Limit of linear viscoelasticity

The viscoelastic response of polymer melts, that is, Eq. 3.1-19 or 3.1-20, become nonlinear beyond a level of strain y0, specific to their macromolecular structure and the temperature used. Beyond this strain limit of linear viscoelastic response, if, if, and rj become functions of the applied strain. In other words, although the applied deformations are cyclic, large amplitudes take the macromolecular, coiled, and entangled structure far away from equilibrium. In the linear viscoelastic range, on the other hand, the frequency (and temperature) dependence of if, rf, and rj is indicative of the specific macromolecular structure, responding to only small perturbations away from equilibrium. Thus, these dynamic rheological properties, as well as the commonly used dynamic moduli... 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

Even aside from the rather puzzling factor of 1/3 difference, the Curtiss-Bird result does not reduce to Doi-Edwards in the limit of linear viscoelasticity. For example, in Curtiss-Bird the dynamic viscoaty = G"(fi))l(o changes from % at tu = 0 to IBe... 

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. 

Many studies were undertaken using this technique leading to the conclusion that the mecheuiical loss factor as a fxmction of frequency and temperature gave the clearest description of how viscoelastic response related to the application characteristics of polymers. In addition since the strain magnitude could be controlled in the experiment it was possible to determine the limit of linear viscoelastic response and its relationship to internal structure . 

It therefore becomes possible to characterize the viscoelastic response above the limit of linear viscoelastic response by a linear relationship that is itself a function of the maximum strain applied and the frequency or time scale of loading. 

Dynamic Mechanical. Spectra and Limit of Linear Viscoelasticity of High Polymers," with Claude Guimon, J. oi App. Vot ZA Scu..,... 

The Limit of Linear Viscoelastic Response in Polymer Melts," with L. H. Gross, TAan6action6 of the Society of PheoZogy ... 

Describing and predicting viscoelastic properties of polymer materials or adhesively bonded joints on the basis of analytical mathematical equations are justified only in the limits of linear viscoelasticity. Linear viscoelasticity is typically limited to strain levels below 0.5%. Furthermore, linear viscoelastic behavior is associated to the Boltzmann superposition principle, the correspondence principle, and the principle of time-temperature superposition. 

It may be shown that any combination of linear elements must be linear, so any models based on these linear elements, no matter how complex, can represent only linear response. Just how realistic is linear response Its most conspicuous shortcoming is that it permits only Newtonian behavior (constant viscosity) in equlibrium viscous flow. For most polymers at strains greater than a few percent or so (or rates of strain greater than 0.1 s" -), linear response is not a good quantitative description. Moreover, even within the limit of linear viscoelasticity, a fairly large number of linear elements (springs and dashpots) are usually... 

To prove this assumption, relaxation experiments below (23°C) and above (120°C) the glass transition temperature were carried out. These experiments confirm the assumption that in the energy elastic state below the glass transition temperature the limit of linear viscoelasticity is much lower than in the entropy elastic state in which the modulus is almost independent of the load level within the investigated region. Figure 6. 

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