Showing papers on "Elastic modulus published in 1988"

Analytic nearest-neighbor model for fcc metals

Abstract: The implications of the mathematical format of the embedded-atom method of computer modeling of metals have been studied with use of a simple nearest-neighbor analytic model for the fcc lattice. The physical inputs into the model are the atomic volume, the cohesive energy, the bulk modulus, the average shear modulus, the vacancy-formation energy, and the slope at the nearest-neighbor distance of the spherically averaged free-atom electron density calculated with Hartree-Fock theory. The model employs an exponential repulsion between nearest-neighboring atoms, an exponentially decreasing function for the free-atom electron density, and a universal equation relating the crystal energy and the lattice constant. The anisotropy ratio of the cubic shear moduli is constrained to be 2 with this model. The dependence of the energies for unrelaxed configurations for vacancy formation, divacancy binding, and low-index plane surfaces on the model parameters has been analyzed. The average shear modulus plays a dominant role in determining these energies relative to the bulk modulus or the cohesive energy because the slope of the embedding function at the equilibrium electron density is linear in the average shear modulus. Embedding functions are not uniquely determined in specific models, and it is shown that the embedding functions used inmore » several models are essentially equivalent.« less

Entropic elastic processes in protein mechanisms. I. Elastic structure due to an inverse temperature transition and elasticity due to internal chain dynamics.

Abstract: Numerous physical characterizations clearly demonstrate that the polypentapeptide of elastin (Val1-Pro2-Gly3-Val4-Gly5)n in water undergoes an inverse temperature transition. Increase in order occurs both intermolecularly and intramolecularly on raising the temperature from 20 to 40 degrees C. The physical characterizations used to demonstrate the inverse temperature transition include microscopy, light scattering, circular dichroism, the nuclear Overhauser effect, temperature dependence of composition, nuclear magnetic resonance (NMR) relaxation, dielectric relaxation, and temperature dependence of elastomer length. At fixed extension of the cross-linked polypentapeptide elastomer, the development of elastomeric force is seen to correlate with increase in intramolecular order, that is, with the inverse temperature transition. Reversible thermal denaturation of the ordered polypentapeptide is observed with composition and circular dichroism studies, and thermal denaturation of the crosslinked elastomer is also observed with loss of elastomeric force and elastic modulus. Thus, elastomeric force is lost when the polypeptide chains are randomized due to heating at high temperature. Clearly, elastomeric force is due to nonrandom polypeptide structure. In spite of this, elastomeric force is demonstrated to be dominantly entropic in origin. The source of the entropic elastomeric force is demonstrated to be the result of internal chain dynamics, and the mechanism is called the librational entropy mechanism of elasticity. There is significant application to the finding that elastomeric force develops due to an inverse temperature transition. By changing the hydrophobicity of the polypeptide, the temperature range for the inverse temperature transition can be changed in a predictable way, and the temperature range for the development of elastomeric force follows. Thus, elastomers have been prepared where the development of elastomeric force is shifted over a 40 degrees C temperature range from a midpoint temperature of 30 degrees C for the polypentapeptide to 10 degrees C by increasing hydrophobicity with addition of a single CH2 moiety per pentamer and to 50 degrees C by decreasing hydrophobicity.(ABSTRACT TRUNCATED AT 400 WORDS)

Rheological Behavior of Filled Polymeric Systems I. Yield Stress and Shear‐Thinning Effects

Abstract: A fundamental investigation of the influence of particulate and matrix properties on the shear viscosity, primary normal stress coefficient, dynamic viscosity, and storage modulus of composite systems was undertaken. As expected, all four rheological properties were observed to increase upon addition of solid particulates and some of the composite systems exhibited a yield stress. The present research showed that a new equation obtained by a phenomenological modification of the Tanaka and White model allowed the a priori prediction of suspensionviscosity for shear‐thinning systems as a function of matrix properties, volume fraction of particulates, and shear rate. It also provided the flexibility of describing suspensionviscosity of systems exhibiting an apparent yield stress. Investigation of the other rheological properties showed that a form of the Kitano et al. expression could describe the relative primary normal stress coefficient and the relative storage modulus; whereas, a form of the Chong et al. expression could describe the relative dynamic viscosity of the various composite systems.

Velocity and attenuation of ultrasound in suspensions of particles in fluids

Abstract: The theory of the scattering of compression waves in viscous fluids is examined. The effects of fluid viscosity, of differences in density and in elastic modulus between the particles and the fluid, of heat transfer and of concentration are considered. Ultrasonic phase velocity and attenuation are derived. Results for the phase velocity are compared with several other formulations. The feasibility of using ultrasound to characterise suspensions is discussed.

