Retardation time, Voigt-Kelvin model

Figure 2 Graphical representation of the Voigt-Kelvin model (a) and the Maxwell model (b) of viscoelasticity. rd is the retardation time and

Consider, for example, the creep response of the four-parameter model (Rgure 15.8). For this model, a logical choice for Xc would be the time constant for its Voigt-Kelvin component, r]2/G2- For De1 (t Xc), the Voigt-Kelvin element and dashpot 1 will be essentially immobile, and the response will be due almost entirely to spring 1, that is, almost purely elastic. For De 0 Xc), the instantaneous and retarded elastic... 

In a similar way, for an infinite number of elements in the generalized Kelvin-Voigt model /(A) maybe used to express the probability density of retardation times and the creep function (f) for the spectrum in the case of the generalized Kelvin-Voigt model can be written as ... 

The mechanical models discussed above are based on single relaxation (or retardation) time. Real polymer fibers have a spectrum or distribution of relaxation and retardation times due to the existence of different types of conformational changes. One convenient way to introduce a range of relaxation times into the problem is to constmct models consisting of a number of Maxwell and/or Kelvin-Voigt sub-models connected in parallel and/or series. Figure 16.24 shows a Maxwell-Wiechert model, which is constmcted by connecting an aibitraiy number of... 

The Maxwell-Wiechert model also can be used to describe the creep behavior of polymer fibers. However, for the creep behavior, it is mathematically more convenient to create a model involving a range of retardation times by connected a number of Kelvin-Voigt sub-models in series. 

Time response of different rheological systems to applied forces. The Maxwell model gives steady creep with some post stress recovery, representative of a polymer with no cross-linking. The Kelvin-Voigt model gives a retarded viscoelastic behavior expected from a cross-linked polymer. 

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