Showing papers on "Elastic modulus published in 1982"
TL;DR: In this paper, a simple indentation technique for measuring the hardness-to-modulus ratio of elastic/plastic materials was developed, which is based on measurement of the elastic recovery of the in-surface dimensions of a Knoop indentation.
Abstract: A simple indentation technique for measuring the hardness-to-modulus ratio of elastic/plastic materials was developed. The method, which is based on measurement of the elastic recovery of the in-surface dimensions of a Knoop indentation, allows ready evaluation of the hardness-to-modulus ratio to an accuracy better than 10%.
473 citations
TL;DR: In this article, a new approach for analyzing indentation plasticity and for determining indentation stress fields is presented, which permits relations to be established between material properties (notably hardness, yield strength, and elastic modulus) and the dimensions of the indentation and plastic zone.
Abstract: A new approach for analyzing indentation plasticity and for determining indentation stress fields is presented. The analysis permits relations to be established between material properties (notably hardness, yield strength, and elastic modulus) and the dimensions of the indentation and plastic zone. The predictions are demonstrated to correlate with observations performed on a wide range of materials. The indentation stress fields are computed along trajectories pertinent to three dominant indentation crack systems: radial, median, and lateral cracks. The peak load and residual tensile stresses are shown to be consistent with observed trends in indentation fracture.
380 citations
TL;DR: In this article, the overall elastic moduli of a composite with an isotropic elastic matrix containing periodically distributed (anisotropic) inclusions or voids, can be expressed in terms of several infinite series which only depend on the geometry of the inclusions and voids.
268 citations
TL;DR: In this paper, the authors investigated the ultrasonic properties of unconsolidated (loose) glass beads and of lightly fused (consolidated) glass bead when the pore space is saturated with water.
Abstract: We have investigated the ultrasonic properties of unconsolidated (loose) glass beads and of lightly fused (consolidated) glass beads when the pore space is saturated with water. At a frequency of 500 kHz we have observed a single compressional wave in the former whose speed is 1.79 km/s and two distinct compressional waves with speeds 2.81 km/s and 0.96 km/s in the latter. The Biot theory is shown to give an accurate description of this phenomenon. We also analyze the acoustics of low temperature He ii in packed powder superleaks; either the fast wave for unconsolidated systems or the slow wave in a highly consolidated (fused) frame may be considered to be the 4th sound mode. In all such systems, the acoustic properties can be very simply understood by considering the velocities of propagation as continuous functions of the elastic moduli of the solid skeletal frames.
245 citations
TL;DR: In this article, the single-crystal elastic moduli of stishovite have been determined experimentally from measured Brillouin scattering spectra and the estimated aggregate (Voigt-Reuss-Hill) adiabatic moduli are K = 3.16 ± 0.04 in units of mbar.
Abstract: The single-crystal elastic moduli of stishovite have been determined experimentally from measured Brillouin scattering spectra. They are C11 = 4.53 ± 0.04, C33 = 7.76 ± 0.05; C44 = 2.52 ± 0.02, C66 = 3.02 ± 0.03; and C12 = 2.11 ± 0.05, C13 = 2.03 ± 0.04 in units of mbar. The estimated aggregate (Voigt-Reuss-Hill) adiabatic moduli are K = 3.16 ± 0.04 and μ = 2.20 ± .03 mbar. Previous values of the isothermal bulk modulus, obtained from hydrostatic compression experiments, are in agreement with the Reuss value of KT = 3.06 ± .04 mbar (as corrected to isothermal conditions). Taken together, these results suggest that the pressure derivative of the bulk modulus for stishovite is low relative to other rutile structure oxides.
224 citations
TL;DR: In this paper, the internal strains associated with the martensitic phase transformation of zirconia were used to introduce microcracks into Al2O3/ZrO2 composites.
