive to the PDLC films were studied resorting to electro-optical studies. Using a fitting model, several parameters were correlated such as the permanent memory effect (PME), the voltage required to achieve 90% of maximum transmittance (E90), the average elastic constant (K) and the rotational viscosity of the director (γ). The use of TX-100 results on an increase on the PME and γ, and decrease on the E90 and K.

Determination of average X-ray strain (AXS) on TiN hard coatings using cos2αsin2ψ X-ray diffraction method

For stress measurement on thin films and coatings using X-ray diffraction (XRD) methods, the uncertainty is commonly acknowledged to be from elastic constants. However, the uncertainty can be due to the statistical fluctuation of strain measured by XRD. In this study, we proposed a method where the average X-ray strain (AXS) was determined using cos2αsin2ψ XRD technique at several rotational (ϕ) angles to improve the accuracy of the measurement of X-ray stress or X-ray elastic constants (XECs). The major concept was to increase sampling volume by measuring X-ray strain at multiple rotational angles. TiN hard coating on Si (100) substrate was selected as the model system, where the residual stress was determined by laser curvature technique and the accompanying lattice strain was measured by cos2αsin2ψ method. The average effective elastic constant (AEXEC) could be attained by substituting the residual stress into the slope of AXS vs. cos2αsin2ψ plot. The AEXEC was served as an indicator to validate the AXS measurement. By substituting AEXEC in conventional sin2ψ XRD stress measurement, the deviation of the result from the stress obtained by laser curvature method was less than 7%, indicating that AXS effectively reduced the uncertainty in XECs and thus increased the accuracy of stress measurement. The concept of increasing sampling volume was also confirmed using synchrotron X-ray source, where the statistical fluctuation in X-ray strain could be further reduced by performing the measurement at all azimuthal direction. The experimental results showed that the uncertainty on XEC measurement by sin2ψ method was less than 10%, if sufficient sampling volume was provided. Furthermore, using AXS and elastic constant measured by nanoindentation (ENIP) to calculate X-ray stress, the stress deviation from that by laser curvature method could be substantially reduced even down to 3% with sufficient sampling points. Therefore, AXS may serve as a convenient parameter, when combining with ENIP, in X-ray stress measurement, by which residual stress of hard coatings comparable to that by laser curvature method can be obtained without using XECs.

Processing and Properties of Niobia-Doped Alumina Sintered at 1400&lt;sup&gt;o&lt;/sup&gt;C

Niobia is used as a sintering additive in alumina processing because it lowers the sintering temperature. This work investigated the influence of sintering dwell time at 1400oC on the properties of 4 wt% niobia doped alumina. The sintered ceramics were characterized by scanning electron microscopy (SEM), and X rays diffraction (XRD) with Rietveld refinement. Measurements of density, average grain size, hardness, and elastic constants were also performed. The results showed that the porosity depend on the time sintering and this influence on the elastic properties. Longer sintering times improved densification and with this the Young's Modulus.

Molecular structure and elastic properties of thermotropic liquid crystals: Integrated molecular dynamics—Statistical mechanical theory vs molecular field approach

The connection between the molecular structure of liquid crystals and their elastic properties, which control the director deformations relevant for electro-optic applications, remains a challenging objective for theories and computations. Here, we compare two methods that have been proposed to this purpose, both characterized by a detailed molecular level description. One is an integrated molecular dynamics-statistical mechanical approach, where the bulk elastic constants of nematics are calculated from the direct correlation function (DCFs) and the single molecule orientational distribution function [D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1973)]. The latter is obtained from atomistic molecular dynamics trajectories, together with the radial distribution function, from which the DCF is then determined by solving the Ornstein-Zernike equation. The other approach is based on a molecular field theory, where the potential of mean torque experienced by a mesogen in the liquid crystal phase is parameterized according to its molecular surface. In this case, the calculation of elastic constants is combined with the Monte Carlo sampling of single molecule conformations. Using these different approaches, but the same description, at the level of molecular geometry and torsional potentials, we have investigated the elastic properties of the nematic phase of two typical mesogens, 4'-n-pentyloxy-4-cyanobiphenyl and 4'-n-heptyloxy-4-cyanobiphenyl. Both methods yield K3(bend) >K1 (splay) >K2 (twist), although there are some discrepancies in the average elastic constants and in their anisotropy. These are interpreted in terms of the different approximations and the different ways of accounting for the structural properties of molecules in the two approaches. In general, the results point to the role of the molecular shape, which is modulated by the conformational freedom and cannot be fully accounted for by a single descriptor such as the aspect ratio.

Mechanical Model and Finite-Element Simulation Analysis of Hemp Stalk

It is assumed that hemp stalk, bast fibre and xylem are the geometrical model of hollow cylinder on the basis of getting the average size and the average elastic constants. The stress and strain distributions of hemp stalk under the transversely even-distributed load are analyzed through ANSYS software. According to the geometrical size and the material attributes of peeling roller, the dynamic simulation model of roller and hemp stalk is built.

