Material properties elastic modulus

A plane of material symmetry exists within a material when the material properties (elastic moduli) at mirror imaged points across the plane are identical. For example, in the sketch given in Fig. 2.15, the yz plane is a plane of symmetry and the elastic moduli would be the same at the material points A and B. 

Thus a measurement of the ultrasonic properties can provide valuable information about the bulk physical properties of a material. The elastic modulus and density of a material measured in an ultrasonic experiment are generally complex and frequency dependent and may have values which are significantly different from the same quantities measured in a static experiment. For materials where the attenuation is not large (i.e., a ca/c) the difference is negligible and can usually be ignored. This is true for most homogeneous materials encountered in the food industry, e.g., water, oils, solutions. 

The velocity is therefore determined by two fundamental physical properties of a material its elastic modulus and density. The less dense a material or the more resistant it is to deformation the faster an ultrasonic wave propagates. Usually, differences in the moduli of materials are greater than those in density and so the ultrasonic velocity is determined more by the elastic moduli than by the density. This explains why the ultrasonic velocity of solids is greater than that of fluids, even though fluids are less dense [1],... 

On the other hand, the mechanical properties of monolithic carbon gels are of importance when they are to be used as adsorbents and catalyst supports in fixed-bed reactors, since they must resist the weight of the bed and the stress produced by its vibrations or movements. A few smdies have been published on the mechanical properties of resorcinol-formaldehyde carbon gels under compression [7,36,37]. The compressive stress-strain curves of carbon aerogels are typical of brittle materials. The elastic modulus and compressive strength depend largely on the network connectivity and therefore on the bulk density, which in turn depends on the porosity, mainly the meso- and macroporosity. These mechanical properties show a power-law density dependence with an exponent close to 2, which is typical of open-cell foams. 

Other mechanical properties of glasses are inherent to the material. The elastic modulus, E, is determined by the individual bonds in the material and by the structure of the network. The hardness of glasses is a function of the strength of individual bonds and the density of packing of the atoms in the structure. 

Hardness H defines the resistance to local deformation of a material when indented, drilled, sawed, or abraded. It involves a complex combination of properties (elastic modulus, yield strength, strain-hardening capacity). The prevailing deformation mechanism depends upon the material and the type of tester. Hardness is either measured by (1) static penetration of the specimen with a standard inden-ter at a known force, (2) dynamic reboimd of a standard indenter of known mass dropped from a standard height, or (3) scratching with a standard pointed tool under a load. The hardness tester, indenter shape, and force employed strongly influence the hardness numbers (1). 

As it is known [4], the parameter x influences essentially on nanocomposites polymer/organoclay properties. One from the most important mechanical characteristics of polymeric materials, namely, elasticity modulus E depends on the value as follows ... 

Microprobing technique applied here is sensitive to the depth distribution of the elastic properties and can provide insight on buried details of the surface distribution of different polymer phases. As demonstrated in Figure 4, elastic modulus for the rubber phase shows the presence of hard PS surface underneath of compliant material. The elastic modulus depth profile shows a large variation at a very low indentation depth (below 20 nm) caused, mainly, by the instability of the first mechanical contact as discussed in our previous papers [12-14]. In the range of indentation depths from 20 to 150 nm, a gradual decrease of elastic modulus is observed that can be related to either surface hardening phenomena or rate dependent (viscoelastic) contribution. At intermediate indentation depth, a stable, virtually constant value of the elastic modulus is recorded. 

Experimental data issued from tensile tests on samples with varying amyl acetate concentration and ageing temperature have evidenced a decrease of mechanical properties (elastic modulus, peak load, cristalUnity) over time. These experimental results match the amyl acetate molecules penetration effect in the polymeric material, inducing a decrease of the intermolecular interactions in the polymer, like a plasticizer should do. 

In any given material, the relaxation modulus will reflect the response of the material on different timescales. To make a measurement, materials are deformed under a periodic load with frequency w. Then, G and G are measured across a wide range of frequencies (typically three to four decades). Measurements of G and G" can be used to characterize the mechanical properties of soft materials, including polymer networks and colloidal systems. The technique is also known as mechanical spectroscopy. In a viscoelastic material, the elastic modulus will cross over the viscous modulus at the transition point from viscous to elastic bulk behavior and indicates a possible sol-gel transition or the onset of rubbery behavior in a polymer network. 

The following elastic properties have been used for the stress analysis Material 1, elastic modulus = 0.33 GPa, Poisson s ratio v, = 0.49 Material 2, 2=3 GPa, V2 = 0.35. The thermal residual stresses caused by the sample preparation are neglected. 

The interconnection of microhardness, determined according to the results of the tests in a very localized microvolume, with such macroscopic properties of pol5mieric materials as elasticity modulus E and yield stress Oy is another problem aspect. At present a large enough number of derived theoretically and obtained empirically relationships between E and Oj, exists [16],... 

Hardness is a measure of a material s resistance to deformation. In this article hardness is taken to be the measure of a material s resistance to indentation by a tool or indenter harder than itself This seems a relatively simple concept until mathematical analysis is attempted the elastic, plastic, and elastic recovery properties of a material are involved, making the relationship quite complex. Further complications are introduced by variations in elastic modulus and frictional coefficients. 

Nonoxide fibers, such as carbides, nitrides, and carbons, are produced by high temperature chemical processes that often result in fiber lengths shorter than those of oxide fibers. Mechanical properties such as high elastic modulus and tensile strength of these materials make them excellent as reinforcements for plastics, glass, metals, and ceramics. Because these products oxidize at high temperatures, they are primarily suited for use in vacuum or inert atmospheres, but may also be used for relatively short exposures in oxidizing atmospheres above 1000°C. 

The most important properties of refractory fibers are thermal conductivity, resistance to thermal and physical degradation at high temperatures, tensile strength, and elastic modulus. Thermal conductivity is affected by the material s bulk density, its fiber diameter, the amount of unfiberized material in the product, and the mean temperature of the insulation. Products fabricated from fine fibers with few unfiberized additions have the lowest thermal conductivities at high temperatures. A plot of thermal conductivity versus mean temperature for three oxide fibers having equal bulk densities is shown in Figure 2. 

The Rheometric Scientific RDA II dynamic analy2er is designed for characteri2ation of polymer melts and soHds in the form of rectangular bars. It makes computer-controUed measurements of dynamic shear viscosity, elastic modulus, loss modulus, tan 5, and linear thermal expansion coefficient over a temperature range of ambient to 600°C (—150°C optional) at frequencies 10 -500 rad/s. It is particularly useful for the characteri2ation of materials that experience considerable changes in properties because of thermal transitions or chemical reactions. 

The design of shape-memory devices is quite different from that of conventional alloys. These materials are nonlinear, have properties that are very temperature-dependent, including an elastic modulus that not only increases with increasing temperature, but can change by a large factor over a small temperature span. This difficulty in design has been addressed as a result of the demands made in the design of compHcated smart and adaptive stmctures. Informative references on all aspects of SMAs are available (7—9). 

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