Static compressibility modulus

Fig. 3.9 Static compressibility modulus e = drr/d In T, at 25°C, calculated from the tt vs T, curve. The dashed lines indicate the limits of the dilute (D), semidilute (SD), and concentrated regimes (C). (From ref. [59])...

FIGURE 6.6 Static compression modulus E (MPa) as a function of pressure (MPa) for various percentage plasticizer (DOP) in rubber samples cured with 2% sulfur. (Reproduced with permission from Rubber Chemistry and Technology, Copyright 1982.55 328-36. A. Accetta and J. M. Vergnaud, Figure 1, Rubber Division, ACS.)... 

An example is given in Figure 6.6 showing the static compression modulus E expressed in MPa as a function of the pressure cr (MPa) for different percentages of plasticizer (DOP) with rubber samples cured with 2% sulfur. There is a significant increase in the static modulus E with the compression pressure on the other hand,... 

A few results are thus given in terms of the static compression modulus which is expressed as a function of the pressure for different percentage of plasticizer with 2% sulfur in Figure 8.1 and with 5% sulfur in Figure 8.2. Moreover, the dynamic in-phase modulus E is measured as a function of the forcing frequency for different scrap rubber vulcanized with sulfur in Figure 8.3, whereas the corresponding values... 

P loss factor, in Figure 8.4 DOP plasticizer, for dioctyl phthalate db for decibel, in Figure 8.5 E static compression modulus, in Figure 8.1 E dynamic in phase modulus, in Figure 8.3... 

The static modulus and dynamic storage modulus were investigated for some open-celled PE foams by static compression tests and dynamic viscoelastic measurements in compression mode. Experimental data were compared with theoretical predictions. 8 refs. 

Straightforward measurements of elastic properties of materials can be made via high-pressure static compression experiments, in which X-ray diffraction (XRD) is used to measure the molar volume (V), or equivalently the density (p), of a material as a function of pressure (P). The pressure dependence of volume is expressed by the incompressibility or isothermal bulk modulus (Kt), where Kp = —V(bP/bV)p. 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

As in true strain, the expression above takes into account cross-sectional area changes in a certain cohesive structure (or cake) of powdered material. If the material is isotropic, another possible expression that includes the Poisson s ratio p (the ratio of transverse strain and axial strain resulting from uniformly distributed axial radial stress during static compression of the material in absolute value). The Poisson s ratio, or bulk modulus, permits prediction of the transverse contraction or expansion that occurs when a stress is applied longitudinally. 

The bulk modulus K (= /H, the reciprocal of the bulk compliance) can be measured in compression with a very low height-to-thickness (h/i) ratio and unlubricatcd flat clamp surfaces. In pure compression with a high h/t ratio, and lubricated clamps, the compressive modulus (= /D, the reciprocal of the compressive compliance) will be measured. Any intermediate hjt ratios will measure part bulk and part compressive moduli. Hence it is vital for comparing samples to use the same dimensions in thermal scans and the same h/t ratio when accurately isotherming and controlling static and dynamic strains and frequencies. 

Specifications should include any specific properties required for the application, such as resilience, hysteresis, static or dynamic shear and compression modulus, flex fatigue and cracking, creep resistance to oils and chemicals, permeability, and brittle point, all in the temperature ranges to be encountered in service. 

Compressive strength ratio -Ratio of static elastic modulus Ratio of dynamic elastic modulus... 

In this paper the compressive strength/elastic modulus of the jointed rock mass was estimated as a function of intact rock strength/modulus and joint factor. The joint factor reflects the combined effect of joint frequency, joint inclination and joint strength. Therefore, having known the intact rock properties and the joint factor, jointed rock properties can be estimated. The test results indicated that the rock mass strength decreases with an increase in the joint frequency and a sharp transition was observed from brittle to ductile behaviour with an increase in the number of joints. It was also found that the rocks with planar anisotropy exhibit the highest strength in the direction perpendicular to the anisotropy and the lowest at an inclination of 30o-45o in jointed samples. The anisotropy of the specimen influences the dynamic elastic modulus more than the static elastic modulus. The results were also compared well with the published works of different authors for different type of rocks. 

The structure of the venous walls is basically similar to that of the arterial walls. The main difference is that they contain less muscle and elastic tissue than the arterial walls, which raises the static elastic modulus two to fourfold [49]. Because the venous walls are much thinner than the arterial wall, they are easily collapsible when they are subject to external compressions. 

Lee JH, Kim KJ (2001) Characterization of complex modulus of viscoelastic materials subject to static compression. Mech Ttme-Depend Mater 5 255-271... 

Figure 9 shows flie measured static deflection in comparison to the two calculated deformation curves according to Eqs. 43 and 44. The DE consists of 30 active dielectric layers each 10 pm in height and has an active electrode area of 25 mm. The determined uniaxial compressive modulus is 500 kPa. 

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. 

There have been several mechanical studies performed on gelled networks of stiff LCPs, some where the liquid crystallinity of the precursors was retained in the gels [278,780] and others where stiff mesogenic segments were connected by rigid branchpoints, leading to loss of mesomorphicity [277, 311, 312, 393, 400, 409]. Thus far, the results are limited to reported stress-strain curves [278, 393] and to values of static shear modulus obtained by linear compression ex-... 

Vo is the volume of unit cell under the standard reference conditions, x = V7Vo is the volume ratio of the unit cell upon the cell being compressed. Bo is the static bulk modulus and B q is the first-order pressure derivative of the Bq [16]. Figure 27.1 presents the d/do-P and V7Vo -P curve with the BM equation and the match of the experimental results of ZnO [16-18] with an optimal polynomial form of V/Vo = 1 + jSp -t- p p = 1 — 6.55 x 10 p + 1.25 x Using the... 

Deformation properties are derived from a static compression test. Young s modulus is defined as the ratio of an axial stress and the resulting axial strain ... 

A considerable range of mechanical material property tests was conducted at the RWTUV facilities, including cold static compressive stress-strain (SCSS) of brick-only and composite samples, cold crushing strength (Sc) of brick-only, creep in compression (CIC) of brick-only and composites, thermal expansion (TE) of brick-only, and modulus of rupture (MOR) of brick-only. 

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