Ultrasonic and structural characterization of anisotropic austenitic stainless steel welds: Towards a higher reliability in ultrasonic non-destructive testing

The non-destructive testing of austenitic stainless steel welds of the primary coolant piping system is a significant problem for the nuclear industry. Ultrasonic techniques would be very helpful to detect, locate and size potential defects. Unfortunately, austenitic welds are coarse-grained, heterogeneous and anisotropic. This leads to aberration and scattering of the ultrasonic waves. In this paper, we present several experimental results of ultrasonic testing of two austenitic welds exhibiting high anisotropy. In order to explain the observed display of wave propagation phenomena such as beam deviation, we use finite element modeling. The modeling is associated with a complete characterization of the inspected welds. Two essential characteristics of the welds are determined: the average elastic constants of the weld and the grain orientations. The capability of the model is illustrated in different testing configurations. This work associating structural characterization and modeling shows that a better understanding of the phenomena of ultrasonic propagation should allow the interpretation and reliability of the industrial inspections of heterogeneous anisotropic welds to be improved .

Excess of low frequency vibrational modes and glass transition: A molecular dynamics study for soft spheres at constant pressure

Using molecular dynamics at constant pressure, the relationship between the excess of low frequency vibrational modes (known as the boson peak) and the glass transition is investigated for a truncated Lennard-Jones potential. It is observed that the quadratic mean displacement is enhanced by such modes, as predicted using a harmonic Hamiltonian for metastable states. As a result, glasses loose mechanical stability at lower temperatures than the corresponding crystal, since the Lindemann criteria are observed, as is also deduced from density functional theory. Finally, we found that the average force and elastic constant are reduced in the glass due to such excess of modes. The ratio between average elastic constants can be approximated using the 2/3 rule between melting and glass transition temperatures.

Elastic constants and thermal expansion averages of a nontextured polycrystal

This paper gives expressions for the overall average elastic constants and thermal expansion coefficients of a polycrystal in terms of its single crystal components. The polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. Upper and lower bounds for the averages are easily found by assuming a uniform strain or stress. The upper bound follows from Voigt’s assumption that the total strain is uniform within the polycrystal while the lower bound follows from Reuss’ original assumption that the stress is uniform. A self-consistent estimate for the averages can be found if it is assumed that the overall response of the polycrystal is the same as the average response of each crystallite. The derivation method is based on Eshelby’s theory of inclusions and inhomogeneities. We define an equivalent inclusion, which gives an expression for the strain disturbance of the inhomogeneity when external fields are applied. The equivalent inclusion is then used to represent the crystallites. For the self-consistent model the average response of the grains has to be the same as the overall response of the material, or the average strain disturbance must vanish. The result is an implicit equation for the average polycrystal elastic constants and an explicit equation for the average thermal expansion coefficients. For the particular case of cubic symmetry the results can be reduced to a cubic equation for the selfconsistent shear modulus. For lower symmetry crystals it is best to calculate the self-consistent bulk and shear modulus numerically.

Cell Motility and Local Viscoelasticity of Fibroblasts

Viscoelastic changes of the lamellipodial actin cytoskeleton are a fundamental element of cell motility. Thus, the correlation between the local viscoelastic properties of the lamellipodium (including the transitional region to the cell body) and the speed of lamellipodial extension is studied for normal and malignantly transformed fibroblasts. Using our atomic force microscopy-based microrheology technique, we found different mechanical properties between the lamellipodia of malignantly transformed fibroblasts (H-ras transformed and SV-T2 fibroblasts) and normal fibroblasts (BALB 3T3 fibroblasts). The average elastic constants, K, in the leading edge of SV-T2 fibroblasts (0.48 ± 0.51 kPa) and of H-ras transformed fibroblasts (0.42 ± 0.35 kPa) are significantly lower than that of BALB 3T3 fibroblasts (1.01 ± 0.40 kPa). The analysis of time-lapse phase contrast images shows that the decrease in the elastic constant, K, for malignantly transformed fibroblasts is correlated with the enhanced motility of the lamellipodium. The measured mean speeds are 6.1 ± 4.5 μ m/h for BALB 3T3 fibroblasts, 13.1 ± 5.2 μm/h for SV-T2 fibroblasts, and 26.2 ± 11.5 μm/h for H-ras fibroblasts. Furthermore, the elastic constant, K, increases toward the cell body in many instances which coincide with an increase in actin filament density toward the cell body. The correlation between the enhanced motility and the decrease in viscoelastic moduli supports the Elastic Brownian Ratchet model for driving lamellipodia extension.

Effects of small neutral osmolytes on the supercoiling free energy and intrinsic twist of p30delta DNA.

