Losses, viscoelastic

CR 3nd tp are the contributions from chain recoiling and interfacial dynamics (i.e. drag forces and disentanglement), respectively, and / ve is the viscoelastic loss function which has interfacial and bulk parts. / is a characteristic length of the viscoelastic medium, t is the contact time and n is the chain architecture factor. Fig. 21 illustrates the proposed rate dependency of adhesion energy. 

Usually tj/ is very much larger than Fq. This is why practical fracture energies for adhesive joints are almost always orders of magnitude greater than works of adhesion or cohesion. However, a modest increase in Fq may result in a large increase in adhesion as and Fo are usually coupled. For some mechanically simple systems where is largely associated with viscoelastic loss, a multiplicative relation has been found ... 

The energy release rate (G) represents adherence and is attributed to a multiplicative combination of interfacial and bulk effects. The interface contributions to the overall adherence are captured by the adhesion energy (Go), which is assumed to be rate-independent and equal to the thermodynamic work of adhesion (IVa)-Additional dissipation occurring within the elastomer is contained in the bulk viscoelastic loss function 0, which is dependent on the crack growth velocity (v) and on temperature (T). The function 0 is therefore substrate surface independent, but test geometry dependent. 

It was pointed out in Section 26.2.1 that the friction coefficient is considerably larger on a rough track than on a smooth one when the log ajv values of the master curve are small, i.e., when the temperature is high, and the speed is low, i.e., when the viscoelastic losses are low. Moreover, the adhesion friction, which enables tangential stresses to be built up, is low. 

The equivalent of the right-hand side of Eq. (15), the dissipation, is composed of two additive terms. One is due to viscous shear within the liqnid, and the other is dne to viscoelastic losses in the wetting ridge. We may thus write ... 

For the films and conditions we have used, the transmission line and lumped element models give indistinguishable results. Fitting of the data of Fig. 13.7 yields G as a function of time. These values increase at short times (due to nucleation phenomena) to long time limiting values of G = 1.9 x 106 dyne cm-2 and G" = 3.0 x 108 dyne cm-2. These values of the shear modulus components show that, in dichloromethane, the PVF film is a very rubbery polymer in which there is considerable viscoelastic loss when the film thickness exceeds 1 p.m. 

Tan S measures the ratio of the work dissipated as heat to the maximum energy stored in the specimen during one cycle of a periodic deformation. The conversion of applied work to thermal energy in the sample is called damping. It occurs because of flow of macromolecular segments past each other in the sample. The energy dissipated per cycle due to such viscoelastic losses is ixy G". 

The tangent of 8 exhibits a prominent peak in this region, and the viscoelastic loss functions G"(co) and J" m) may also exhibit an absorption in the transition zone. The relative location of the maxima of the loss functions G"(co) and if they exist, can be obtained by taking into... 

An increasing value of toughness with crack velocity is commonly found in elastomeric systems however, in this case, the increase in Qc is attributed to the viscoelastic losses in the bulk of the elastomer which increase with increasing deformation rate and decreasing temperature [61,62]. 

For glassy polymers the same argument does not hold since, except in specific cases where secondary relaxations in the glass are active, the viscoelastic losses in the polymer, if any, should decrease with increasing crack velocity. However, we can still interpret the experimental results with Eq. (24) and note that the only two parameters that will vary with deformation rate are oc and Clear-... 

Preliminary nanoindentation results on other teeth (premolars, incisors and canines) indicate variations in mechanical properties as large as those discussed for molars [unpubl. data]. In each case the exact distribution of mechanical properties within the enamel appears to correlate with the extent of mechanical loading experienced by the tooth during mastication. However, there appears to be an increase in the viscoelasticity (loss modulus) for the enamel of anterior teeth when compared to posterior teeth, again this may be related to their function. 

As indicated by the values, the VHB 4910 acrylic elastomer gave the highest performance in terms of strain and actuation pressure. Extensive lifetime tests have not been made, but acrylic films have been operated continuously for several hours at the 100% relative area strain level with no apparent degradation in relative strain performance. However, the acrylic elastomer has relatively high viscoelastic losses that limit its half-strain bandwidth (the frequency at which the strain is one-half of the 1-Hz response) to about 30-40 Hz in the circular strain test. By comparison, HS3 silicone has been used for prototype loudspeakers at frequencies as high as 2-20 kHz [16,17]. The acmation of CF19-2186 silicone, albeit at lower strains and fields than reported here, has been measured directly via laser reflections with full... 

The dielectric elastomer films presented here appear promising as actuator materials because their overall performance can be good. The available literature indicates that the actuated strains of silicone are greater than for any known highspeed electrically actuated material (that is, a bandwidth above 100 Hz). Silicone elastomers also have other desirable material properties such as good actuation pressures and high theoretical efficiencies (80-90%) because of the elastomers low viscoelastic losses and low electrical leakage [12]. 

As already mentioned, the value of d> is usually far higher than that of W, and the energy dissipated can then be considered as the major contribution to the adhesion strength G. In the case of assemblies involving elastomers, it has been clearly shown in various studies [3,4,58,60-62] that the viscoelastic losses during peel experiments, and consequently, the function , follow a time-temperature equivalent law such as that of Williams et al. [63]. 

Effectively, when viscoelastic losses are negligible (i.e., when performing experiments at very low peel rate or high temperature), 4>-> 1 and G must tend toward IV. However, the resulting threshold value Gq is generally 100 to 1000 times higher than the thermodynamic work of adhesion, IV. 

However, one important energy loss which was explained was the effect of the viscoelastic behavior of the polymer. This was studied by varying the crosslink density of the rubber, to alter the loss of elastic energy as the material relaxed. As the viscoelastic loss increased, so did the adhesive hysteresis, as shown in Fig. 8.13. 

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