Mechanical behavior, dynamic damping

Dynamic mechanical behaviors of CNTs are of importance in various applications, such as high frequency oscillators and sensors [56]. By adding CNTs to polymer the fundamental frequencies of CNT reinforced polymer can be improved remarkably without significant change in the mass density of material [57]. It is importance indicate that the dynamic mechanical analysis confirms strong influence of CNTs on the composite damping properties [58]. 

Based on damping theory (Kim and Sperling 1997 Sophiea et al. 1994a), the damping behavior of a polymer can be evaluated from its dynamic mechanical behavior by expressing it as the area under the tan 8 versus temperature curve (Keskkula et al. 1971) or the area under the linear loss modulus versus temperature... 

Figure 6.5 Dynamic mechanical behavior of polyurethane nanocomposite in the presence of various types of nanoparticles, (a and b) Storage modulus and damping factor in the presence of alumina [84], (c and d) storage modulus and damping factor in the presence of CNTs [86],...

Dynamic mechanical analysis measures changes in mechanical behavior, such as modulus and damping as a function of temperature, time, frequency, stress, or combinations of these parameters. The technique also measures the modulus (stiffness) and damping (energy dissipation) properties of materials as they are deformed under periodic stress. Such measurements provide quantitative and qualitative information about the performance of materials. The technique can be used to evaluate reinforced and unreinforced polymers, elastomers, viscous thermoset liquids, composite coating and adhesives, and materials that exhibit time, frequency, and temperature effects or mechanical properties because of their viscoelastic behavior. 

Dynamic mechanical experiments yield both the elastic modulus of the material and its mechanical damping, or energy dissipation, characteristics. These properties can be determined as a function of frequency (time) and temperature. Application of the time-temperature equivalence principle [1-3] yields master curves like those in Fig. 23.2. The five regions described in the curve are typical of polymer viscoelastic behavior. 

As shown in Chapter 10, molecular dynamics in polymers is characterized by localised and cooperative motions that are responsible for the existence of different relaxations (a, (3, y). These, in turn, are responsible for energy dissipation, mechanical damping, mechanical transitions and, more generally, of what is called a viscoelastic behavior - intermediary between an elastic solid and a viscous liquid (Ferry, 1961 McCrum et al., 1967). 

Dynamic mechanical property (DMP) measurements are used to evaluate the suitability of a polymer for a particular use in sound and vibration damping. Since the dynamic mechanical properties of a polyurethane are known to be affected by polymer morphology (4), it is important to establish the crystallization and melting behavior as well as the glass transition temperature of each polymer. Differential scanning calorimetry (DSC) was used to determine these properties and the data used to interpret the dynamic mechanical property results. 

Using a computerized data reduction scheme that incorporates a generalized WLF equation, dynamic mechanical data for two different polymers were correlated on master curves. The data then were related to the vibration damping behavior of each material over a broad range of frequencies and temperatures. The master curves are represented on a novel reduced temperature nomograph which presents the storage modulus and loss tangent plots simultaneously as functions of frequency and temperature. ... 

These equations are often used in terms of complex variables such as the complex dynamic modulus, E = E + E", where E is called the storage modulus and is related to the amount of energy stored by the viscoelastic sample. E" is termed the loss modulus, which is a measure of the energy dissipated because of the internal friction of the polymer chains, commonly as heat due to the sinusoidal stress or strain applied to the material. The ratio between E lE" is called tan 5 and is a measure of the damping of the material. The Maxwell mechanical model provides a useful representation of the expected behavior of a polymer however, because of the large distribution of molecular weights in the polymer chains, it is necessary to combine several Maxwell elements in parallel to obtain a representation that better approximates the true polymer viscoelastic behavior. Thus, the combination of Maxwell elements in parallel at a fixed strain will produce a time-dependent stress that is the sum of all the elements ... 

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