Both theory and experiments are employed to investigate the effects of small neutral osmolytes on the average intrinsic twist (l0), the torsion and bending elastic constants, and the twist energy parameter (ET) that governs the supercoiling free energy. The experimental data for ethylene glycol and acetamide at 37 degrees C suggest, and are interpreted in terms of, a model wherein the DNA exhibits an equilibrium between two distinct conformational states that possess different numbers of bound water molecules and exhibit different intrinsic twists and torsion and bending elastic constants. Expressions are derived to relate the effective ET and l0 to the equilibrium constant, water activity (aw), and number (n) of bound water molecules released per cooperative domain undergoing the two-state transition. The variations of l0 and ET with -ln(aw) are similar for acetamide and ethylene glycol at 37 degrees C. Fitting the theory to those data yields the range n = 103-125 for ethylene glycol and n = 71-113 for acetamide, depending on the assumed value of ET for the dehydrated state. The cooperative domain size of the two-state transition is estimated to exceed about 25-30 base pairs (bp). Between 0 and 19.4 w/v % ethylene glycol, the torsion elastic constant, measured by time-resolved fluorescence polarization anisotropy (FPA), increases by 1.37-fold, whereas the measured ET decreases by 1.15-fold over that same range. The implied decrease in bending rigidity over that range is by a factor of about 0.7. The variations of l0 and ET with increasing -ln(aw) due to added ethylene glycol at 37 degrees C are far smaller than the corresponding variations observed previously at 14 and 15 degrees C. However, at 21 degrees C, upon adding either ethylene glycol or acetamide, l0 and ET initially decline steeply with increasing -ln(aw), with slopes possibly comparable to those seen at 14 and 15 degrees C, but then flatten out and follow curves similar to those at 37 degrees C. Possible origins of such mixed behavior are discussed. The effects of betaine at both 37 and 21 degrees C differ qualitatively and quantitatively in various respects from those of ethylene glycol and acetamide. Upon adding sucrose, l0 initially jumps to higher plateaus at both 37 and 21 degrees C, but its effects on ET cannot be reliably assessed, due to the limited range of -ln(aw).

Local elastic constants in thin films of an fcc crystal.

In this work we present a formalism for the calculation of the local elastic constants in inhomogeneous systems based on a method of planes. Unlike previous work, this formalism does not require the partitioning of the system into a set of finite volumes over which average elastic constants are calculated. Results for the calculation of the local elastic constants of a nearest-neighbor Lennard-Jones fcc crystal in the bulk and in a thin film are presented. The local constants are calculated at exact planes of the (001) face of the crystal. The average elastic constants of the bulk system are also computed and are consistent with the local constants. Additionally we present the local stress profiles in the thin film when a small uniaxial strain is applied. The resulting stress profile compares favorably with the stress profile predicted via the local elastic constants. The surface melting of a model for argon for which experimental and simulation data are available is also studied within the framework of this formalism.

Self-Consistent Calculation of the X-Ray Elastic Constants of Polycrystalline Materials for Arbitrary Crystal Symmetry

For the calculation of load or residual stresses from measured strain data by means of x-rays or neutrons, the x-ray elastic constants are required. Usually they are calculated from the corresponding single crystal data assuming some models such as Voigt(strain compatibility), Reuss(stress equilibrium), Hill(arithmetic average of Voigt and Reuss) or Kroner. All these models, however, make assumptions of the coupling of the grains. Historically, the Voigt and Reuss limits have been investigated first assuming constant strain respectively constant stress in the grains. Hill proved that the average elastic constants for a macroscopically isotropic aggregate should fall within the limits imposed by the Reuss and Voigt models Although the Kroner model is often recommend for the calculation of the x-ray elastic constants, it assumes the polycrystalline material to behave as a model or perfect disorder. In this paper, the finite element method is used to guarantee both, stress equilibrium and strain compatibility across the grain boundaries. The polycrystalline material is assumed to behave as a three-dimensional mixture of macroscopic isotropic and fully orthotropic grains under elastic loading where the relative ratio of both types of grains can be varied between 0 and 100%. The macroscopically isotropic bulk values are calculated by an iteration procedure which was first proposed by Kneer. The method is applicable to materials with a random texture by calculating the hkl dependent quasiisotropic x-ray elastic constants as well as to specimens with a given texture using the information of the Orientation Distribution Function (ODF) by calculating the corresponding hkl- and orientation dependent stress factors. All crystal structures from cubic to triclinic are supported. The method is demonstrated on monoclinic SiO 2 with a random texture.

A Brillouin scattering study of the effect of chemical passivation on the elastic properties of porous silicon

Brillouin scattering has been performed to probe acoustic waves in porous silicon films that have been chemically modified with either 1-decene, decyl aldehyde, undecylenic acid, or ethyl undecylenate. The shift in the frequencies of acoustic modes in the passivated porous silicon samples, relative to those in freshly prepared porous silicon, is different for different chemical modifiers. The magnitude of the frequency shift is qualitatively correlated with the change, caused by the passivation, in the average densities and elastic constants of the samples.