Static and dynamic modulus

A polymeric matrix is strengthened or stiffened by a particulate second phase in a very complex manner. The particles appear to restrict the mobility and deformability of the matrix by introducing a mechanical restraint, the degree of restraint depending on the particulate spacing and on the properties of the particle and matrix. In the simplest possible case, two bounds have been predicted for the composite elastic modulus (Broutman and Krock, 1967, Chapters 1 and 16 Lange, 1974 see also Section 2.6.4 of this book)  

Ashton et al (1969, Chapter 5). Over certain ranges of filler concentration and modulus, some of these equations become approximately equivalent on simplification, while over other ranges, considerable divergence may be noted. 

One of the first fundamental studies illustrating the effects of fillers on modulus was described by Nielsen et al. (1955), who showed that the shear modulus of polystyrene in the glassy state was increased by the incorporation of from 20 to 60 vol % of mica, calcium carbonate, or asbestos. The magnitude of the increase depended on the filler, about eightfold for mica, but less for asbestos. In addition, as shown by damping measurements, the apparent glass temperature was increased by the presence of the filler, by up to 15°C. 

It was proposed that the modulus of a filled glassy or rigid polymer could be represented by an equation of the form 

Additional evidence for the validity (to a good approximation) of a Kerner-type equation—in this case, the unmodified Kerner equation— as applied to rigid polymeric matrices filled with rigid particles (up to a filler volume fraction of 0.5) has been given by Kenyon and Duffey (1967), Ishai and Cohen (1967), Moehlenpah et al. (1970, 1971), Manson and Chiu (1972) [based on Chiu (1973)], and Brassell and Wischmann (1974). 

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Fig 4. Typical arrangement for Fig 5. Quasi-static and dynamic modulus results for the dynamic modulus test. each of the three materials. 

An instrument for measuring the mechanical properties of rubbers in relation to their use as materials for the absorption and isolation of vibration. These properties are resilience, modulus (static and dynamic), kinetic energy, creep and set. The introduction of an improved version has recently been announced. 

For steel, the modulus of elasticity is the same in the elastic region and yield plateau for static and dynamic response. In the strain hardening region the slope of the stress-strain curve is different for static and dynamic response, although this difference is not important for most structural design applications. 

In the active probe approach, SFM acquires both static and dynamic mechanical properties (Sect. 2.2.2). The former includes the shear and Young s modulus (G,E) as well as the surface indentation and contact area (S,a). Dynamic meas-... 

Foams usually possess a finite low-frequency elastic modulus, along with static and dynamic yield stresses. These and other aspects of foam flow and rheology can be captured qualitatively and even semiquantitatively by cellular foam models. 

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. 

Strip modulus effects on the structural response of a panel made from strip hybrid composite and subjected to static and dynamic loading conditions. 

The rheological parameters of primary scientific and practical concern are the static and dynamic shear modulus, the yield stress, and the shear rate-dependent viscosity. The aim is to understand and predict how these depend on the system parameters. In order to accomplish this with any hope of success, there are two areas that need to be emphasized. First, the systems studied must be characterized as accurately as possible in terms of the volume fraction of the dispersed phase, the mean drop size and drop size distribution, the interfacial tension, and the two bulk-phase viscosities. Second, the rheological evaluation must be carried out as reliably as possible. 

Static and Dynamic Elastic Modulus of Jointed Rock Mass... 

With the help of these equations the uniaxial compressive strength/elastic modulus of jointed rocks can be determined for known values ofjoint factor and uniaxial compressive strength/elastic modulus of intact rock. It is observed that the ratios of both static and dynamic elastic modulus decreases with an increase inthe jointfactorunder unconfinement. The test results of POP and the POP-cement mix specimens are given in Table 5. Figure 14 shows the experimental values of uniaxial compressive strength ratio versus joint factor along with a fitted curve. 

INFLUENCE OF JOINTS ON STATIC AND DYNAMIC ELASTIC MODULUS... 

The influence of joints on static and dynamic elastic modulus was investigated based on the data provided in Table 4 and Table 5. Regression analysis was done for the data on ratios of static and dynamic elastic modulus of plaster of Paris (POP) specimen. Plaster of Paris-cement mix specimen and mixed data of plaster of Paris and Plaster of Paris-cement mix specimen. The curves were plotted for the ratio of static elastic modulus and dynamic elastic modulus for all the three groups of data. The plotted curves are shown in Figure 24 to Figure 26. Figure 24 shows the experimental values of ratio of static elastic modulus versus ratio of dynamic elastic modulus for POP specimens. Figure 25 shows the trend of ratio of static elastic modulus versus ratio of dynamic elastic modulus for POP-cement mix specimens. The plot of ratio of static elastic modulus versus ratio of dynamic... 

Exponential correlations were established for the prediction of uniaxial compressive strength ratio/ratio of static and dynamic elastic modulus of rock mass from the intact rock uniaxial compressive strength/elastic modulus and joint factor (Ramamurthy, 1993), which includes joint frequency, joint inclination andjoint strength. These relations are useful in characterisation of jointed rock mass by knowing the intact rock properties and the joint factor. 

There are many significant mechanical-physical properties, e.g. tensile strength, elongation at break point, tensile modulus, elastic recovery, tension-relaxation/creep under static and dynamic loading, specific weight, shrinkage, moisture absorption and knot strength. 

The main intention of the present contribution is to gain further inside into the relationship between disordered filler stmctures and the reinforcement of elastomers which is discussed mainly for the static and dynamic (shear or tensile) modulus. We will recognize that the classical approaches to (filled) mbber elasticity are not sufficient to describe the physics of such disordered systems. Instead, different theoretical methods have to be employed to deal with the various interactions and, consequently, reinforcing mechanisms on different length scales (see [1] and references therein). 

Reinforcement of elastomers by particulate fillers is pursued in order to improve, by an order of magnitude, static and dynamic moduli as well as ultimate properties such as tensile strength and elongation at break. The simultaneous improvement of modulus and elongation is known as the paradox of elastomers . 

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