Abstract: The internal strains asSociated with the martensitic phase transformation of zirconia were used to introduce microcracks into Al2O3/ZrO2 composites. The degree of transformation was found to be dependent on the volume fraction of ZrO2 and its size, the latter of which could be controlled by suitable heat treatments. The microstructural changes that occurred during the heat treatments were studied using quantitative microscopy and X-ray diffraction. For materials containing more than 7.5 vol% Zr02, the ZrO2 particles were found to pin the Al2O3 grain boundaries, thus limiting the Al2O3 grain growth. The limiting grain size was found to be dependent on size and volume fraction of ZrO2. Heat treatments for the higher volume fraction materials (>7.5 vol% ZrO2) caused micro-structural changes which resulted in increased amounts of monoclinic ZrO2 at room temperature; elastic modulus measurements indicated that this was occurring concurrently with microcracking. By combining the ZrO2 grain-size distributions with the X-ray analysis it was possible to calculate the critical ZrO2 size required for the transformation. The critical size was found to decrease with increasing amounts of ZrO2. Hardness and indentation fracture toughness were measured on the composites. Grain fragmentation was observed at the edge of the indentations and microcracks were observed directly, using an AgNO3 decoration technique, near the indentations.
207 citations
TL;DR: In this paper, the elastic properties of apatite solids were determined from measurements of elastic wave velocities through powders under pressure, and these elastic constants were used to model the elastic behaviour of a two-phase composite material having one phase more rigid than the other by a factor of 2.4.
Abstract: One of the prime motives for studying the elastic properties of the apatites stems from the occurrence of hydroxyapatite, OHAp, in calcified tissue. In this paper the isotropic elastic contents of crystalline apatite solids are determined from measurements of elastic wave velocities through powders under pressure. Once obtained, these elastic constants are used to model the elastic behaviour of a two-phase composite material having one phase more rigid than the other by a factor of 2.4. The results are then used in a general discussion of the probable order of magnitude of the elastic constants of the organic non-crystalline phase in bones and teeth, under the assumption of a two-phase system.
201 citations
TL;DR: Continuous silicon carbide fiber yarn has been used as a reinforcement for borosilicate and 96% silica glass matrices as discussed by the authors, and the resultant composites exhibit excellent levels of strength and elastic modulus up to temperatures of 600 ˚ C and 1100 ǫ C, respectively.
Abstract: Continuous silicon carbide fibre yarn has been used as a reinforcement for borosilicate and 96% silica glass matrices. The resultant composites exhibit excellent levels of strength and elastic modulus up to temperatures of 600‡ C and 1100‡ C, respectively. At higher temperatures excessive matrix softening causes a significant reduction in composite flexural strength.
187 citations
TL;DR: In this article, the authors show how the McCoy bounds on the effective shear modulus of a statistically isotropic composite can be simplified and expressed in terms of the volume fraction, f 1, and two geometric parameters.
Abstract: W e show in detail how the McCoy bounds on the effective shear modulus of a statistically isotropic composite, can be simplified and expressed in terms of the volume fraction, f 1 , and two geometric parameters. ζ 1 and η 1 . We simplify Silnutzer's bounds on the effective elastic moduli of fibre-reinforced composites and find they can be expressed in terms f 1 and two geometric parameters, ζ' 1 and η' 1 . The parameter ζ' 1 also determines bounds on the transport and optical constants of such composites. Also, the Elsayed-McCoy bounds on the transport properties of fibre-reinforced, symmetric-cell materials are shown to depend on three geometric parameters.
178 citations
TL;DR: In this paper, the Young's modulus of the Al3 Li and AlLi intermetallic phases are estimated to be 96 GPa and 105 GPa respectively, the major contribution to this increased modulus arises from lithium in solid solution.
Abstract: Young's modulus measurements have been made on Al-Li alloys containing up to 32 at % lithium, in an attempt to determine the cause of the high modulus that characterizes this potentially important alloy system. In alloys of commercial interest (7–11 at %, 2–3 wt % lithium) the modulus is in the range 79 to 83 GPa, the actual value depending on heat-treatment conditions. The major contribution to this increased modulus arises from lithium in solid solution. The Young's moduli of the Al3 Li and AlLi intermetallic phases are estimated to be 96 GPa and 105 GPa respectively. Additions of magnesium to the Al-Li system produce a small decrease of the modulus, e.g. 4.5 at % (4 wt %) magnesium reduces the modulus by approximately 2 GPa.
