Showing papers on "Elastic modulus published in 1986"

A method for interpreting the data from depth-sensing indentation instruments

Abstract: Depth-sensing indentation instruments provide a means for studying the elastic and plastic properties of thin films. A method for obtaining hardness and Young’s modulus from the data obtained from these types of instruments is described. Elastic displacements are determined from the data obtained during unloading of the indentation. Young’s modulus can be calculated from these measurements. In addition, the elastic contribution to the total displacement can be removed in order to calculate hardness. Determination of the exact shape of the indenter at the tip is critical to the measurement of both hardness and elastic modulus for indentation depths less than a micron. Hardness is shown to depend on strain rate, especially when the hardness values are calculated from the data along the loading curves.

Fatigue of composites-fatigue modulus concept and life prediction

Abstract: Fatigue behavior of glass fiber reinforced epoxy composite materials has been studied analytically. A new concept called "fatigue modulus," which is defined as a slope of applied stress and resultant strain at a specific cycle is introduced. Fatigue modulus degradation is studied using an assumption that the fatigue modulus degrada tion rate follows a power function of fatigue cycle. Theoretical equation for predicting fatigue life is formulated using the fatigue modulus and its degradation rate. This rela tion is simplified by strain failure criterion for the practical application. It is proved that the final formula predicts the fatigue life of a glass fiber epoxy composite material better than S-N curve or Basquin's relation. An attempt is made to find the relation ship between fatigue modulus and elastic modulus by the geometric relation from stress-strain curve under the cyclic loading.

Elasticity of enstatite and its relationship to crystal structure

Abstract: The nine adiabatic single-crystal elastic moduli of a natural orthopyroxene of enstatite composition (Mg0.94Fe0.06SiO3) have been measured at ambient conditions by Brillouin spectroscopy. The single-crystal elastic stiffnesses in gigapascals (GPa) are C11 = 229.3 ± 1.1; C22 = 167.0 ± 1.1; C33 = 193.9 ± 1.5; C44 = 79.7 ± 0.7; C55 = 76.1 ± 0.6; C66 = 77.1 ± 0.9; C12 = 73.6 ± 1.7; C13 = 49.8 ± 1.6; and C23 = 46.6 ± 1.6. The average Hashin-Shtrikman bulk and shear moduli are 102.2 and 73.9 GPa, respectively. The results of this study are generally consistent with those obtained for other Mg-rich pyroxenes. Some of the individual moduli along the enstatite-ferrosilite join can be related to specific chemical and structural features. The most variable modulus is C33, and it appears to be a complicated function of both chemistry and structure. Its magnitude relative to C11 is most easily explained by the presence or absence of more than one tetrahedral chain. For orthopyroxenes of intermediate composition C11 is higher than expected, probably due to a combination of the effects of site ordering and impurities in the Ml site. The third longitudinal modulus, C22, is observed to increase linearly as a function of enstatite composition from En0 to En100. An alternative interpretation for C11 and C22 is that between En100 and En50, C11 is constant and C22 decreases linearly with increasing iron content, while between En50 and En0, C11 decreases linearly and C22 is constant. The shear and off-diagonal moduli vary nonsystematically but tend to vary in similar ways. With the exception of C12, the averaged moduli also show nonsystematic variations. Cation site ordering appears to strongly affect C44. The modulus C11 is also nonsystematic but for reasons which are not obvious. Our results are consistent with the interpretation that the bulk modulus does not vary with composition whereas the shear modulus does so in a linear fashion.

Mechanics of low density materials

Abstract: Mechanics analyses are used to derive the effective elastic moduli for low density materials. Both open cell and closed cell geometric models are employed in the case of isotropic media. The five independent effective moduli are derived for a low density transversely isotropic medium. Compressive strength, as defined by elastic stability, is also derived for open cell and closed cell isotropic materials. The theoretical results are compared with some experimental results, and also are assessed with respect to previous work.

Composites for use in posterior teeth: mechanical properties tested under dry and wet conditions.

Abstract: The purpose of this investigation was to determine some mechanical properties of eight different posterior composites, and how they are affected by water sorption. Creep characteristics in compression were expressed as compliance/log time functions. Stress-strain relationship at a constant loading rate was determined both in compression and flexure, and presented as elastic modulus, ultimate strength, and ultimate strain. Water sorption increased creep values for all materials. Generally, the materials with the highest water sorption had the highest increase in creep. Water sorption decreased the elastic modulus and ultimate strength values. The creep values decreased and the elastic modulus increased with increasing quantity of inorganic fillers.

