Bulk compressive modulus

Note 1 Also known as bulk compressive modulus. 

Here, C is a constant for material stiffness that needs to be determined experimentally. Figure 5.10b shows the pore size distribution obtained using this equation. It should be noted that densification curves may also be used to determine the bulk compression modulus of silica aerogels (Scherer et ah, 1995b). 

The bulk compression modulus for an isotropic material can be determined from the relationship between the spherical stress and strain tensors, that is. 

For the bulk compression modulus, an expression can be taken that is often used to describe the interaction between two charged particles, as follows ... 

Linden [49]. To our knowledge the theory has not yet been applied to experimental results. E. v. d. Linden assumes that multilamellar vesicles (droplets) are deformed in shear flow from a spherical to an elliptical shape. Turning into the deformed state the energy of closed shells is shifted because their curvature as well as their interlamellar distance D are changed. Due to the interaction of the bilayers, expressed by the bulk compression modulus B, the inner shells are deformed and the total deformation energy of the lamellar droplet gets minimized. Assuming that the volume of a droplet is not modified by the deformation, the surface A must increase. One can define an effective surface tension (Tef[=ElAA. E. v. d. Linden obtains ... 

Both, bulk compression modulus and bending constant, depend on the charge density of the bilayers and the shielding of the charges with excess salt. 

The occurrence of this cavitation process can be readily understood by noting that the elastic tensile modulus, , of a typical PSA is about 4-5 orders of magnitude lower than its bulk compressive modulus. A mechanical analysis of the growth of an existing cavity in an elastic rubber shows that in such a medium, a preexisting cavity is predicted to grow in an unstable manner if the applied hydrostatic tensile pressure exceeds the tensile modulus, E, of the adhesive [ 18,19]. This expansion condition can be roughly written as ... 

The loeal eompressive strength of polyethylene is of more interest commercially than its bulk compressive modulus. Local compressive strength is normally referred to as hardness, microhardness or microindentation hardness (MH). Microhardness is important in terms of the retention of a good surface finish on molded articles. 

So for an incompressible material v = 0.5 and Equation 2.4 is recovered. The value of Poisson s ratio for rubber is usually close to 0.5 but for many other solids the value is lower and we find 0.25 < v < 0.33. We may also describe a Bulk rigidity modulus, K, such as we would measure when we compress a material with hydrostatic pressure, in terms of Young s modulus ... 

Now, in rheological terminology, our compressibility JT, is our bulk compliance and the bulk elastic modulus K = 1 /Jr- This is not a surprise of course, as the difference in the heat capacities is the rate of change of the pV term with temperature, and pressure is the bulk stress and the relative volume change, the bulk strain. Immediately we can see the relationship between the thermodynamic and rheological expressions. If, for example, we use the equation of state for a perfect gas, substituting pV = RTinto a = /V(dV/dT)p yields a = R/pV = /Tand so for our perfect gas ... 

Bulk Modulus and Bulk Compressibility Tests. See Vol 1, pIX and Vol 2, p B323... 

In addition to the tensile and shear moduli, a compressive modulus, or modulus of compressibility, K, exists to describe the elastic response to compressive stresses (see Fignre 5.7). The compressive modulus is also sometimes called the bulk modulus. It is the proportionality constant between the compressive stress, CTc, and the bulk strain, represented by the relative change in bulk volume, AV/Vo-... 

Bulk Compressibility and Bulk Modulus is one of the important constants of aa elastic solid Bulk modulus is defined as the tatio of stress to atrsin when the stress is a pressure applied equally on all surfaces of the sample and the strain is the resulting change in volume per suit volume. The reciprocal of bulk modulus Is called bulk compressibility. One apparatus for the direct exnd measurement of the dynamic bulk modulus of a solid was developed at the NOL, White Oak, Md(Ref 1). Some data obtained, on several HE a, using this apparatus are given in Refa 2, Refs l)NAVORD Kept No 1534(1950) 2)NAVORD Rept No 4380(1956) 3)PATR 1740,Rev 1(1958)... 

Bulk compressibility and bulk modulus 2 DC see Bulk modulus and bulk compressibility 2 B323-B324... 

When the shape factor is high, such that Ec/K (where K = bulk modulus) exceeds 0.1, the effective modulus will be below that expected, due to the bulk compression being appreciable. The effective modulus can then be estimated from99 ... 

Bulk Compressibility. See Bulk Modulus and Bulk Compressibility... 

For description of an apparatus used by Philipoff Brodnyan, see Ref 3, and of that used by McKinney et al, see Ref 4 Refs l)E.Meyer K.Tamm, AkustZeitschr 7, 45 50(March 1942), "An Accustic Method for Determining the Dynamic Compressibility and Loss Factor of Elastic Substances 2)C.S. Sandler, NAVORD Rept 1524(Sept 1950), "An Accoustic Technique for Measuring the Effective Dynamic Bulk Modulus of Elasticity and Associated Loss Factor in Rubber and Plastics 3)W.Philipoff J.Brodnyan, JApplPhys 26, 846-9(1955), "Preliminary Results in Measuring Dynamic Compressibilities 4)J. E. McKinney et al, JApplPhys 27, 425-30(1956), "Apparatus for the Direct Determination of the Dynamic Bulk Modulus 5)W.S.Cramer, NAVORD Rept 4380(Sept 1956), "Bulk Compressibility Data on Several Explosives 6)J.Alster, PicArsn, Dover, NJ private communication(1961)... 

Type of Material Apparent Density, kg/m3 Bulk Modulus, MPa Compressive Modulus, MPa... 

Hartmann already pointed out that the reducing parameter B0 is equal to the compression modulus or bulk modulus K, extrapolated to zero temperature and pressure and that T0 is related to the glass transition temperature. 

The compressibility k is the reciprocal of the compression modulus or bulk modulus of the material. This important property will be discussed in Chap. 13 (Mechanical properties of solid polymers). The application of Eq. (7.27) is restricted to polymer melts. For amorphous polymers below the melting point, the internal pressure n may be defined as well ... 

In solids the situation is more complicated than in liquids. Here we have two types of waves, viz. the longitudinal and the shear waves. In contrast with liquids the longitudinal wave in solids is not only determined by the bulk or compression modulus but also by the shear modulus, or alternatively by the Poisson ratio. 

Considering a mass of ceramic powder about to be molded or pressed into shape, the forces necessary and the speeds possible are determined by mechanical properties of the diy powder, paste, or suspension. For any material, the elastic moduli for tension (Young s modulus), shear, and bulk compression are the mechanical properties of interest. These mechanical properties are schematically shown in Figure 12.1 with their defining equations. These moduli are mechanical characteristics of elastic materials in general and are applicable at relatively low applied forces for ceramic powders. At higher applied forces, nonlinear behavior results, comprising the flow of the ceramic powder particles over one another, plastic deformation of the particles, and rupture of... 

This expression indicates that a decrease in the thickness d produces an increase in S, with the consequent repercussion on the bulk relaxation modulus [Eq. (3.50)] and the rigidity under compression [Eq. (3.48)]. Figure 3.24 shows the stress-strain curves under compression for elastomer blocks of different shapes. It can be seen that as S increases the curves lose the linearity displayed in a large interval of extensions when S has a low... 

Figure 4. Evolution of the combined elastic modulus (25 i3 + 5 33) and bulk compressibility of aker-manite, showing significant static softening close to the phase transition. Values of (25i3 + 533) were calculated from consecutive data points as c- dctdp)=2(c, i - py, and values...

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