Introduction to Viscoelasticity

When a polymer is extruded through an orifice such as a capillary die, a phenomenon called die swell is often observed. In this case, as the polymer exits the cylindrical die, the diameter of the extrudate increases to a diameter larger than the diameter of the capillary die, as shown in Fig. 3.9. That is, it increases in diameter as a function of the time after the polymer exits the die. Newtonian materials or pure power law materials would not exhibit this strong of a time-dependent response. Instead they may exhibit an instantaneous small increase in diameter, but no substantial time-dependent effect will be observed. The time-dependent die swell is an example of the polymer s viscoelastic response. From a simplified viewpoint the undisturbed polymer molecules are forced to change shape as they move from the large area of the upstream piston cylinder into the capillary. For short times in the capillary, the molecules remember their previous molecular shape and structure and try to return to that structure after they exit the die. If the time is substantially longer than the relaxation time of the polymer, then the molecules assume a new configuration in the capillary and there will be less die swell. 

In this introduction, the viscoelastic properties of polymers are represented as the summation of mechanical analog responses to applied stress. This discussion is thus only intended to be very introductory. Any in-depth discussion of polymer viscoelasticity involves the use of tensors, and this high-level mathematics topic is beyond the scope of what will be presented in this book. Earlier in the chapter the concept of elastic and viscous properties of polymers was briefly introduced. A purely viscous response can be represented by a mechanical dash pot, as shown in Fig. 3.10(a). This purely viscous response is normally the response of interest in routine extruder calculations. For those familiar with the suspension of an automobile, this would represent the shock absorber in the front suspension. If a stress is applied to this element it will continue to elongate as long as the stress is applied. When the stress is removed there will be no recovery in the strain that has occurred. The next mechanical element is the spring (Fig. 3.10[b]), and it represents a purely elastic response of the polymer. If a stress is applied to this element, the element will elongate until the strain and the force are in equilibrium with the stress, and then the element will remain at that strain until the stress is removed. The strain is inversely proportional to the spring modulus. The initial strain and the total strain recovery upon removal of the stress are considered to be instantaneous. 

When dash pot and spring elements are connected in parallel they simulate the simplest mechanical representation of a viscoelastic solid. The element is referred to as a Voigt or Kelvin solid, and it is shown in Fig. 3.10(c). The strain as a function of time for an applied force for this element is shown in Fig. 3.11. After a force (or stress) elongates or compresses a Voigt solid, releasing the force causes a delay in the recovery due to the viscous drag represented by the dash pot. Due to this time-dependent response the Voigt model is often used to model recoverable creep in solid polymers. Creep is a constant stress phenomenon where the strain is monitored as a function of time. The function that is usually calculated is the creep compliance/(f) /(f) is the instantaneous time-dependent strain e(t) divided by the initial and constant stress o.  

Here is the element viscosity, is the element modulus, and Ay is the relaxation time. If this model material is placed in a constant stress environment for a fixed time and then the stress is removed, then the time-dependent strain will have the recovery characteristics shown in Fig. 3.11. 

As shown by Fig. 3.11 for an applied force, the creep strain is increasing at a decreasing rate with time because the elongation of the spring is approaching the force produced by the stress. The shape of the curve up to the maximum strain is due to the interaction of the viscosity and modulus. When the stress is removed at the maximum strain, the strain decreases exponentially until at an infinite time it will again be zero. The second half of this process is often modeled as creep recovery in extruded or injection-molded parts after they cool. The creep recovery usually results in undesirable dimensional changes observed in the cooled solid with time. 

Following the manner of presentation in the previous sections, the subject of viscoelasticity will be explained by reference to experiments familiar to the practitioner of rubber technology. This is a rather unorthodox approach and different from the usual one, which begins with an introduction of the theory. The experiment is tensile stress-strain measurement. In the rubber industry tensile measurements are routinely performed with crosslinked specimens. Here, we are concerned with gum-rubber behaviour. Therefore, we must perform the measurements with uncrosslinked specimens. First, compression-moulded specimens must be prepared they require special attention, which will be described next. 

Reprinted with permission from N. Nakajima, International Polymer Processing, 

Reprinted with permission from N. Nakajima, international Polymer Processing, 1996, 11, 1, 3. Copyright 1996, Hanser Publishers, Munich. 

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As an introduction to viscoelasticity the mechanical behavior of these viscoelastic plastics is dominated by such phenomena as tensile strength, elongation at break, stiffness, and rupture energy, which are often the controlling factors in a design. The viscous attributes of plastic melt flow are also important considerations in the fabrication of plastic products. 

J. J. Aklonis and W. J. MacKnight, Introduction to Viscoelasticity, John Wiley Sons, Inc., New York, 1983. 

Aklones, J. J., Mac Knight, W. J., and Shen, M., Introduction to Polymer Viscoelasticity,VIiley-lnteTScience, New York, 1972. 

This book is intended primarily for students in the various fields of engineering but it is felt that students in other disciplines will welcome and benefit from the engineering approach. Since the book has been written as a general introduction to the quantitative aspects of the properties and processing of plastics, the depth of coverage is not as great as may be found in other texts on the physics, chemistry and stress analysis of viscoelastic materials, this has been done deliberately because it is felt that once the material described here has been studied and understood the reader will be in a better position to decide if he requires the more detailed viscoelastic analysis provided by the advanced texts. 

FIGURE 28.8 Idealized cyclic stress-strains, showing the viscoelastic curve split up into its two primary components, elastic and viscous. (Redrawn from Andrew, C., Introduction to Rubber Technology, Knovel e-book publishers, 1999.)... 

Shaw, M.T. and MacKnight, W.J. 2005. Introduction to Polymer Viscoelasticity. Wiley, Hoboken, NJ. Strobl, G. 2007. The Physics of Polymers. Springer, New York. 

Aklonis JJ, MacKnight WJ and Shen M, "Introduction to Polymer Viscoelasticity", Wiley, Inc, New York, 1972. Alfrey T, "Mechanical Behaviour of High Polymers", Interscience, New York, 1948. 

Stauffer, D., Introduction to Percolation Theory, Taylor Friends, London, 1985. Yanez, J.A., Laarz, E., and Bergstrom, L., Viscoelastic properties of particle gels, J. Colloid Interface ScL, 209, 162, 1999. 

J Aklonis, WJ MacKnight. Introduction to Polymer Viscoelasticity. 2nd ed. New York Wiley, 1980. 

The measurement of rheological properties at the surface of a solution or the interface between a solution and, for example, a biological film is called surface or interfacial rheology. In this technique also, experiments are performed either in tension, compression or shear, and phenomena observed in bulk rheology such as flow and viscoelasticity are also observable. An introduction to the techniques available and some key findings are discussed by Warburton. ... 

Pbticolas, W. L. Introduction to the molecular viscoelastic theory of polymers and its application. Rubber Chem. Technol. 36, 1422 (1963). 

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