Creep of chemically vapour deposited SiC fibres

Abstract: The creep, thermal expansion, and elastic modulus properties for chemically vapour deposited SiC fibres were measured between 1000 and 1500°C. Creep strain was observed to increase logarithmically with time, monotonically with temperature, and linearly with tensile stress up to 800 MPa. The controlling activation energy was 480 ± 20 kJ mol−1. Thermal pretreatments near 1200 and 145O° C were found to significantly reduce fibre creep. These results coupled with creep recovery observations indicate that below 1400°C fibre creep is anelastic with negligible plastic component. This allowed a simple predictive method to be developed for describing fibre total deformation as a function of time, temperature, and stress. Mechanistic analysis of the property data suggests that fibre creep is the result of β-SiC grain boundary sliding, controlled by a small percentage of free silicon in the grain boundaries.

Elasticity of uvarovite and andradite garnets

Abstract: The adiabatic single-crystal elastic properties of synthetic end-member uvarovite garnet (Ca3Cr2Si3O12) and a natural sample of 96% andradite garnet (Ca3Fe2Si3O12) have been measured at ambient conditions by Brillouin spectroscopy. The bulk modulus (Ks) and shear modulus (μ) of andradite (And) are Ks = 158 ± 2 GPa, μ = 90 ± 1 GPa, and those of uvarovite (Uv) are Ks = 165 ± 2 GPa and μ = 94 ± 1 GPa. Observed trends of the single-crystal elastic moduli (Cij) as a function of composition, and specifically the deviation from the Cauchy relation c12 = C44 are analogous between the Ca-bearing garnets grossular (Gr = Ca3Al2Si3O12)-And-Uv and other chemical systems such as the rock salt and corundum structure oxides, whereas other silicate garnets exhibit distinctly different behavior. Ks of andradite is substantially higher than previously estimated from data on garnet solid solutions. Garnets on the Gr-And join show a pronounced minimum in the Ks-composition relationship at a composition of approximately Gr24And76, indicating that ideal linear mixing of end-member elastic properties is inadequate to explain the elasticity of garnet solid solutions. The elastic properties of Gr-And and Al2O3-Cr2O3 solid solutions can be explained by incorporating a composition-dependent volume of mixing term into the expression for solid-solution elasticity. An evaluation of elasticity systematics relating the bulk sound speed and mean atomic weight, or Ks and molar volume, indicates that these relationships yield closer estimates of garnet elastic properties than does the seismic equation of state of Anderson (1967).

Frequency and temperature dependence of elastic moduli of polymers

Abstract: The frequency and temperature dependence of the elastic moduli of a number of commercially available polymers has been studied in the temperature range of 0–35 °C and for frequencies 102–106 Hz. Away from transitions a significant new relationship has been obtained, i.e., the Young’s modulus of these polymers is proportional to log of frequency. Using this relationship, together with the low and high frequency data, transitions in some of the polymers were identified.

Elastic Stiffness of Three-Dimensional Braided Textile Structural Composites

Abstract: A methodology based upon the concept of fabric unit cell structure and an energy approach has been developed for studying the elastic properties of three-dimensional fabric composites. In general, the unit cell assumes the shape of a parallelepiped with its size determined by the weaving parameters. The yams can assume the positions along the edges and diagonals in a unit cell, and each unit cell is centered around an "interlock" of yams. To facilitate the analysis of complex yam interactions, the unit cell is projected onto mutually orthogonal planes. Strain energies due to yam axial extension, bending, and lateral compression are then considered in the two-dimensional plane weave structures. Closed-form expressions for axial elastic moduli and Poisson's ratios have been derived as functions of fiber volume fractions and fiber orientations. Numerical examples and experimental results of elastic properties for three-dimensional braided composites are presented.

Elastic modulus of polyethylene in the crystal chain direction as measured by X-ray diffraction

Abstract: Mesure du module de reseau cristallin dans la direction de l'axe moleculaire, de films avec differents taux d'etirage (50, 100, 200 et 300)

The elastic constants and structure of the vitreous system Mo-P-O

Abstract: The preparation of glasses with compositions spanning the entire vitreous range obtainable from melting phosphorous pentoxide with molybdenum trioxide, and phosphoric acid with ammonium molybdate, in open crucibles, is described. The second order elastic constants of these Mo-P-O glass systems have been obtained from ultrasonic wave velocity measurements. The most striking features of the results are two discontinuities in the compositional gradient of each elastic modulus, at compositions of ∼53 and 63 mol% MoO3 content. These compositions approximate to those of molybdenum metaphosphate and molybdenum pyrophosphate crystals. A second noteworthy feature is that the elastic moduli display a substantial overall increase with molybdenum content, 36% for bulk and 83% for shear over the entire composition range, even though the Mo-O bond stretching force constant is less than half that of the P-O bond. A detailed qualitative interpretation of these features is made, in terms of the proposed compositional dependence of the crosslink densities of the molybdenum and phosphorus atoms, and the atomic ring sizes.

