Burger model, deformation

Both models, the Maxwell element and the Kelvin-Voigt element, are limited in their representation of the actual viscoelastic behaviour the former is able to describe stress relaxation, but only irreversible flow the latter can represent creep, but without instantaneous deformation, and it cannot account for stress relaxation. A combination of both elements, the Burgers model, offers more possibilities. It is well suited for a qualitative description of creep. We can think it as composed of a spring Ei, in series with a Kelvin-Voigt element with 2 and 772. and with a dashpot, 771... 

The viscoelastic properties of films were determined by stress relaxation tests with a texture analyzer TA.XT2i (SMS). The films were cut into strips of 15 mm width and 100 mm lengths and affixed to the instrument. The initial grip separation and crosshead speed were 80 mm and 0.9mm/sec, respectively. The instrument was set for a deformation of 1 %, which was held constant for 70 sec. The force required to maintain this deformation was monitored by a microcomputer in real time. The viscoelastic properties were calculated according to the Burgers model (Equation 1) ... 

The time-dependent deformation of the foundation rock, caused by loadings, is described by a Burgers model, which is composed of a Kelvin model and Maxwell model in series, as showed in Figure 2, The partial strain expression of Burgers model is... 

Figure 9. Four-parameter or Burger model for the deformation behaviour of polymers.

The Burger model provides a correct graphic description of the elongation-time behavior of most plastics in a first approximation. The spring 1 results in spontaneous elastic load application and relaxation elongation, 1 + 2 in parallel cause creep during load application and creep recovery (delayed viscoelastic reverse deformation) after relaxation, damper 2 results in residual elongatimi. 

The second model (Figure 4.15d) describes the complicated viscoelastic behaviour of bitumen. Upon application of stress, the model immediately presents elastic deformation and continues to deform at a non-linear rate. Thus, for a given temperature, if a constant stress (oi) is applied, the strain (e) after time (t) could be calculated using the Burgers model by the following equation ... 

If we now stress the Burgers model in a creep test, it is easy to see what will happen, see figure 3 first, the unrestrained spring Gi will instantaneously deform to its expected extent, while the isolated dashpot will start to deform at its expected rate. However, the spring in the Kelvin-Voigt element cannot immediately respond, being hindered (i.e. retarded) by its dashpot. Nevertheless, it does begin to deform, and eventually comes to its expected steady-state deformation. It is possible to show that the overall deformation can be written down as ... 

Some examples of real materials whose creep deformation at low stresses are described quite well by the Burgers model are... 

Figure 3-1. a) Edge dislocation model b) Burgers vector h with Burgers circuit and glide plane indicated. Dislocation motion during plastic deformation under the action of force F. Jog and kink. 

Although the Maxwell-Wiechert model and the extended Burgers element exhibit the chief characteristics of the viscoelastic behaviour of polymers and lead to a spectrum of relaxation and retardation times, they are nevertheless of restricted value it is valid for very small deformations only. In a qualitative way the models are useful. The flow of a polymer is in general non-Newtonian and its elastic response non-Hookean. 

In more detail, the flow of glass is more complex due to the combined elastic and viscous response to any type of applied stress, known as viscoelasticity. Several models have been proposed to describe viscoelasticity. Among them. Burger s model has been shown to characterize reasonably well the behavior of inorganic glasses [5]. In this version, illustrated in Fig. 3a, viscous (771) and elastic (El) elements are combined in series with a Kelvin solid, where two other elements (772, 2) are arranged in parallel and reflect the slow elastic properties. The rate of deformation under constant tensile stress a and zero initial deformation is made up from the rate of Newton s viscous deformation,... 

In Fig. 8.9, one sees a 2D crack dislocation with a giant Burgers vector, nb, of length c. Stroh s [52] dislocation model for spontaneous microcrack formation, calculates the elastic energy associated with the wedge deformation of length, c, extending to a barrier by means of ... 

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