Mechanical Property Compressive Bulk Modulus

In order to investigate the deformation properties and mechanical memory, it is of interest to study the behavior of polymer fine particles while in an applied external force. One of the experimentally obtained values of those properties is known as Young s modulus, which is a ftmdamental measure of the stiffness of a material. Numerous calculations have been performed for the mechanical property of bulk-like crystalline PE polymer using force field [187-190] semi-empirical [236], ab initio calculation [237,238],and ab initio MD methods [239,240]., We have calculated the compressive (bulk) modulus for the amorphous PE particles using MD with an external force as shown in Fig. 19. At the start, a plate treated as a continuous wall is set at 10 A from the closest atom of the particle in 

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Mechanical Properties. Measuremeat of the mechanical properties of diamoad is compHcated, and references should be consulted for the vahous qualifications (7,34). Table 1 compares the theoretical and experimental bulk modulus of diamond to that for cubic BN and for SiC (29) and compares the compressive strength of diamond to that for cemented WC, and the values for the modulus of elasticity E to those for cemented WC and cubic BN. 

The isotropic moduli, particularly the initial bulk modulus and its pressure derivative, are key ingredients in specifying the mechanical equation of state. As noted above, determination of these properties from experimental hydrostatic compression data is difficult due to issues with acquisition of high precision at low pressures and particular sensitivity in the choice of equation of state fitting form to data below about one GPa. Alternative routes to this information at low pressures included impulsive stimulated light scattering (ISLS) and resonant ultrasound spectroscopy (RUS), which can in principle provide the complete elastic tensor (ISLS) and isotropic bulk and shear moduli (RUS). 

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 ... 

One of the basic mechanical properties of the foam is its compressibility (elasticity). By definition the bulk modulus of elasticity Ev is expressed by... 

Tensile and shear forces are not the only types of loads that can result in deformation. Compressive forces may as well. For example, if a body is subjected to hydrostatic pressure, which exists at any place in a body of fluid (e.g. air, water) owing to the weight of the fluid above, the elastic response of the body would be a change in volume, but not shape. This behavior is quantified by the bulk modulus, B, which is the resistance to volume change, or the specific incompressibihty, of a material. A related, but not identical property, is hardness, H, which is defined as the resistance offered by a material to external mechanical action (plastic deformation). A material may have a high bulk modulus but low hardness (tungsten carbide, B = 439 GPa, hardness = 30 GPa). 

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... 

The modulus is the most important small-strain mechanical property. It is the key indicator of the "stiffness" or "rigidity" of specimens made from a material. It quantifies the resistance of specimens to mechanical deformation, in the limit of infinitesimally small deformation. There are three major types of moduli. The bulk modulus B is the resistance of a specimen to isotropic compression (pressure). The Young s modulus E is its resistance to uniaxial tension (being stretched). The shear modulus G is its resistance to simple shear deformation (being twisted). 

On the other hand, the mechanical properties of monolithic carbon gels are of importance when they are to be used as adsorbents and catalyst supports in fixed-bed reactors, since they must resist the weight of the bed and the stress produced by its vibrations or movements. A few smdies have been published on the mechanical properties of resorcinol-formaldehyde carbon gels under compression [7,36,37]. The compressive stress-strain curves of carbon aerogels are typical of brittle materials. The elastic modulus and compressive strength depend largely on the network connectivity and therefore on the bulk density, which in turn depends on the porosity, mainly the meso- and macroporosity. These mechanical properties show a power-law density dependence with an exponent close to 2, which is typical of open-cell foams. 

Table 1 illustrates selected improvements in bulk tensile modulus and tensile strength for PP made on bulk specimens and indicates that there is considerable improvement in mechanical properties in the Z and Y directions with corresponding enhancement for compression in the X direction of these rolltruded specimens. High-frequency sonic measurements show that there is a moderate increase in tensile modulus (up to X 1.5-2) for deformation ratios up to X20. Other poljmers have been found to behave similarly. 

The important properties of carbon fibers include mechanical stiffness (Young s modulus), tensile and compressive strength, thermal stability, thermal conductivity (along the fiber axis), thermal resistivity (of bulk fibers), low coefficient of thermal expansion, and electrical conductivity. 

The mechanical properties of polymeric materials including blends are reported in detail in commercial product literature and provide a basis of comparison of the engineering properties of materials for various end-use applications. The specific mechanical properties of interest include the modulus (tensile, flexural or bulk), strength (tensile, flexural or compressive), impact strength, ductility, creep resistance as well as the thermomechanical properties (e.g., heat distortion temperature). The mechanical property profile can be employed to determine the compatibility of the blend by comparison with the unblended constituents. Compatibi-lization methods can be evaluated easily by comparison of the mechanical property profile with and without compatibihzation. 

The mechanical performance is an essential requirement for any biomedical application. Two features must be considered the bulk properties should be compatible with, as much as possible, the host mechanical ones, and a proper interface should transfer load from the scaffold to the native tissue. Values of modulus and tensile/ compressive strength of the materials determine the final mechanical properties of the scaffolds. The analysis of Fig. 5.3 demonstrates the range of tensile modulus and strength values of biological materials (Mano et al., 2004), and that neither polymers alone, nor ceramics/metals by themselves, provide the necessary array of properties. 

The increasing of NOjc was shown to be related to a small shift in fuel injection timing caused by the different mechanical properties of biodiesel relative to conventional diesel. Because of the higher bulk modulus of compressibility (or speed of sound) of biodiesel, there is a more rapid transfer of the fuel pump pressure wave to the injector needle, resulting in earlier needle lift and producing a small advance in injection timing (Knothe et ah, 2005). 

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