147 citations
TL;DR: In this article, the effective moduli of a two-component composite material were derived up to fourth order in the sense that the effective bulk modulus involved three microstructural parameters whereas eight parameters were needed in the bounds on the effective shear modulus.
Abstract: Based on the perturbation solution, we derive new bounds on the effective moduli of a two-component composite material which are exact up to fourth order in $\delta\mu$ = $\mu\_1$ - $\mu\_2$ and $\delta\kappa$ = $\kappa\_1$ - $\kappa\_2$, where $\mu\_i$ and $\kappa\_i$, i = 1, 2, are the shear and bulk modulus, respectively, of the phases. The bounds on the effective bulk modulus involve three microstructural parameters whereas eight parameters are needed in the bounds on the effective shear modulus. For engineering calculations, we recommend the third-order bounds on the effective shear modulus which require only two geometrical parameters. We show in detail how Hashin-Shtrikman's bounds can be extended and how Walpole's bounds can be improved using two inequalities on the two geometrical parameters that appear in the third-order bounds on the effective shear modulus. The third- and fourth-order bounds on the effective moduli are shown to be more restrictive than, or at worst, coincident with, existing bounds due to Hashin and Shtrikman, McCoy, Beran and Molyneux and Walpole.
TL;DR: In this paper, a self-consistent theory for the determination of elastic moduli of cracked solids is presented, and worked out for an isotropic distribution of cracks.
Abstract: A self-consistent theory for the determination of elastic moduli of cracked solids is presented, and worked out for an isotropic distribution of cracks. A missing ingredient of the previous theory of O'Connell and Budiansky is the correct accounting of crack interaction energy. The new theory leads to a set of differential equations for the effective elastic moduli which are easily solved. The solutions always lie within the physical range, and show that the influence of the cracks on the effective moduli is considerably less than has been previously calculated.
TL;DR: In this article, the stresses of thermally grown and chemically vapor deposited (CVD) silicon dioxide were measured by the cantilever beam technique using x-ray diffraction, and it was concluded that their average linear thermal expansion coefficient in the temperature range of −170-115 C is 4×10−6 °C−1, while their biaxial elastic modulus is only 4.6-5.1×1011 dyn/cm2.
Abstract: The stresses of thermally grown as well as chemically vapor deposited (CVD) silicon dioxide were measured by the cantilever beam technique using x‐ray diffraction. Thermally grown oxide shows reversible stress changes upon heating or cooling of the films. The linear thermal expansion of such films is similar to that of bulk vitreous silica, 5×10−7 °C−1, the biaxial elastic modulus was found to be 6.3×1011 dyn/cm2. CVD oxides show extensive hysteresis in the stress‐temperature curves when tested in ambient air. From stress measurements of such films, deposited on Si and GaAs, it was concluded that their average linear thermal expansion coefficient in the temperature range of −170–115 °C is 4×10−6 °C−1, much higher than that of thermally grown oxide, while their biaxial elastic modulus is only 4.6–5.1×1011 dyn/cm2. The stress in such films was found to increase when the films were exposed to a dry ambient or vacuum. The time constant for this change was found to be several minutes at room temperature.
TL;DR: In this paper, the elastic constants of single crystal tungsten monocarbide were determined using highfrequency (20 to 50 mHz) ultrasonic pulse-echo measurements.
Abstract: The elastic constants of single crystal tungsten monocarbide were determined using highfrequency (20 to 50 mHz) ultrasonic pulse-echo measurements. The measured values from this study are a full order of magnitude lower than the previously reported values estimated from X-ray elastic constants. The elastic modulus of polycrystalline tungsten carbide was also measured to verify the accuracy of the ultrasonic method used.
TL;DR: Aluminum-silicon carbide whisker composites containing nominally 3 to 5 pct Li in the matrix alloys have been fabricated and tested as mentioned in this paper, and they have been conducted at room temperature and compression creep tests at elevated temperatures.
Abstract: Aluminum-silicon carbide whisker composites containing nominally 3 to 5 pct Li in the matrix alloys have been fabricated and tested. Tensile and compression tests have been conducted at room temperature, and compression creep tests have been conducted at elevated temperatures. Lithium additions were found to increase the strengthening effect of silicon carbide whiskers at room and elevated temperatures. Lithium also reduced the density of the composites and increased the elastic modulus. Transmission electron microscopy showed no obvious chemical reaction between the whiskers and the aluminum-lithium alloy matrix.
