Elastic modulus discussion

For water the values of the constants discussed in the previous section are given in Table 4.1. The value of the elasticity modulus increases as the pressure and temperature increase. At a pressure of 10 MPa and temperature 373 K, the elasticity modulus E is 2,7 x 10 Pa. 

The problem of concentration dependence of yield stress will be discussed in detail below. Here we only note that (as is shown in Figs 9 and 10) yield stress may change by a few decimal orders while elastic modulus changes only by several in the field of rubbery plateau and, moreover, mainly in the range of high concentrations of a filler. 

The peculiarities of dynamic properties of filled polymers were described above in connection with the discussion of the method of determining a yield stress according to frequency dependence of elastic modulus (Fig. 5). Measurements of dynamic properties of highly filled polymer melts hardly have a great independent importance at present, first of all due to a strong amplitude dependence of the modulus, which was observed by everybody who carried out such measurements [3, 5]. 

Sounds and vibrations in electrical appliances or vehicles are in some cases unpleasant. If we can reduce these sounds and vibrations as we desire, we will have a more happy and comfortable life in the next century. Sections 4 and 5 discuss a new smart polymer gel for actively reducing sounds and vibrations. The smart gel can vary its elastic modulus in an electric field. 

Because an electric field also involves a magnetic field, it is suggested that the materials which increase elastic modulus in external magnetic fields (MR gel) can be prepared using particles which can polarize in a magnetic field. An MR gel will be discussed in Sect. 5.1. 

In this section, we discuss theoretically the influence of microscopic interaction between polarized particles on the macroscopic mechanical properties of the composite gel, in particular, the elastic modulus. 

As is obvious from the above discussion, a very detailed understanding of entangling in elastomeric networks is required for interpretation of the elastic modulus, in particular its dependence on deformation and swelling. 

In this paragraph comparatively much attention will be paid to the curve in which tensile stress is plotted out in relation to relative elongation, because important properties can be inferred from this curve. One of these is the elastic modulus, a material property which was briefly discussed in chapter 9. This E-modulus often depends on the temperature and this relationship is represented in a log E-T curve. Next properties of the three groups of materials are compared in a table and finally some attention will be paid to processing and corrosion . 

The main subject of the following discussion is the mechanical behaviour of networks in terms of the behaviour of the system of weakly coupled macromolecules. The network modulus of elasticity is small in comparison to the values of the elasticity modulus for low-molecular solids (Dusek and Prins 1969 Treloar 1958). Nevertheless, large (up to 1000%) recoverable deformations of the networks chains are possible. 

Elastic and viscous stress-strain curves can be experimentally determined from incremental stress-strain curves measured on samples of different tendons. Typical elastic and viscous stress-strain curves for rat tail and turkey tendons are shown in Figures 7.4 and 7.5. For both types of tendons the curves at high strains are approximately linear. As we discuss in Chapter 8, the elastic modulus can be calculated for collagen, because most of the tendon is composed of collagen and water, by dividing the elastic slope by the collagen content of tendon. When this is done the value of the elastic modulus of collagen in tendon is somewhere between 7 and 9 GPA. 

If the elastic modulus is obtained from the slope of the elastic stress-strain curve, then we can evaluate the first term on the right-hand side in Equation (8.3) from experimental data elastic stress-strain curves. The second term on the right-hand side in Equation (8.3) can be evaluated from the product of the strain rate, which is set in a constant strain-rate experiment, and the viscosity. As we discussed in Chapter 3, the viscosity of a macromolecule is related to the shape factor v, therefore we can evaluate the second term on the right-hand side of Equation (8.3) from the product of the shape factor and the strain rate. 

On the basis of what has been discussed, we are in the position to provide a unified understanding and approach to the composite elastic modulus, yield stress, and stress-strain curve of polymers dispersed with particles in uniaxial compression. The interaction between filler particles is treated by a mean field analysis, and the system as a whole is macroscopically homogeneous. Effective Young s modulus (JE0) of the composite is given by [44]... 

As previously noted, this chapter has been concerned mainly with those models for the creep of ceramic matrix composite materials which feature some novelty that cannot be represented simply by taking models for the linear elastic properties of a composite and, through transformation, turning the model into a linear viscoelastic one. If this were done, the coverage of models would be much more comprehensive since elastic models for composites abound. Instead, it was decided to concentrate mainly on phenomena which cannot be treated in this manner. However, it was necessary to introduce a few models for materials with linear matrices which could have been developed by the transformation route. Otherwise, the discussion of some novel aspects such as fiber brittle failure or the comparison of non-linear materials with linear ones would have been incomprehensible. To summarize those models which could have been introduced by the transformation route, it can be stated that the inverse of the composite linear elastic modulus can be used to represent a linear steady-state creep coefficient when the kinematics are switched from strain to strain rate in the relevant model. 

We can readily extend our discussion to include a pressure-volume, or P-K curve, which has proved useful for analyzing the water relations of plant organs such as leaves. In particular, the earliest calculations of internal hydrostatic pressure and cellular elastic modulus were based on P-V curves. To obtain such a curve, we can place an excised leaf in a pressure chamber (Fig. 2-10) and increase the air pressure in the chamber until liquid just becomes visible at the cut end of the xylem, which is viewed with a dissecting microscope or a hand-held magnifying lens so that water in individual conducting cells in the xylem can be observed. When the leaf is excised, the... 

The work [9] discusses publications analysing physico-chemical indices and the specifics of the chemical structure of cast aminoplasts modified with 20-50% (with respect to the mass of melamine) of caprolactam and other lactams. Materials of this type, havin an increased impact strength, thermal stability, strength and elasticity modulus in bending, are manufactured in Czechoslovakia under the trade mark UmaLur MK-1, MK-2, MK-3. 

In the papers quoted above, the authors followed the crystallization kinetics from calorimetric data. From the point of view of rheokinetic methods discussed here, no less interesting is one more example of describing crystallization kinetics given in Fig. 26, where there is a comparison of experimental (obtained in Ref. [126]) and calculated by Eq. (18) time dependences of the relative elastic modulus of crystallization of cis-l,4-polybutadiene. A good agreement between experimental and calculated data implies the possibility of describing the crystallization kinetics, with the help of formulas of the type of Eq. (18). 

Elastic Modulus. The third key issue relates to improvements required in the elastic modulus of these ceramic fibers. Studies indicate that modulus improvements will depend on careful control of composition and increases in fiber density (24). Earlier discussions in this chapter summarized the low densities of these ceramic fibers relative to their crystalline counterparts, as well as the existence of considerable pore volume. 

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