Elastic Properties of Materials

To this point, it has been assnmed that elastic deformation is time independent—that is, that an applied stress produces an instantaneous elastic strain that remains constant over the period of time the stress is maintained. It has also been assumed that upon release of the load, the strain is totally recovered—that is, that the strain immediately returns to zero. In most engineering materials, however, there will also exist a time-dependent elastic strain component—that is, elastic deformation will continue after the stress application, and upon load release, some finite time is required for complete recovery. This time-dependent elastic behavior is known as anelasticity, and it is due to time-dependent microscopic and atomistic processes that are attendant to the deformation. For metals, the anelastic component is normally small and is often neglected. However, for some polymeric materials, its magnitude is significant in this case it is termed viscoelastic behavior, which is the discussion topic of Section 15.4. 

A piece of copper originally 305 mm (12 in.) long is pulled in tension with a stress of 276 MPa (40,000 psi). If the deformation is entirely elastic, what will be the resultant elongation  

Because the deformation is elastic, strain is dependent on stress according to Equation 6.5. Furthermore, the elongation A/ is related to the original length Zq through Equation 6.2. Combining these two expressions and solving for AZ yields 

The values of o- and Zq are given as 276 MPa and 305 mm, respectively, and the magnitude of E for copper from Table 6.1 is 110 GPa (16 X10 psi). Elongation is obtained by substitution into the preceding expression as 

Definition of Poisson s ratio in terms of lateral and axial strains 

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Elasticity Property of materials whereby they tend to retain or recover... 

For practical applications of (2.15), i.e., the exploration of the elastic properties of materials, it is convenient to eliminate instrumental parameters by referring the measured intensities to a base intensity, usually measured at 4.2 K. The corresponding expression is then [6] ... 

The elastic properties of materials can be understood, at least qualitatively, by considering the attractive and repulsive forces between atoms and molecules. 

Straightforward measurements of elastic properties of materials can be made via high-pressure static compression experiments, in which X-ray diffraction (XRD) is used to measure the molar volume (V), or equivalently the density (p), of a material as a function of pressure (P). The pressure dependence of volume is expressed by the incompressibility or isothermal bulk modulus (Kt), where Kp = —V(bP/bV)p. 

Photoacoustic (PA) spectroscopy is a combination of optical spectroscopy and calorimetry [58]. It is a technique for studying those materials that are unsuitable for the conventional transmission or reflection methodologies. It can be used to measure thermal and elastic properties of materials, to study chemical reactions, to measure the thickness of layers and thin films, and to perform a variety of other non-spectroscopic investigations. This technique can be applied to different types of inorganic, organic and biological materials in the gas-, liquid-, or solid phase. Nowadays, PA spectroscopy is mainly employed for material characterization [59]. Compared with other spectroscopic techniques, PA spectroscopy provides a non-destructive analysis and does not require any sample preparation. 

Tensors for the small-strain elastic properties of materials... 

The elastic properties of materials exert pressure on calender rolls which causes their deformation. This is controlled by honing the surface of rolls, roll bending, or cross-axes. Modem calender automatically adjusts the gaps based on the data from the gauges scanning the entire width of the material. 

As we have seen, it is possible to study stractural elements of concrete from two different perspectives. On one hand, we can base the theory on elastic properties of materials. Within this view concrete is considered as behaving as an elastic material up to a load which leads to mpture. Determination of rupture conditions and other properties of the material are based on the assumption that the material up to rupture is elastic. That gives one theoretical framework on which both practical and theoretical analyses of stractural elements can be founded. Structural elements are then construed as model objects which are within the range of elasticity. 

Another advantage of instrumented nanoindentation is that the elastic properties of materials can be determined. The composite modulus (specimen-tip) E is extracted from... 

A number of simple empirical potential functions were presented in Chapter 3. We will now attempt to use some of these functions in order to derive relationships between the various elastic properties of materials. 

There are some approximate empirical relations between the hardness and elastic properties of materials (152), and we can speculate upon the elastic constants of cBN from its hardness. 

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