TL;DR: The orthorhombic layer theory as mentioned in this paper has been used to model a stratified rock mass as a series of parallel layers, each of which is represented by a homogeneous orthormbic elastic material.
TL;DR: The glasses were translucent to transparent to transparent, very hard, and had elastic moduli as high as 186 GPa as mentioned in this paper, which is a very high level of elasticity.
Abstract: Glasses containing up to 15 at.% N were prepared and tested. The glasses were translucent to transparent, very hard, and had elastic moduli as high as 186 GPa.
TL;DR: In this paper, a contribution to the unusual changes of the elastic constants of composition-modulated alloys can be obtained by extending the effects of screening singularities on the atomic pair potential following Krivoglaz and Moss.
Abstract: A contribution to the unusual changes of the elastic constants of composition‐modulated alloys can be obtained by extending the effects of screening singularities on the atomic pair potential following Krivoglaz and Moss. The formalism is presented, and the effect of the shape of Fermi surface on this elastic anomaly is discussed. Agreement is found between the theory and the observed enhancement of elastic moduli in foils with composition modulations. Predictions are offered as to which systems might produce large and small changes, if this is the major contributing factor.
TL;DR: In this paper, a method is developed which predicts the elastic moduli of homogeneous isotropic two-phase materials of arbitrary phase geometry using three parameters, the magnitudes of which characterize any type of composite (particulate, phase-symmetric powder materials etc.).
TL;DR: Using unfilled resins as bonding agents between the composites and enamel resulted in increased bond strength with half of the Composites, and mechanical properties that were most highly correlated with bond strength to enamel were proportional limit and elastic modulus.
Abstract: The strength of bonding of dental composites to enamel was measured in shear. The compressive strength, proportional limit, elastic modulus, and tensile strength of the composites were measured for correlation with the bond strength. Conventional and microfilled composites with a range of filler concentrations were studied. The densities of the composites and their fillers and the concentrations of the fillers were determined. The mechanical properties that were most highly correlated with bond strength to enamel were proportional limit and elastic modulus. Tensile strength and filler concentration had lower correlation coefficients, and compressive strength was not correlated with bond strength. Using unfilled resins as bonding agents between the composites and enamel resulted in increased bond strength with half of the composites.
TL;DR: In this paper, it was demonstrated that a unique form of composite material can be achieved by reinforcing glass matrices with discontinuous graphite fibres, which exhibited high strength, high fracture toughness, low density and low thermal expansion coefficient.
Abstract: It is demonstrated that a unique form of composite material can be achieved by reinforcing glass matrices with discontinuous graphite fibres. The graphite fibres were utilized in the form of a paper, purchased in large sheets, and composites were formed by hot-pressing glass-powder-impregnated paper plys. The resultant composites exhibit high strength, high fracture toughness (compared to ceramics), low density and low thermal expansion coefficient. Of particular note is the unique tensile stress-strain curve achieved which exhibits both high strength and high failure strain. Its very non-linear shape differs markedly from that of either the unreinforced glass or a similarly reinforced epoxymatrix composite. In addition, the elastic modulus of the resultant composite, despite being reinforced with a high stiffness fibre, is lower than that of the parent matrix resulting in an unusually compliant ceramic material.
TL;DR: In this paper, the shear modulus of two-dimensional electrons at the surface of liquid helium was deduced from measurements of the finite frequency of the $k √ √ n −1/n −2/n 0$ limit of the coupled electron-substrate transverse sound mode.
Abstract: The shear modulus of two-dimensional electrons at the surface of liquid helium is deduced from measurements of the finite frequency of the $k\ensuremath{\rightarrow}0$ limit of the coupled electron-substrate transverse sound mode. Its behavior on the approach to melting is compatible with the Kosterlitz-Thouless model for two-dimensional melting.
TL;DR: In this paper, the 3D elastic moduli were measured from testing simple ten sion, compression, and shear specimens, and the bounds of Poisson's ratio for transversely isotropic materials were shown to be zero and unity.
