The Nature of Viscoelasticity

The results of typical creep experiments are shown in Fig. 4.1. We discuss here specimens subjected to shear related effects are, of course, observed in tension. If a constant shear stress Oi is applied to a viscoelastic specimen (4.N.1) the strain is observed to be time dependent (see Fig. 4.1 (a)). Suppose the specimen to be allowed to recover and a larger constant stress 02 applied. The time dependence of the strain is shown in Fig. 4.1(b). Now, if the strains at a particular time say r, after the application of the stress, are plotted against the stress it then is observed that these strains y(t ) are linear in the stress (see Fig. 

1 (c)). For a later time, say after the application of the stress, the strains y (f ) are again linear in the stress. Thus, if at an entirely arbitrary time t the strains at the two stresses are y,(/) and 72(0. then 

The strains in the two experiments at the same time t are proportional to the imposed stresses. This fact leads to the definition of the creep compliance at time t 

Polymers exhibit this property of linear viscoelastic creep at low stresses (stresses sufficiemly low that the strains are below 0.5 x 10 ). In a creep experiment, the plot of strain against stress at a specific time is known as an isochronal. 

If J ) is measured over a number of decades of time and plotted against log f, it has, in general, the form indicated in Fig. 4.1(d). At very short and very long times J (r) shows little or no time dependence in the period in between it is a sigmoid-shaped curve. If the measurements are taken over only a few decades of time, the whole sigmoid is not revealed only part of it (for an example of this, see Fig. 4.4). 

The ratio G /G is the tangent of the of the phase angle 5 which is defined as  

This is an important parameter to analyze the viscoelastic behavior of different materials mainly in the case of polymeric materials where the dependence of tan 8 with the chemical structure of the polymeric materials give important information about the relaxation processess that take place is these systems. tan8 is commonly used as a first experimental approach to obtain information about the viscoelastic behavior of polymers as function of the frequency, where it is possible to reach experimental information about the effect of the side chain structure of the polymers on conformational and relaxational responses. 

Polymers are viscoelestic at all temperatures. Nevertheless they are not simple elastic solids and the effect of temperature on the response of viscoelastic systems to the perturbation show a very interesting trend. At T = Tg the strain against time remain approximately constant. As the temperature increases the variation of strain with time increases in a square root shape which is larger the higher temperature. See Fig. 2.3. 

The state that it is possible to find a polymeric material is strongly dependent on the chemical structure. In fact, depending on the nature of the chemical functional groups inserted in the polymeric chain, is the thermal, mechanical and dielectric behavior. Depending of the chemical structure of the main chain as well as of the polymeric material is the general behavior of the polymer. Nevertheless, a polymer can be change from one state to other with the variation of the temperature [1-14], This is one of the most important thermodynamic variables to be taken into account 

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Polymeric materials are all viscoelastic. The face each polymer shows to the observer—elastic, viscous flow, a combination of both—depends on the rate and duration of force application as well as on the nature of the material and external conditions including the temperature T. We discuss the nature of viscoelasticity below and additionally in Section 5. In general, properties of viscoelastics depend on time, in contrast to metals and ceramics. 

Because of the nature of viscoelastic relaxation processes (discussed briefly under Viscoelasticity), the effect of increasing the temperature is equivalent to allowing more time in a given test. The equivalence is expressed in general in relation to a chosen standard temperatnre To by a shift factor aj defined as the ratio... 

The traditional discussion of mechanical (spring and dashpot) models and the related topic of differential forms of the constitutive equations will not be included here, but are treated extensively in several older references, Gross (1953), Ferry (1970), Bland (1960) for example. See also Nowacki (1965), Flugge (1967) and Lockett (1972). A consistent development of the theory is possible without these concepts. However, they do provide insights into the nature of viscoelastic behaviour and physically motivate exponential decay models. 

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