Dissipation, 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). 

At high frequencies, the viscoelastic behavior of suspensions is primarily dissipative, as the particles are forced to move through the solvent much faster than they can relax by Brownian motion. The high-frequency behavior is characterized by a constant high-frequency viscosity = lim >oo G" jay, which has been subtracted from the data plotted in Fig. 

Dissipation phenomena generally occur during measurement of the adherence of polymer materials, leading to an adherence energy function of both the number and nature of interfacial interactions (adhesion) and dissipative properties, mainly due to viscoelastic behavior [1-5]. Friction properties of polymers are also governed by interfacial interactions and dissipation mechanisms. Common phenomena (interfacial interaction and dissipation) therefore control adherence and friction behaviors. However, the relationship between the two phenomena is still vague or undefined. The first objective of this experimental work is then to compare adherence and friction of polydimethylsiloxane (PDMS) networks in order to establish relationships between these two properties. 

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 ... 

As has been pointed out, viscoelastic behavior is frequently associated with flowing polymeric systems. Usually, such behavior is especially pronounced in molten or thermally softened polymers. Elastic effects should be contrasted with the viscous effects (i.e., viscous heating). In the latter case, the energy necessary to move the fluid is dissipated as heat. In the former instance, however, energy put into an elastic system can be recovered. This suggests the possibility of a form of energy storage in a viscoelastic system. 

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. 

The dissipated energy causes a rise in temperature, whose magnitude of course depends on the heat capacity of the system. The temperature may reach a steady-state value for continuous sinusoidal deformation, depending on the rate of heat loss to the surroundings. Equation 10 can be used to estimate heat production in various experimental procedures, where the strains are often purposely kept very small at high frequencies to prevent temperature rise as well as to insure linear viscoelastic behavior. It can also be used to estimate heat production in practical situations of cyclic deformations, such as the performance of automobile tires. Values can be compared on a relative basis even though the stress distribution in a loaded tire is complicated and the strains exceed the limitations of linear viscoelasticity and the cyclic deformation does not follow a simple sinusoidal pattern. 

The nonlinear viscoelastic behavior of elastomers is usually related to their inner structure interaction, namely, the interaction between the matrix molecules, the interaction between the matrix molecules and fillers, and the interaction between the fillers. Of course, the effect of characteristics of the inner structure on the nonlinear viscoelastic behavior of elastomers cannot be ignored, since it is also related to portion of the energy dissipated during dynamic deformation. For instance, the filler parameters are important which influence the dynamic properties of rubber compounds, dynamic hysteresis in particular, as well as their temperature... 

XRD, SEM, and TEM are widely used for morphological characterization of nanocomposites. Rheology has also been used extensively in complement to these techniques in several studies as it is very sensitive to the morphology of nanocomposites [23,75-80]. The summary of the most significant results from these studies is the transition from liquid-like to solid-like viscoelastic behavior for nanocomposites, even at low-volume fractions of silicate layers, as well as a strong shear-thinning behavior. The solid-like behavior has been attributed to the formation of a percolated network of clay particles that occurs at relatively low clay loading, due to the anisotropy of the particles, which prevents their free rotation and the dissipation of stress. 

This part of the book moves from the chemical structure and reactions used to form polymers to their physical properties. Some of the material in this section may be familiar to one who has studied the mechanics of materials, but it is worth delving deeper into polymers and discover some of their unusual characteristics (viscoelasticity, for one). Topics that are addressed here include mechanical strength, flexibility, polymer responses to compression, stretching and shear forces, and the equipment used to test these properties. One chapter is devoted to mathematical models to describe viscoelastic behavior (using combinations of so-called springs and dashpots) to approximate the complex response of polymers to stresses that include both elastic stretch (which is particularly useful in the waistbands of underwear) and viscous deformation (which is very useful in automobile bumpers to dissipate the energy of a collision). 

The enhanced plasticity and toughness of modem adhesives have become an important property in applications where dissipation of energy in the case of impact, the ability to compensate thermal movement, or the reduction of vibration lead to added value and improved service performance. Viscoelastic behavior can theoretically be predicted and analyzed by means of mechanical models including combinations of elastic and viscous elements to simulate the time-dependent viscoelastic stress-strain response to mechanical loads. 

It is useful to note that the dynamic behavior of any system that incorporates both energy storage and energy dissipation must have at least one characteristic time. Another example is an electrical circuit that includes both resistance and capacitance. Furthermore, we note that Eq. 4.15 is the same as Eq. 4.12, with Fq replaced by Gq and % by T. The Maxwell element is thus said to be a mechanical analog of the viscoelastic behavior described by Eq. 4.12. It will often prove useful in our discussion of the linear viscoelastic behavior of polymers to refer to the viscoelastic analog of the Maxwell element. 

Viscoelastic polymers essentially dominate the multi-billion dollar adhesives market, therefore an understanding of their adhesion behavior is very important. Adhesion of these materials involves quite a few chemical and physical phenomena. As with elastic materials, the chemical interactions and affinities in the interface provide the fundamental link for transmission of stress between the contacting bodies. This intrinsic resistance to detachment is usually augmented several folds by dissipation processes available to the viscoelastic media. The dissipation processes can have either a thermodynamic origin such as recoiling of the stretched polymeric chains upon detachment, or a dynamic and rate-sensitive nature as in chain pull-out, chain disentanglement and deformation-related rheological losses in the bulk of materials and in the vicinity of interface. 

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