Process and apparatus for abrasive machining of a wafer-like workpiece

Abstract: A process is provided for bilateral abrasive machining of wafer-like workpieces, especially semiconductor wafers. The process uses carrier disks in which the outer periphery on which the driving forces mesh, is made of a material having a tensile strength of at least 100 N/mm 2 , while in the area that comes into contact with the workpieces to be machined, there is provided a plastic material having an elasticity modulus of from 1.0 to 8.10 4 N/mm 2 .

Computer simulations of the structures of the metallic superlattices Au/Ni and Cu/Ni and their elastic moduli

Abstract: The atomic structures of the FCC/FCC metallic superlattices Au/Ni and Cu/Ni were simulated by the molecular dynamics method, which Morse potentials were used as the interatomic potentials. In contrast to the other previous studies, the authors have treated here incoherent realistic structural models. The simulated structures were used to calculate the Young's modulus along the FCC (111) direction, YY(111), and the biaxial modulus, Yb(111). The biaxial moduli for Au/Ni and Cu/Ni were compared with the experimental results and it is shown that the enhancement of elastic moduli can be well reproduced qualitatively by the authors' incoherent models. The enhancement of elastic moduli can be ascribed to the existence of periodic strain in the multi-layered films.

Elastic Moduli of Silica Gels Prepared with Tetraethoxysilane

Abstract: The elastic moduli of several organometallic silica gels were measured using pulse-superposition interferometry (PSP). A series of gels were prepared under acid-catalyzed conditions where the molar ratio of water to tetraethoxysilane (TEOS) in the sol was varied (4:1, 12:1, 16:1, and 24:1). It was found that the elastic moduli varied systematically with the hydrolysis conditions used to prepare the gels, as well as with the relative humidity used to equilibrate the gels before and during the PSP measurement. The experimental PSP data for the gels were evaluated using a composite model (matrix plus pores) and then the elastic moduli of the gel matrix were determined by applying a correction for porosity based on a self-consistent-scheme (SCS) approximation. The results show that the elastic moduli of the gel matrix also exhibit a systematic dependence upon the preparation conditions, but they always fall below the corresponding values for fused silica. Even when excess water Was used to hydrolyze the TEOS, this did not lead to a fully polymerized silica matrix structure. It is suggested that the lowered matrix moduli values are due to the presence of residual hydroxy and ethoxy groups which are internal to a polymeric structure.

Strength and elastic modulus of a porous brittle solid: an acousto-ultrasonic study

Abstract: The strength and elastic modulus of a porous brittle solid such as gypsum have been studied using an acousto-ultrasonic technique. Acousto-ultrasonics has been found to be a sensitive indicator of strength and porosity which are linearly related to some powers of a stress wave factor. New equations for porosity dependence of ultrasonic velocity, elastic modulus and strength of brittle solids have been proposed.

Multiple scattering of compressional and shear waves by fiber‐reinforced composite materials

Abstract: A multiple scattering formalism using a T matrix to characterize the response of a single fiber to an incident wave is presented to describe P‐ and SV‐wave propagation in a fiber‐reinforced composite. A convenient numerical procedure is then developed to compute the effective elastic moduli, attenuation, and phase velocity as a function of frequency and fiber concentration.

Polyimide film and process for producing the same

Abstract: A polyimide film, which is produced from polyamide acid prepared through the reaction of p-phenylenebis(trimellitic acid monoester anhydride), oxydiphthalic acid dianhydride, p-phenylenediamine, and 4,4′-diaminodiphenylether in an organic solvent, and which has a high elastic modulus, a high elongation, a low coefficient of linear expansion which is not quite different from that of copper, and a low coefficient of hygroscopic expansion.

Relation between the critical exponent of elastic percolation networks and the conductivity and geometrical exponents

Abstract: The author discusses the relation between the critical behaviour of elastic percolation networks in which the bond-bending forces are present, and that of percolation conductivity. They propose that if the elastic and geometrical thresholds of the network are equal, the critical exponent f of the elastic moduli, is given by, f=t+2 nu , where t is the conductivity exponent and nu the correlation length exponent. This predicts that f(d=2) approximately=3.96, in complete agreement with the most recent and accurate estimate of f. They also discuss the applicability of the present elastic percolation models to real systems such as gels.