Elastic Anisotropy in Zirconia Single Crystals

Abstract: Results are presented for the measured single-crystal elastic constants of yttria-stabilized zirconia, for yttria contents of 1.7 to 20 mol%. The results cover a range of materials which vary from a mixture of monoclinic, tetragonal, and cubic to those which are fully cubic. These single-crystal measurements are used to calculate the bounds on the elastic moduli for polycrystalline materials. Comments are made on the elastic anisotropy of zirconia relative to a number of other single-crystal ceramics, with graphical comparisons of the anisotropy of Young's moduli of these ceramics.

Mechanical Properties of Nanometre Volumes of Material: use of the Elastic Response of Small Area Indentations

Abstract: A new, differential method for determining the stiffness of a sub-micron indentation contact area is presented. This allows measurement of elastic modulus as well as plastic hardness, continuously during a single indentation, and without the need for discrete unloading cycles. Some of the new experiments that become possible with this technique, especially at the nanometre scale, are described. We show quantitatively that electropolished tungsten reproducibly exhibits the ideal theoretical lattice strength at small indentation loads.

Engineering Properties of Concrete Affected by Alkali-Silica Reaction

Abstract: A detailed study of the effects of alkali-silica reaction (ASR) on the engineering properties of concrete such as compressive and tensile strength, elastic modulus, and pulse velocity is presented. Two types of reactive aggregate - a naturally occurring Beltane opal and synthetic fused silica - were used. The tests wee carried out at 20 C and 96 percent relative humidity (RH). The results showed that losses in engineering properties do not all occur at the same rate or in proportion to the expansion undergone by the ASR-affected concrete. The two major properties affected by ASR were flexural strength and dynamic modulus of elasticity. Compressive strength was not a good indicator of ASR, but the flexural strength proved to be a reliable and sensitve test for mointoring ASR. Nondestructive tests like dynamic modulus and pulse velocity were also able to identify deterioration of concrete by ASR. The data indicate that critical expansion limits due to ASR would vary depending on the type and use of a concrete structure.

A microscopic model of electrorheology

Abstract: An electrorheological fluid is modeled as a concentrated suspension of hard spheres with aligned field‐induced electric dipole moments. The presence of dipole moments causes clustering of the particles into an anisotropic suspension characterized by a particle probability distribution function. The elastic shear modulus and the dynamic viscosity are calculated from a perturbation to the particle distribution as a result of a small amplitude, high frequency, oscillatory flow. The high frequency elastic shear modulus and the dynamic viscosity are shown as a function of particle concentration and electric dipole strength. Both the modulus and the viscosity increase strongly with particle concentration. Dynamic viscosity is insensitive to dipole strength, but elastic shear modulus increases strongly with dipole strength indicating the relative importance of the particle distribution to elastic properties. The results of these calculations provide insight into the relationship between the macroscopic properties of an electrorheological fluid and microscopic structural changes.

Effects of fiber length and orientation distribution on the elastic modulus of short fiber reinforced thermoplastics

Abstract: A method including the effects of fiber length and orientation distribution to predict elastic moduli of short fiber reinforced thermplastics (FRTP) is presented. The fiber length distribution in FRTP has an asymmetric character with a tail at the long fiber end. Statistical distribution functions such as Weibull or log-normal can be used to represent this kind of distribution. Orientation distribution of fibers in FRTP can be characterized by a single parameter exponential function, . A large λ indicates a highly oriented material whereas small λ represents a quasi-isotropic material. As fiber length and orientation distribution functions have been characterized, the elastic moduli of FRTP can be predicted. First, the mean elastic moduli of unidirectional plies are predicted through the fiber length distribution. Then the stacking sequence of laminate is assumed to be as the fiber orientation distribution of FRTP, and the overall elastic moduli of FRTP are estimated based on the laminate-plate method.

Entropic elastic processes in protein mechanisms. II. Simple (passive) and coupled (active) development of elastic forces

