Stress-relaxation curve, viscoelastic behavior

Figure 16.20A shows the stress-time curve for the Maxwell model in a stress relaxation test At t = 0, the initial stress is the result of the elastic response (representedby the spring). As time goes on, the stress decreases due to the contribution of viscous response (represented by the dashpot). Therefore, the Maxwell model gives a reasonable approximation of the stress relaxation behavior of viscoelastic polymer fibers in a relative short period of time. However, when the time scale of experiment become longer, the Maxwell model is no longer able to reproduce the entire stress relaxation curve (e.g.. Figure 16.16). In a real polymer fiber, many different types of conformational changes could occur at different temperatures, and each conformational change is characterized by a different relaxation time. The Maxwell model only contains one relaxation time, and hence it cannot reproduce the entire stress relaxation curve over a long period of time. Nevertheless, the Maxwell model is a classical initial treatment of the viscoelastic behavior and often is used to describe the stress relaxation of polymer fibers in a relatively short time period.

Viscoelastic stress-relaxation data are usually presented in one of two ways. In the first, the stress manifested as a function of time. Families of such curves may be presented at each temperature of interest. Each curve representing the stress-relaxation behavior of the material at a different level of... 

The creep of a viscoelastic body or the stress relaxation of an elasacoviscous one is employed in the evaluation of T] and G. In such studies, the long-time behavior of a material at low temperatures resembles the short-time response at high temperatures. A means of superimposing data over a wide range of temperatures has resulted which permits the mechanical behavior of viscoelastic materials to be expressed as a master curve over a reduced time scale covering as much as twenty decades (powers of ten). 

L. H. Sperling, H. F. George, V. Huelck, and D. A. Thomas, Viscoelastic Behavior of Interpenetrating Polymer Networks Poly(ethyl acrylate)-Poly(methyl methacrylate), J. Appl. Polym. Sci. 14, 2815 (1970). Creep behavior of sequential IPNs. Stress relaxation. Master curves. 

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. 

The value t = q/G has the units of time and is referred to as the relaxation period. This value graphically corresponds to the point at which the line tangent to the t(0 curve at point t = 0 intersects with the x axis (Figure 3.9). This gradual decrease of the stress stress relaxation) is typical in viscoelastic systems. The energy that was previously stored in the elastic element dissipates in the viscous element. As a result, the behavior of such a system is mechanically and thermodynamically irreversible. 

Furthermore, the magnitude of the relaxation modulus is a function of temperature to more fuUy characterize the viscoelastic behavior of a polymer, isothermal stress relaxation measurements must be conducted over a range of temperatures. Figure 15.6 is a schematic log ,(f)-versus-log time plot for a polymer that exhibits viscoelastic behavior. Curves generated at a variety of temperatures are included. Key features of this plot are that (1) the magnitude of EXt) decreases with time (corresponding to the decay of stress. Equation 15.1), and (2) the curves are displaced to lower EXt) levels with increasing temperature. 

The viscoelastic nature of polymers results in deformation behavior that is both time (frequency) and temperature dependent. It is valuable to assess the long-term behavior of polymers at a fixed temperature to predict lifetimes in various applications. It is possible to do using the WLF equation, which expresses the shift factor, ax, as a function of temperature. By this time-temi)erature superposition (TTS) approach, viscoelastic parameters measured at various temperatures are used to construct a master curve of sample deformation by means of a shift along the log time axis. Thus, stress relaxation and creep experiments enable effective predictions of long-term behavior over various temi)eratures that can be acquired in a short period of time. 

The age-related viscoelastic properties of the ocular lens have not been fully characterized. Most of the attempts have been at elucidating only the elastic modulus, since the lens has been treated as an elastic substance (19,26). The process of accommodation however is mechanically analogous to a stress-relaxation experiment, where the stress is allowed to decay at constant strain (refractive power). Hence, the lens is truly viscoelastic. Researchers investigating the viscoelastic characteristics of the lens performed creep-recovery or frequency scan techniques ex-vivo ( 1 8). Ejiri et al. (28) investigated creep properties of a decapsulated dog lens by compression and fitted the time-displacement curve with three Kelvin units. The time constants for the three units were 0.09 s, 7.0 s, and 106 s. The elastic modulus could not be obtained, as the applied stress was unknown due to the aspheric geometry of the lens. In this article, we have investigated the creep behavior of cylindrical disc shaped hydrogels in order to obtain the time constants as well as the elastic modulus of the viscoelastic units. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

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