Modulus volumetric

Bulk Modulus of oil, [3 = Volumetric stress/Volumetric strain... 

The frictional properties of TPs, specifically the reinforced and filled types, vary in a way that is unique from metals. In contrast to metals, even the highly reinforced plastics have low modulus values and thus do not behave according to the classic laws of friction. Metal-to-thermoplastic friction is characterized by adhesion and deformation resulting in frictional forces that are not proportional to load, because friction decreases as load increases, but are proportional to speed. The wear rate is generally defined as the volumetric loss of material over a given unit of time. Several mechanisms operate simultaneously to remove material from the wear interface. However, the primary mechanism is adhesive wear, which is characterized by having fine particles of plastic removed from the surface. 

Munns, R., Greenway, H., Stelter, T.L. Kuo, J. (1983). Turgor pressure, volumetric elastic modulus, osmotic volume and ultrastructure of Chlorella emersoni grown at high and low external NaCl. Journal of Experimental Botany, 34,144-55. 

TMA measures the mechanical response of a polymer looking at (1) expansion properties including the coefficient of linear expansion, (2) tension properties such as measurement of shrinkage and expansion under tensile stress, i.e., elastic modulus, (3) volumetric expansion, i.e., specific volume, (4) single-fiber properties, and (5) compression properties such as measuring the softening or penetration under load. 

One of the consequences of close packing in solids and liquids is much higher densities in comparison with gases for instance, ice and water have densities that are a thousand times higher than water vapor at room pressure. Another consequence is that solids and liquids have much lower compressibility, so that the density is not sensitive to the pressure. The bulk modulus B is defined as B = —AP/ AV/V), which has the units of pressure. This parameter measures the fractional volumetric response of a material, when pressure is applied to all faces of the material at the same time. 

TMA measures the mechanical responses of a polymer as a function of temperature. Typical measurements include (1) expansion properties, i.e., the expansion of a material leading to the calculation of the linear expansion coefficient (2) tension properties, i.e., the shrinkage and expansion of a material under tensile stress e.g., elastic modulus (3) dilatometric properties, i.e., the volumetric expansion within a confining medium e.g., specific volume ... 

Fluids that show elasticity to some extent are termed viscoelastic fluids, and some polymer solutions demonstrate such behavior. Elasticity is the tendency of a substance or body to return to its original form, after the applied stress that caused strain (i.e., a relative volumetric change in the case of a polymer solution) has been removed. The elastic modulus (Pa) is the ratio of the applied stress (Pa) to strain (-). The relaxation time (s) of a viscoelastic fluid is defined as the ratio of its viscosity (Pa s) to its elastic modulus. 

This approach can be illustrated by unsaturated polyesters based on an almost equimolar combination of maleate and phthalate of propylene glycol, crosslinked by styrene (45 wt%) (Mortaigne el al., 1992). Six samples differing by the prepolymer molar mass were analyzed. The chain-ends concentration, b, was determined by volumetric analysis of alcohols and acids in the initial reactive mixture. Then, the system was cured, elastic measurements were made in the rubbery state at Tg + 30° C, and the shear modulus G was plotted against chain-ends concentration (Fig. 14.7). The following relationship was obtained ... 

In this equation is the deviator and a is the spherical part of the stress tensor <7, eij is the strain deviator and e the volumetric part of the strain tensor ij, K = (2M + 3A) /3 is bulk modulus with M and A corresponding to the familiar Lame coefficients in the theory of elasticity, while r) and n can be termed the viscous shear and bulk moduli. 

Figure 6. Pressure dependencies of the bulk modulus obtained by the direct numerical differentiation of the in situ volumetric measurements of the glassy B203 under pressure ( relaxed modulus) in the two different runs of compression (solid symbols) and decompression (open symbols). The significant jumps of the effective bulk modulus between the final of compression and onset of decompression for both runs correspond to the jumps between relaxed and almost unrelaxed values. The inset shows pressure dependences of the first coordination number for B from the recent X-ray diffraction data. Both data are from Ref. [129].

Bulk modulus B V(AP/AV) The change in pressure divided by the volumetric strain. 

For other cases, the uptake or internal production of osmotically active solutes can control cell growth, including effects that involve the reversible cell extension caused by changes in internal hydrostatic pressure and are quantitatively described by the volumetric elastic modulus e (Eq. 1.17). For instance, when reversible or elastic changes in volume exist, then (1 )dPidt should be added to the right-hand side of Equation 2.33. Using Equation... 

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. 

Comparing the calculated and experimental stress-strain diagrams for real plastic foams, we will take Eo in Eq. (77) as the elasticity modulus of the polymer base Y and y are foam and polymer base densities (volumetric weights), respectively ... 

---