Abstract: The first part of this review on entropic elastic processes in protein mechanisms (Urry, 1988) demonstrated with the polypentapeptide of elastin (Val1-Pro2-Gly3-Val4-Gly5)n that elastic structure develops as the result of an inverse temperature transition and that entropic elasticity is due to internal chain dynamics in a regular nonrandom structure. This demonstration is contrary to the pervasive perspective of entropic protein elasticity of the past three decades wherein a network of random chains has been considered the necessary structural consequence of the occurrence of dominantly entropic elastomeric force. That this is not the case provides a new opportunity for understanding the occurrence and role of entropic elastic processes in protein mechanisms. Entropic elastic processes are considered in two classes: passive and active. The development of elastomeric force on deformation is class I (passive) and the development of elastomeric force as the result of a chemical process shifting the temperature of a transition is class II (active). Examples of class I are elastin, the elastic filament of muscle, elastic force changes in enzyme catalysis resulting from binding processes and resulting in the straining of a scissile bond, and in the turning on and off of channels due to changes in transmembrane potential. Demonstration of the consequences of elastomeric force developing as the result of an inverse temperature transition are seen in elastin, where elastic recoil is lost on oxidation, i.e., on decreasing the hydrophobicity of the chain and shifting the temperature for the development of elastomeric force to temperatures greater than physiological. This is relevant in general to loss of elasticity on aging and more specifically to the development of pulmonary emphysema. Since random chain networks are not the products of inverse temperature transitions and the temperature at which an inverse temperature transition occurs depends on the hydrophobicity of the polypeptide chain, it now becomes possible to consider chemical processes for turning elastomeric force on and off by reversibly changing the hydrophobicity of the polypeptide chain. This is herein called mechanochemical coupling of the first kind; this is the chemical modulation of the temperature for the transition from a less-ordered less elastic state to a more-ordered more elastic state. In the usual considerations to date, development of elastomeric force is the result of a standard transition from a more-ordered less elastic state to a less-ordered more elastic state. When this is chemically modulated, it is herein called mechanochemical coupling of the second kind. For elastin and the polypentapeptide of elastin, since entropic elastomeric force results on formation of a regular nonrandom structure and thermal randomization of chains results in loss of elastic modulus to levels of limited use in protein mechanisms, consideration of regular spiral-like structures rather than ramdom chain networks or random coils are proposed for mechanochemical coupling of the second kind. Chemical processes to effect mechanochemical coupling in biological systems are most obviously phosphorylation-dephosphorylation and changes in calcium ion activity but also changes in pH. These issues are considered in the events attending parturition in muscle contraction and in cell motility.

Elastic properties of hedenbergite

Abstract: The single-crystal elastic moduli of hedenbergite (CaFeSi2O6) hare been measured at 20°C and 1 bar using Brillouin spectroscopy. The moduli are (in gigapascals): C11 = 222, C22 = 176, C23 = 249, C44 = 55, C55 = 63, C66 = 60, C12 = 69, C13 = 79, C33, = 86, C15 = 12, C25 = 13, C35 = 26, C46 = −10. The comparison of elastic properties among Mg-Fe-Ca bearing pyroxenes, known as quadrilateral pyroxenes, reveals only weak variations with changes in composition. Of the four quadrilateral pyroxenes, orthoferrosilite has elastic properties distinctive from the others. The principal differences among these pyroxenes are due to subtle structural differences. In particular, the mechanical linkage between the M2 polyhedral chains in clinopyroxenes enhances the importance of the cation in this site. In contrast to the orthopyroxenes, the aggregate shear modulus μ of the calcium-bearing clinopyroxenes (diopside and hedenbergite) exhibits no dependence on the amount of iron (Fe2+) present in the structure, while the ratio K/μ does. As a result, the compressional and shear acoustic velocities of the calcium-bearing clinopyroxenes show a smaller dependency on iron content than do the orthopyroxenes.

Viscoelasticity in silica gel

Abstract: The elastic modulus, modulus of rupture (MOR), and viscosity of wet silica gels were measured as functions of age of the gels, using a beam-bending method. The gels were prepared by acid-catalyzed hydrolysis of tetraethyl orthosilicate (TEOS) with a water/TEOS ratio of 16/1. The gels were aged and their properties were measured while immersed in the pore liquid. The modulus increased by about two decades and the MOR and viscosity increased by about one decade over a two-week period. Measurements of stress relaxation showed a strong dependence on sample size that is attributed to the flow of pore liquid out of the samples. The gels were found to be linearly viscoelastic.

