Elasticity, static modulus

Static modulus of elasticity test with 100x 100x200mm specimen. 

The compressive static modulus of elasticity is shown in Table 4. The static modulus decreases when water cement ratio is increased, and the static modulus increases when the packing ratio of wood-chip is decreased. 

Table 4. Compressive static modulus of elasticity of wood chip concrete unit 103MPa...

ASTM C 469/C 469M. 2010. Standard test method for static modulus of elasticity and Poisson s ratio of concrete in compression. West Conshohocken, PA ASTM International. 

Major effects of vulcanization [2-4] on use-related properties are illustrated by the idealization of Fig. 2. It should be noted that static modulus increases with vulcanization to a greater extent than does the dynamic modulus. (Here, static modulus is more correctly the equilibrium modulus, approximated by a low strain, slow-strain-rate modulus. Dynamic modulus is generaUy measured with the imposition of a sinusoidal, small strain at a frequency of 1-100 Hz.) The dynamic modulus is a composite of viscous and elastic behavior, whereas static modulus is largely a measure of only the elastic component of rheological behavior. 

In addition to the adiabatic or isothermal difference, acoustically determined elastic constants of polymers differ from static values because polymer moduli are frequency-dependent. The deformation produced by a given stress depends on how long the stress is applied. During the short period of a sound wave, not as much strain occurs as in a typical static measurement, and the acoustic modulus is higher than the static modulus. This effect is small for the bulk modulus (on the order of 20%), but can be significant for the shear and Young s modulus (a factor of 10 or more) (5,6). 

Static modulus ( ) for homogenous isotropic elastic substances is a quantitative measure of the elasticity of a material defined as ... 

The quantity K is the static modulus of compression, S and T are the correspSnding relaxation amplitudes. These equations describe the frequency dependence of the moduli in a liquid in nfhich a single relaxation process is effective, characterized by the shear and the bulk relaxation times X 3f,and x and the corresponding amplitudes T and S. If there are more relaxation pro -cesses, we sum over their respective contributions. The connection between the elastic moduli and the Brillouin shift and linewidth is given by the two equations for the real and the imaginary part of the longitudinal modulus as a function of the frequency ... 

Static modulus of elasticity This lab test measures stress/strain rate and gives an indication of the brittleness of rock. 

Fig. 2). If the excitation frequency (oj) is much faster than tu , then the molecules do not have time to respond and there is no flow if to < o , then the molecules slide easily past one another (i.e., the viscosity is low) and little energy is dissipated. Similarly, if the frequency is fixed, but the degree of reaction (extent of cross-linking) is low, the sol is fluid and W (or G") is small as the reaction proceeds p increases), the viscosity increases and G" passes through a maximum before the gel becomes purely elastic (when the network is too stiff to flow) and dissipation is arrested. The storage modulus, G, is the familiar elastic (static) shear modulus when (o> u>o, but G (

There are two types of elastic moduli. First, there is the static elastic modulus that is measured from the stress-strain response of the solder when subjected to tension or compression testing (Ref 25). The second type is referred to as the dynamic elastic modulus and is measured by the passage of sound waves through the material (Ref 26). In the latter case, because sound wave propagation in a solid is based upon atomic vibrations that are very rapid, inelastic deformation is largely ehminated from the material response. Therefore, the modulus is determined from nearly pure elastic deformation. On the other hand, the static modulus is sometimes preferred when calculating plastic strain because it accounts for aU deformation leading up to the yield stress as defined by the 0.2% offset criterion. 

Most obvious was that fact that the moduli values are nearly an order of magnitude less than expected, based upon previous data for lOOSn, 96.5Sn-3.5Ag, and 95.5Sn-5Sb alloys (Ref 27). The role of inelastic deformation was examined by measuring the stafic elastic modulus at faster strain rates. The results are shown in Fig. 6(b). A general trend was observed, in which the modulus increased with strain rate, particularly at the lower temperatures, thereby implying that inelastic deformation likely had a role in the static modulus measurements at low strain rates. However, the faster strain rates did not bring the moduli to within range of the expected values. 

Elastic modulus values are classified into two groups one is the static modulus, and the other is the dynamic modulus. The former is called the isothermal modulus and is obtained from the linear relationship between load and displacement of a specimen. The latter is called the adiabatic modulus and is determined from the resonance frequency or the velocity of an ultrasonic wave (USW) in a specimen. The difference between them is caused by thermal expansion, which results from the adiabatic behavior of the specimen during the propagation of an ultrasonic wave pulse in the latter. Some difficulties cannot be avoided in the determination of the isothermal modulus. For example, a relatively large specimen is needed for the static measurement of a small strain. Thus, the elastic modulus is usually determined from the velocity of an ultrasonic wave in a single crystal of a material, for which it is difficult to prepare a large specimen. 

Fig. 13-11. Stress-strain relationships for INOR-8 at 1200°F. Initial slope (represented by dashed line at left) is equivalent to a static modulus of elasticity in tension of 25,200,000 psi. The dashed line at right is the curve for plastic deformation of 0.002 in/in its intersection with the stress-strain curve indicates a yield strength of 25,800 psi for 0.2% offset. Ultimate tensile strength, 73,895 psi gage length, 3.25 in. material used was from heat 3038.

From these tests, the failure stress and the static modulus of elasticity can be determined at various temperatures over the material s operating range. These data can then be applied to the mathematical model. 

In structural applications for plastics, which generally include those in which the product has to resist substantial static and/or dynamic loads, it may appear that one of the problem design areas for many plastics is their low modulus of elasticity. The moduli of unfilled plastics are usually under 1 x 106 psi (6.9 x 103 MPa) as compared to materials such as metals and ceramics where the range is usually 10 to 40 x 106 psi (6.9 to 28 x 104 MPa). However with reinforced plastics (RPs) the high moduli of metals are reached and even surpassed as summarized in Fig. 2-6. 

The important elastic properties of a material undergoing deformation under static tension are stiffness, elastic strength and resilience. For a material obeying Hooke s law, the modulus of elasticity, E (= o/e), can be taken to be a measure of its stiffness. The elastic... 

Response of a material under static or dynamic load is governed by the stress-strain relationship. A typical stress-strain diagram for concrete is shown in Figure 5.3. As the fibers of a material are deformed, stress in the material is changed in accordance with its stress-strain diagram. In the elastic region, stress increases linearly with increasing strain for most steels. This relation is quantified by the modulus of elasticity of the material. 

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. 

Ultimate strength for concrete is greater under dynamic loads. Though the modulus of elasticity is also greater, this difference is small and is usually ignored. Figure 5.6 describes the relationship between dynamic and static response for... 

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