Behavior at Large Strains

Figure 3.2 Trouton ratio, Tr, of uniaxial extensional viscosity to zero-shear viscosity jq after start-up of steady uniaxial extension at a rate of 1 sec i for a Boger fluid consisting of a 0.185 wt% solution of flexible polyisobutylene (Mu, = 2.11 x 10 ) in a solvent composed mostly of viscous polybutene with some added kerosene (solid line). The dashed line is a fit of a multimode FENE dumbbell model, where each mode is represented by a FENE dumbbell model, with a spring law given by Eq. (3-56), without preaveraging, as described in Section 3.6.2.2.I. The relaxation times were obtained by fitting the linear viscoelastic data, G (co) and G"(cu). The slowest mode, with ri = 5 sec, dominates the behavior at large strains the best fit is obtained by choosing for it an extensibility parameter of = 40,000. The value of S — = 3(0.82) n/C(x, predicted from the...

Rubber becomes harder to deform at large strains, probably because the long flexible molecular strands that comprise the material cannot be stretched indefinitely. The strain energy functions considered up to now do not possess this feature and therefore fail to describe behavior at large strains. Strain-hardening can be introduced by a simple modification to the first term in Eq. (1.18), incorporating a maximum possible value for the strain measure J, denoted Jm (Gent, 1996) ... 

For the splitting of the quasi-static stress - obtained after the substraction of (Tr from the measured stress a - into its two components, the asymptotic behavior at large strains can be used. It is dominated by the network forces and thus determined by the associated network shear modulus. The properties of the crystallite branch, i.e., the associated elasticity and finite plasticity, follow from step-cycle tests. 

Dynamic mechanical measurements are performed at very small strains in order to ensure that linear viscoelasticity relations can be applied to the data. Stress-strain data involve large strain behavior and are accumulated in the nonlinear region. In other words, the tensile test itself alters the structure of the test specimen, which usually cannot be cycled back to its initial state. (Similarly, dynamic deformations at large strains test the fatigue resistance of the material.)... 

Eq. (1) has been applied with apparent success to stresses measured at large strains (120). This is not justified by the original theory, which is limited to linear behavior and, therefore, applies strictly only to infinitesimal strains. The extension to large strains is wholly empirical and is justified only by the ability of the equation to fit experimental data. 

A fundamental difficulty in the study of the linear viscoelastic behavior of filled rubbers is the secondary aggregation of filler particles, which greatly influences the behavior at small strains, where the response is linear. The effect of this aggregation is overcome at large strains, but now non-linearity and a number of other complications become problems. 

It is certain that the relaxation behavior of filled rubbers at large strains involves numerous complications beyond the phenomena of linear viscoelasticity in unfilled amorphous polymers. Breakdown of filler structure, strain amplification, failure of the polymer-filler bond, scission of highly extended network chains and changes in network chain configuration probably all play important roles in certain ranges of time, strain rate, and temperature. A clear understanding of the interplay of these effects is not yet at hand. 

It is now easy to understand why the viscoelastic behavior of filled vulcanizates at large strains is so complex and why it is so difficult to investigate in definitive manner. None of the processes responsible for stress-softening occur instantaneously (16,182), nor can they generally be expected to obey the time-temperature relationships of linear viscoelasticity. Since time-temperature superposition is no longer applicable,... 

It should be noted that the Doi and Ohta theory predicts oifly an enhancement of viscosity, the so called emulsion-hke behavior that results in positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity vs. concentration dependencies of PET/PA-66 blends [Utracki et ah, 1982]. The NDB deviation was introduced into the viscosity-concentration dependence of immiscible polymer blends in the form of interlayer slip caused by steady-state shearing at large strains that modify the morphology [Utracki, 1991]. 

Studies performed by Yuan et al. on conductive polyaniline (PANI) nanofibers, P3DOT, and CNT thin films show that aU three are capable of forming highly compliant electrodes with fault tolerant behavior [225]. Nanowires and tubes are of particular interest since they are capable of maintaining a percolation network at large strains, thus reducing the required electrode thickness while still allowing for maximum strain performance. 

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