Elastic properties of three-dimensional percolation networks with stretching and bond-bending forces

Abstract: We report the results of the first numerical simulations of elastic properties of three-dimensional percolation networks in which both central and bond-bending forces are present Using extensive Monte Carlo simulations and finite-size scaling analysis and taking into account corrections to scaling, we find $f\ensuremath{\simeq}378$ with an error of about 3%, where $f$ is the critical exponent that characterizes the power-law behavior of the elastic moduli near the percolation threshold ${P}_{c}$ This agrees excellently with the experimental measurements of $f$ for sintered materials and for gels near the gelation point It also agrees with the relation $f=t+2v$, where $t$ is the critical exponent of the electrical conductivity of the network, and $v$ the correlation-length exponent Also studied is the ratio of the bulk and shear modulus of the system As ${P}_{c}$ is approached, this ratio approaches a value close to 4/3

Nonlinear mechanical behavior in striated muscle and its relationship to underlying crossbridge activity

Abstract: Small muscles dissected from the frog (Rana pipien) toe were submersed in a cooled (0 degrees C) Ringers solution and attached at opposite ends to a tension transducer and a length regulating servo device. Muscle stiffness was measured by imposing a length disturbance (bandlimited (0-500 Hz) noise or single-frequency sinusoid) on an initially isometric muscle preparation and recording this disturbance and the concomitant tension response. If active muscle stiffness was to be measured, the muscle was electrically stimulated to produce a fused tetanus prior to imposing the length disturbance. The passive muscle was characterized as highly compliant, almost linear elasticity (elastic modulus 638 kN/m/sup 3/). Estimates of the muscle stiffness as a function of frequency were obtained using spectral density methods. The active muscle appears to 'soften' in response to release and 'harden' in response to stretch. The linear behavior of active muscle was modeled as a linear spring (elastic modulus 102040 kNm/sup 3/) in parallel with a linear dampener (viscous modulus 810 kN*s/m/sup 3/). >

Oxycarbide Glasses in the Mg-Al-Si-O-C System

Abstract: Oxycarbide glasses in the Mg-Al-Si-O-C system were produced at initial carbon levels of 0.0, 0.5, 1.0, 1.5, 2.0, and 2.5 wt%. Carbon was incorporated into the glass melts by means of SiC additions. The glasses were melted between 1750° and 1800°C under nitrogen atmospheres. The limit of carbon incorporation was reached at the 2.5% carbon level, as these glasses crystallized (predominantly cordierite, 2MgO˙2Al2O3˙5SiO2) upon gradual cooling from the meit. Glasses containing less than 2.5% carbon were amorphous according to standard X-ray diffraction methods. Further examination of these oxycarbide glasses by transmission electron microscopy indicated the lack of microcrystalline phases and the potential for producing clear inclusion-free glasses. The Mg-Al-Si-O-C glasses showed significant increases in density, Young's elastic modulus, shear modulus, Vickers hardness, and fracture toughness with increasing carbon content.

Tensile performance of carbon-fibre-reinforced glass

Abstract: The tensile behaviour of unidirectional and [±θ]s angle-ply HMU carbon-fibre-reinforced borosilicate glass was determined as a function of the angle between the fibre and the applied load. Both the longitudinal and transverse strain of the composite are reported and discussed relative to the microstructural features responsible for the observed composite behaviour. Stress-strain behaviour for static and cyclic loading conditions is presented. The experimentally determined values of the composite elastic modulus and strength are also compared with those predicted from classical laminate theory. The composite tensile strength is accurately predicted by the Tsai-Hill failure criterion. The elastic modulus measurements indicate that the shear modulus of the uniaxially reinforced composites is higher than that of the multiaxially reinforced composites. This observation is attributed to more extensive matrix microcracking being present in the multiaxially reinforced composite as a result of fabrication. The failure modes present in the composite are also documented.

Thermal and rheological properties of poly(vinyl alcohol) hydrogels prepared by repeated cycles of freezing and thawing

Abstract: Differential scanning calorimetry and scanning electron microscopy were carried out in order to study the relation between the structure and properties of poly(vinyl alcohol) hydrogels prepared by repeated cycles of freezing-thawing. The effect of the number N of repeated cycles of freezing-thawing, of the degree of saponification (DS), and of the degree of polymerization (DP) on structure and properties was examined. The elastic modulus and the endothermic enthalpy, estimated from the area surrounded by the endothermic peak, increase with increasing N, DS, and DP. The melting temperature Tm shifts to higher temperatures with increasing DS and DP, but it is almost independent of N for gels with high DS or DP. In PVA gels with lower DP or DS, Tm shifts to higher temperatures with increasing N. The temperature dependence of the elastic modulus is discussed on the basis of a theory on thermoreversible gels.

