Dissipation, viscoelastic

It has often been pointed out for a long time that the hysteresis energy given from the hysteresis loop under large extension is too big compared with the viscoelastic dissipation energy. For example, the hysteresis loop given from the stress relaxation is only 20%-30% of that from the stress-strain curve, when both measurements are performed at the same relaxation time and the... 

It has been shown that the kinetics of the spreading of a liquid on a rubber is largely dependent on viscoelastic dissipation in the wetting ridge of the substrate near the triple line. This behavior may, in practice, be slightly altered by moderate swelling that modifies the solid/liquid interactions for long contact times. 

The consequences of the wetting ridge in the capillary penetration of a liquid into a small-diameter tube have been evaluated. Viscoelastic braking reduces the liquid flow rate when viscoelastic dissipation outweighs the viscous drag resulting from Poiseuille flow. 

Numerically, this estimate gives fmmw = 6.3x 10 12 N/monomer. This result should be compared with the estimate obtained with Eq. (8) which is four times higher. The discrepancy between the two results is due to the viscoelastic dissipation that was not taken into account in the energy calculation. Clearly, excess dissipation takes place near the interface even in the straight pullout regime. 

Since dynamic friction of polymers has a large contribution from internal viscoelastic dissipation, plots of the friction force, determined, e.g., by AFM, vs./D are qualitatively similar to plots of tan<5 vs. fa. Hence, by measuring dynamic friction forces under well-controlled conditions, the dynamics of a given polymer can be directly probed at the free surface of a sample specimen. Thereby surface vs. bulk properties can be probed as well as confinement effects. 

Modern processing equipment usually employs an Archimedes-type screw that conveys the solid polymer (powder or granules) and causes it to melt progressively through heat transfer from the barrel and heat generation by viscoelastic dissipation of the energy introduced by the screw rotation. 

Introducing a dimensional constant (ki = (2nR) ), this relationship becomes Eq. (6) or (7), where G is the separation energy and/(Me, v, T) is a viscoelastic dissipation function which depends on the network molecular structure (Me), temperature T and separation rate v. 

Table 3.5 Average viscoelastic dissipation function deduced from calculated thermodynamic work of adhesion.

The function /is constant for a given grafting and whatever the substrate Me value. Values of Wq are also in agreement with values quoted in the literature. Indeed, usual work of adhesion values He between 40 and 70 mj m for organic-organic contacts, such as between two silanated siheas [10], and between 40 and 145 mJ m for a contact between a raw material such as silica and a silanated silica. Finally we have reported in Fig. 3.7 the evolution of the dissipative function / versus Me, the mass between crosslinks. A linear relationship is obtained. Therefore a modified expression for G, the separation energy, is proposed (Eq. (8), where/(v, T) represents a viscoelastic dissipation function which depends only on the temperature T and separation rate v). 

In a car ully designed high quality resonator, the dissipation processes 2), 3), and 4) can be kept negligibly small. It is important to minimize the perturbations caused by these effects, because a theoretical treatment is difficult. It was shown in Ref. and that such an optimization of the cell is in fact possible and then only viscous and thermal boundary layer losses ne be taken into account. Throughout the principal portion of the volume of the resonator, the expansion and contraction of the gas occurs adiabatically. Near the walls, however, this process becomes isothermal. This leads to heat conduction, which is responsible for the thermal dissipation process. The viscous dissipation can be explained by the boundary conditions imposed by the wails. At the surface, the tangential component of the acoustic velocity is 2 0, whereas in the interior of the cavity, it is proportional to the gradient of the acoustic pressure. Thus, viscoelastic dissipation occurs in the transition region. 

Because of their characteristic rigidity and brittleness in their cured state, when MF resins are used for impregnated paper overlays, small amounts (typically 3 to 5%) of modifying compounds are often copolymerized with the MF resin during its preparation to give better flexibility to the finished product and better viscoelastic dissipation of stress in the joint. Most commonly used are acetoguanamine, s-caprolactam, and p-toluene-sulfonamide (Formula 2). 

Acoustic emission has been frequently used in studies of the fracture behavior of fiber-reinforced composites. This method was also adopted to studies of blends. Since the sound is most frequently generated by debonding of two phases, there should be a drastic difference in the acoustic activity for blends located on the two sides of spinodal. To quantify miscibility between PVC and EVAc, acoustic emission measurements during a peel test of a-PVC/EVAc/PVC sandwich were carried out (Muniz et al. 1992). The authors considered that the acoustic emissions at slow rates of peeling are related not to the viscoelastic dissipation processes, but rather to the work necessary to puU apart polymeric chains or break bonds. The highest acoustic emission was obtained for VAc content in EVAc of 18 and 29 wt%. 

The thickness of the adhesive, and of any backing used, will affect the peel strength in several ways. It directly enters the strain-energy density term Wj) and may also alter some of the dissipation terms in Eqn. 7 by changing the actual angle at the peel front (see Fig. 2) or by altering the volume of polymer in which plastic or viscoelastic dissipation occurs. Many of the terms in Eqn. 7 will be temperature and rate dependent, so the peel strength will also depend on these variables. 

Energy loss through viscoelastic dissipation usually contributes to the fracture energy of an adhesive bond sometimes that contribution is dominant. Adhesives are often designed to operate in the regions where viscoelastic losses (tan 5) are high. Further discussion can be found under Adhesion - fundamental and practical. Peel tests and Tensile tests see also Creep and Durability creep rupture. 

From Figure 9, it can be seen that if the bodies separate beyond z ax, there is no restoring force and the two bodies will remain apart. If the bodies are the same, then this must be the cohesive strength of the material. It must be realized, however, that this strength is for a perfect material having no viscoelastic dissipation of energy and, as will be seen later, no flaws. 

In Table II, the ultimate stresses of materials calculated from their Young s modulus are compared with the measured values of F ax- It is apparent that the measured values for the failure stress are far below the theoretical values. The situation is worse than it looks, however, because the measured values are partially due to viscoelastic dissipation of the applied stress, while the calculated values assume no such viscoelastic dissipation. Needless to say, this indicates that the theoretical values are far in excess of the measured values. An explanation of these discrepancies is presented in the next section, which gives a short introduction to fracture mechanics. 

Polymers generally exhibit complex tribological behaviors due to different energy dissipation mechanisms, notably those induced by internal friction (chain movement), which is dependent on both time and temperature. Polymer friction is then governed by interfacial interactions and viscoelastic dissipation mechanisms that are operative in the interfacial region and also in the bulk, especially in the case of soft materials. Friction of a polymer can be closely linked to its molecular structure. The role of chain mobility has been studied in the case of elastomers, based on dissipation phenomena during adhesion and friction processes of the elastomer in contact with a silicon wafer covered by a grafted layer [1-5]. 

For both PDMSs, for both substrates, and for all friction speeds, a great effect of normal force is observed. The higher friction coefficient observed at low normal force could be explained by the role of adhesion, which is magnified at low load (where the bulk contribution is lower). The contribution of interfacial interactions (or adhesive contact) is then magnified. These interfacial interactions will activate viscoelastic dissipation mechanisms, increasing the friction resistance. 

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