Creep curve, mechanical model

In practice, viscoelastic properties can be determined by static and dynamic tests. The typical static test procedure is the creep test. Here, a constant shear stress is applied to the sample over a defined length of time and then removed. The shear strain is monitored as a function of time. The level of stress employed should be high enough to cause sample deformation, but should not result in the destruction of any internal structure present. A typical creep curve is illustrated in Fig. 13A together with the four-element mechanical model that can be used to explain the observations. The creep compliance represents the ratio between shear strain rate and constant stress at any time t. 

After the stress has been removed (point D in Fig. 13A), the recovery phase follows a pattern mirroring the creep compliance curve to some degree First, there is some instantaneous elastic recovery (D-E return of spring 1 into its original shape Fig. 13A, B). Second, there is a retarded elastic recovery phase (E-F slow movement of the Kelvin unit into its original state Fig. 13A, B). However, during the Newtonian phase, links between the individual structural elements had been destroyed, and viscous deformation is non-recoverable. Hence, some deformation of the sample will remain this is in the mechanical model reflected in dash-pot 2, which remains extended (Fig. 13B). 

Fig. 13 (A) Typical creep curve refer to the text for details. (B) Mechanical model to describe a typical creep curve.

Solids of different classes, including polymers, are characterized typically with a complex non-uniform structure on various morphological levels and the presence of different local defects. The theoretical approaches describe the deformation of solid polymers via local defects in the form of dislocations (or dislocation analogies ) and disclinations, or in terms of dislocation-disclination models even for non-crystalline polymers [271-275, 292]. In principle, this presumes the localized character and jump-like evolution of polymer deformation at various levels. Meantime, the structural heterogeneity and localized microdeformation processes revealed in solids by microscopic or diffraction methods, could not be discerned typically in the mechanical (stress-strain or creep) curves obtained by the traditional techniques. This supports the idea of deformation as a monotonic process with a smoothly varying rate. Creep process has been investigated in the numerous studies in terms of average rates (steady-state creep). For polymers, as the exclusion. 

To relate the viscoelastic behavior of plastics with an S-S curve the popular Maxwell model is used, this mechanical model is shown in Fig. 3.8. This model is useful for the representation of stress relaxation and creep with Newtonian flow analysis that can be related to plastic s non-Newtonian flow behavior. It consists of a spring [simulating modulus of elasticity (E)] in series with a dashpot of coefficient of viscosity (ij)- It is an isostress model (with stress the strain (e) being the sum of the individual strains in the spring and dashpot. 

Figure 8.38 A typical creep and recovery curve for a visco-elastic material and an insert of the mechanical model used to describe the creep results.

The analysis of full rheological curve illustrates how the complex mechanical behavior can be subdivided into several regions, and how within each of these regions it can be represented by a simple model that utilizes only one or two constant parameters. For this reason, such phenomena as Schwedov s creep and Bingham s viscoplastic flow, whose molecular mechanisms are so different, can be described by substantially different parameters within otherwise the same model. Such subdivision of complex behavior into a finite number of simpler constituents with particular quantitative characteristics illustrates the universal role of macrorheology. At the same time, detailed description of a mechanism involved in each of these elementary stages requires the use of molecular-kinetic concepts and may be characterized as a microrheological approach. 

Viscoelastic characteristics of polymers may be measured by either static or dynamic mechanical tests. The most common static methods are by measurement of creep, the time-dependent deformation of a polymer sample under constant load, or stress relaxation, the time-dependent load required to maintain a polymer sample at a constant extent of deformation. The results of such tests are expressed as the time-dependent parameters, creep compliance J t) (instantaneous strain/stress) and stress relaxation modulus Git) (instantaneous stress/strain) respectively. The more important of these, from the point of view of adhesive joints, is creep compliance (see also Pressure-sensitive adhesives - adhesion properties). Typical curves of creep and creep recovery for an uncross-Unked rubber (approximated by a three-parameter model) and a cross-linked rubber (approximated by a Voigt element) are shown in Fig. 2. 

In the section, a viscoelastic constitutive model for rPET polymer concrete is discussed. To model the mechanical response of polymers is difficult because of resin composition, stress level, temperature sensitivity and other factors. For a composite mixture of recycled polymers, the situation is more complicated than for virgin polymer concrete. Due to these factors, empirical formulae developed from the curve fitting of experimental data are most suitable for predicting the creep response of rPET polymer concrete. 

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