Flexural stiffness and modulus of elasticity of flower stalks from allium sativum as measured by multiple resonance frequency spectra

Abstract: Multiple resonance frequency spectra (MRFS) provide a rapid and repeatable method for determining the flexural stiffness and modulus of elasticity, E, of segments of plant stems and leaves. Each resonance frequency in a spectrum can be used to compute E, and removal of the distal portion of an organ produces characteristic shifts in spectra dependent upon the geometry of an organ. Hence, MRFS can be used to quantitatively determine the extent to which a particular leaf or stem morphology can be modelled according to beam theory. MRFS of flower stalks of Allium sativum L. are presented to illustrate the technique. The fundamental, f, and higher resonance frequencies, f2 . .. fn, of stems and the ratios of f2/f,, f3/f, and f3/f2 increase as stalk length is reduced by clipping. The magnitudes of these shifts conform to those predicted from the MRFS of a linearly tapered beam. Morphometric data confirm this geometry in 21 flower stalks. Based on this model, the average modulus equals 3.71 x 108 ? 0.32 x 108 N/M2, which compares favorably with values of E determined by static loading (3.55 x 108 ? 0.22 x 108 N/M2) and is in general agreement with ultrasonic measurements (3.8 x 108 to 4.4 x 108 N/M2). Data indicate that determinations of E from a single resonance frequency are suspect, since each resonance frequency yields slightly different values for E. Statistical evaluations from all the frequencies within a MRFS are more reliable for determining E and testing the appropriateness of beam theory to evaluate the biomechanical properties of plants. THE EXTENT to which a stem can support a weight at its tip or continue to grow vertically before buckling under its own weight depends upon its flexural stiffness and the modulus of elasticity of constituent tissues (McMahon, 1975; King, 1981; Givnish, 1982). Provided it can be modelled according to some beamlike geometry, the critical buckling weight and critical buckling length of a stem can be calculated from empirically determined values of the elastic modulus, E, which measures the proportionality between stress and strain for a structure (Silk, Wang, and Cleland, 1982; Niklas and O'Rourke, 1982, 1987). Consequently, a number of workers have devised methods to determine E. Among the most common is the Instron method of testing specimens under a ' Received for publication 1 October 1987; revision accepted 25 January 1988. The authors wish to thank Mr. William Holmes and Scott Copeland (Department of Theoretical and Applied Mechanics, Cornell University) for their technical assistance, Ms. Barbara Bernstein (Section of Plant Biology, Cornell University) for rendering figures from computer hard-copy printouts, and Professor Wolfgang H. Sachse and Mr. Howard J. Susskind (Theoretical and Applied Mechanics, Cornell University) for providing preliminary data from a longitudinal ultrasonic examination of flower stalks. Support from a National Science Foundation grant BSR 8320272 (KJN) is gratefully acknowledged. uniaxial, constant strain rate (Cleland, 1967, 1971, 1984). Although this technique provides rapid and repeatable measurements of E, the appropriateness of a beam geometry to model a particular stem morphology often remains conjectural. In addition, plant organs capable of supporting their own static weight can undergo dynamic mechanical failure. We present a technique for measuring the flexural stiffness and modulus of elasticity of plant stems which can also be used to evaluate the extent to which a particular stem morphology conforms to each of a variety of beam models. The technique is based on the mathematical relationship between the elastic properties and the multiple resonance frequencies of vibration of tapered or untapered beams with various transverse geometries (Timoshenko and Gere, 1961; Gorman, 1975; Blevins, 1979). A large body of empirical and theoretical studies underpin this approach, and to a limited extent it has been applied to examining the turgor pressure and rigidity of tissues (Virgin, 1955; Falk, Hertz, and Virgin, 1958). However, to our knowledge, multiple resonance frequency patterns have not been used to study plant organs in the method presented here. We have selected the flower stalk of Allium sativum L., to illustrate this method. Garlic

Elastic properties of silicon oxynitride films determined by picosecond acoustics

Abstract: The sound velocity and elastic modulus of a series of amorphous silicon oxynitride films produced by reactive sputtering have been measured as a function of nitrogen content. The acoustic pulses were generated and detected with ultrashort light pulses. The sound velocity was found to depend linearly on the nitrogen content.

Hygrothermal effects on the stability of a cylindrical composite shell panel

Abstract: The finite element method is applied to study the problem of moisture and temperature effects on the stability of a general orthotropic cylindrical composite shell panel subjected to axial or in-plane shear loading. The element employed is a nine-node isoparametric shell element. As the hygrothermal effects on the elastic properties of the matrices and the fibers are very different, the degradation of elastic moduli, the transverse shear effect and the induced initial stress are all considered. Numerical investigation shows that if the temperature increases from 300 to 422 K and the moisture concentration is saturated, the buckling load with both the degradation of elastic moduli and transverse shear deformation considered is ca . 12% lower than Snead and Papazotto's result where only the degradation of elastic moduli was considered. In addition, it is shown that the influence of the initial stress, induced by the same environmental variations, on the buckling load is far less significant.