Static elastic measurements

Ladizesky has measured longitudinal extension, transverse contraction, and hence Poisson s ratio under constant stress, of sheets on which an accurate grid had been evaporated. Photographs of the grid, taken on glass plates at various times after loading, were measured using a microscope. 

Similar measurements were made by Darlington and Saunders using sensitive extensometers, with displacements measured by a capacitative transducer. The lateral contraction extensometer, in which rigid feelers rested lightly against the specimen sides, showed some irregularities at strains below OOl. 

Two earlier methods of obtaining Poisson s ratio V13 of filaments have been reported E avis ° measured the changes due to extension in the diffraction pattern formed by a single filament and Frank and Ruoff deduced the diameter change of a filament confined in a capillary from the displacement of mercury occupying the annulus between the filament and the rapillary walls. Both methods were relatively insensitive, and their use was confined to nylon, since this material shows negligible permanent set for extensional strains up to 5 . 

Typical apparatus for torsional measurements is that described by Raumann - and in a modified form by Ladizesky and Ward. The sitmple is fastened betw een two clamps, the lower of which may be fixed in any required orientation, and the upper of which is attached rigidly to a small mirror and then to the lower end of a long phosphor-bronze strip. When the top of this strip is rotated both the suspension and the sample will twist, the former through an angle p and the latter through 0. At equilibrium torques in suspension and sample are equal, giving 

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Indices are dimensionless parameters derived from various mechanical and physical properties of the tablet blend and resulting compacts. Mechanical properties typically measured include indentation hardness (kinetic and static), elastic modulus, and tensile strength (10,11). Physical properties include particle size, shape, and size distribution, density (true, bulk, and tapped), flow properties and cohesive properties. 

The grafted layer also affects two other features of the rheology. First, thicker polymer layers enhance the elasticity due to the longer range of the repulsion relative to the hard core size. Thus, samples formulated at 4>cff mo possess easily measurable static elastic moduli. Second, the softer repulsion apparently suppresses the shear thickening observed at high volume fractions for the harder particles, in accordance with earlier measurements by Willey and Macosko (1978). 

Abstract. Variations in the chemical composition of surfactants from natural sea slicks are compared to variations in surface elasticity using mass spectrometry, Langmuir film balance measurements, and multivariate statistical techniques. It is shown that the information on chemical class and molecular structure contained in the mass spectra is strongly correlated with measured static elasticity and can be used to estimate film elasticity at a given surface pressure. 

The Chemometricks analysis developed discriminant functions that distinguished each sample or sample class from every other based on the principal mass components of the spectra. Applied to individual spectra, the discriminant functions yielded a function score that reflected the abundance of those chemical components in the sample mixture that distinguished the sample or class from the others. Experimentally measured static elasticities for the samples were then compared with the discriminant scores to determine the degree of correlation between the spectral patterns and surface elasticity. 

Corresponding film pressure values P surfactant concentration P calculated from the wavelength measurements are shown in Figure 3, arrow bars are shown in the last graphic. In Figure 3 the static elasticity values, estimated from the pressure-concentration curves as H / JdP/dP) are also presented (the scale for the values of elasticity and film pressure is the same). 

Fig. 3. Film pressure-concentration curves, retrieved from wavelength measurements for films of oleyl alcohol (a), oleic acid (b) and Emkarox (c). o - static elasticity values...

By measuring the static elastic properties of human thoracic and abdominal aortas in vitro, Langewouters et al. [35] proposed the following empirical relationship between the cross-sectional area of the lumen (A) and the pressure in the vessel (p) ... 

The compressibility of the rare earth metals was first investigated up to 40 kbar by Bridgman (see Lawson s review, 1956) for most of the members of the series, and in some cases to about 90 kbar. Since Bridgman s earlier measurements, Stephens (1964) has published compression data on Pr, Eu, Tb, Yb and Sc to 45 kbar and Perez-Albuerne et al. (1966) have reported on the compressibility of Ho, Er and Tm to about 200 kbar (see Drickamer et al., 1966). More recently Liu et al. (1973) and Liu (1975) have measured the compressibility of Tm and Lu respectively in a diamond anvil high pressure X-ray apparatus to several hundred kbar. Syassen and Holzapfel (1975) have reported on the compression of La to 120 kbar. Anomalies corresponding to the phase transitions discussed earlier were noted in some cases in these static compression measurements at the y to a-Ce transition near 7 kbar (ch. 4, section 2.1) and in La at the dhep-fee transition near 25 kbar (Bridgman, see Lawson s review, 1956), in Yb at the fcc-bcc transition near 40 kbar (Stephens, 1964) and in Lu from the hep to Sm-type transition near 230 kbar (Liu, 1975). Bulk moduli evaluated from these data are plotted in fig. 9.11. For Gd, Dy, and Er single crystal elastic constant data and their pressure variation have been obtained (Fisher et al., 1973). 

Shear elasticity G and viscosity r are defined as a ratio of stress to deformation and that to the rate of deformation, respectively, and the ratio ri/G is the relaxation time t. G and tj are measured by various methods, dynamic methods with oscillating devise, and static methods measuring deformation [1]. 

The static (mechanical) elastic modulus is determined in the linear part of the elastic deformation at the strain-deformation diagram of the sample at static load. The difficulty in determining the static elastic modulus is in the fact that the deformation before the fracture is only microns and a precise apparatus is required. The static elastic modulus may be measured at strength tests (compression, bending, tensile), and, of course, the sample will be broken. In reality, the measurement of the dynamic elastic modulus is more popular. 

There are two types of elastic moduli. First, there is the static elastic modulus that is measured from the stress-strain response of the solder when subjected to tension or compression testing (Ref 25). The second type is referred to as the dynamic elastic modulus and is measured by the passage of sound waves through the material (Ref 26). In the latter case, because sound wave propagation in a solid is based upon atomic vibrations that are very rapid, inelastic deformation is largely ehminated from the material response. Therefore, the modulus is determined from nearly pure elastic deformation. On the other hand, the static modulus is sometimes preferred when calculating plastic strain because it accounts for aU deformation leading up to the yield stress as defined by the 0.2% offset criterion. 

Most obvious was that fact that the moduli values are nearly an order of magnitude less than expected, based upon previous data for lOOSn, 96.5Sn-3.5Ag, and 95.5Sn-5Sb alloys (Ref 27). The role of inelastic deformation was examined by measuring the stafic elastic modulus at faster strain rates. The results are shown in Fig. 6(b). A general trend was observed, in which the modulus increased with strain rate, particularly at the lower temperatures, thereby implying that inelastic deformation likely had a role in the static modulus measurements at low strain rates. However, the faster strain rates did not bring the moduli to within range of the expected values. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

The important elastic properties of a material undergoing deformation under static tension are stiffness, elastic strength and resilience. For a material obeying Hooke s law, the modulus of elasticity, E (= o/e), can be taken to be a measure of its stiffness. The elastic... 

Elastic and quasi-elastic (NSE) neutron scattering experiments were performed on dilute solutions of linear poly(isoprene) (PIP) polymers and of PIP stars (f = 4,12,18) [150]. In all cases the protonated polymers were dissolved in d-benzene and measured at T = 323 K, where benzene is a good solvent. Figure 50 shows the results of the static scattering profile in a scaled Kratky representation. In this plot the radii of gyration, obtained from a fit of the... 

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