Abstract: The 3-dimensional elastic moduli are measured from testing simple ten sion, compression, and shear specimens. The results are in good agreement with the isotropic and reciprocal relations for a transversely isotropic material. Existing data obtained by ultrasonic techniques and another mechanical testing technique compare well with our data. The bounds of Poisson's ratio for transversely isotropic materials are shown to be zero and unity.
TL;DR: In this article, the impact force of a fruit falling on a rigid plate was analyzed using fast Fourier transform algorithms and it was found that there exists a relationship between the magnitude of the force components and firmness parameters of the fruit as given by the elastic modulus or Magness-Taylor values.
Abstract: THE application of fast Fourier transform algorithms to the impact force of a fruit falling on a rigid plate was discussed. Analysis of the force in the frequency do-main indicated that there exists a relationship between the magnitude of the force components and firmness parameters of the fruit as given by the elastic modulus or Magness-Taylor values. It was found that non-destructive sorting for firmness could be accomplished based on the electronic processing of the fruit impact force measurement.
TL;DR: In this article, high-density polyethylene was filled with chalk in various concentrations ranging from 10% to 60% by weight, and the mechanical properties of these composites showed that high density polyethylenes with chalk have quite high ultimate elongation and impact strength.
Abstract: High-density polyethylene was filled with chalk in various concentrations ranging from 10% to 60% by weight. Ethylene oxide oligomer Mw = 300 was used as a liquid modifier for chalk in the amount 0 ÷ 20 wt % of the filler. The mechanical properties of these composites showed that high density polyethylene filled with chalk have quite high ultimate elongation and impact strength while their elastic modulus and tensile strength are very near to those values for pure high density polyethylene. On the base of mechanical properties and microscopical observations, the crack and microcrack damping is attributed to the presence of ethylene oxide oligomer.
TL;DR: In this article, the elastic moduli and fracture toughness of a series of PbO-ZnO-B2O3 glasses were measured for different ratios and for B2O 3 contents from 30 to 70 mol%.
Abstract: The elastic moduli and fracture toughnesses of a series of PbO-ZnO-B2O3 glasses were measured for different PbO/ZnO ratios and for B2O3 contents from 30 to 70 mol%. Substituting ZnO for PbO increased both the elastic modulus and fracture toughness at all B2O3 levels with the fracture toughness being related to the elastic modulus. Structural effects on these properties are discussed.
TL;DR: In this paper, the elastic compressibility of gas vesicles isolated from Anabaena flos-aquae has been measured with a specially constructed apparatus, which was contained in a glass tube, closed at one end with a piston allowing volume adjustment and attached at the other end to a microcapillary, and was subjected to pressure from compressed air.
Abstract: Theelastic compressibility of gas vesicles isolated from Anabaena flos-aquae has been measured with a specially constructed apparatus. The gas vesicle suspension was contained in a glass tube, closed at one end with a piston allowing volume adjustment and attached at the other end to a microcapillary, and was subjected to pressure from compressed air. The elastic compressibility of the gas vesicle suspension was determined by applying or removing pressure and measuring the ensuing displacement of the meniscus in the capillary with a vernier microscope. After allowing for the compressibility of the compression tube and of water in the suspension, the compressibility of the intact gas vesicles has been calculated to be 0.00155 bar -1 , and the elastic bulk modulus 645 bar. The elastic modulus of the protein that forms the gas vesicle wall can also be calculated from these measurements; it is 27500 bar. These measurements confirm that the gas vesicle is a rigid structure and show that the buoyancy provided by them will be relatively unaffected by pressures that do not actually cause gas vesicle collapse. The apparatus described can also be used to provide a direct measurement of the volume of gas vesicle gas space present in a suspension of a gas-vacuolate organism, and to investigate the gas vesicle critical collapse pressure. Gas vesicles appear to collapse by instability failure but the pressure at which this occurs, about 6 bar, is higher than would be predicted from knowledge of the dimensions and elastic modulus of the gas vesicle wall. This supports the idea that the orientation of the ribs, which form the structure, provides ring-stiffening support.