Recovery curves, viscoelastic behavior

The steady-flow viscosity qo and the steady-state compliance can easily be determined from creep data in the region of linear viscoelastic behavior as shown-in Fig. 1-12, from equation 40 of Chapter 1, provided steady-state flow has been attained. However, it is easy to be misled into believing prematurely that the linear portion of the creep curve has been reached in general, it cannot be expected to become linear until the flow term t/vo is at least as large as the intercept / . It is always desirable to perform the recovery experiment shown in Fig. 1-12 to conflrm the calculation. 

It is important to understand the creep behavior shown in Figure 16.4 is not a simple superposition of linear elastic and viscous responses. Figure 16.5 shows the typical strain-time curves of ideal elastic material, ideal viscous material, and viscoelastic polymer fibers under constant stress. The ideal elastic material deforms instantaneously as the stress is applied and the stain remains constant with time. The removal of the stress causes the ideal elastic material to return to its original dimension. For the ideal viscous material, the strain increases linearly with time as long as the stress is applied. The removal of the stress does not return the ideal viscous material to the original dimension. This is because the eneigy introduced by the woik of the external stress is dissipated in the flow, leading to a permanent deformation. Both the ideal elastic and viscous responses contribute to the creep-recovery curve of the viscoelastic polymer fibers. However, the creep-recovery curve of viscoelastic polymer fibers is not a simple superposition of these two ideal behaviors. In addition to the ideal responses, the creep-recovery curve of the polymer fibers also includes retarded elastic response, in which... 

Researchers have examined the creep and creep recovery of textile fibers extensively (13-21). For example, Hunt and Darlington (16, 17) studied the effects of temperature, humidity, and previous thermal history on the creep properties of Nylon 6,6. They were able to explain the shift in creep curves with changes in temperature and humidity. Lead-erman (19) studied the time dependence of creep at different temperatures and humidities. Shifts in creep curves due to changes in temperature and humidity were explained with simple equations and convenient shift factors. Morton and Hearle (21) also examined the dependence of fiber creep on temperature and humidity. Meredith (20) studied many mechanical properties, including creep of several generic fiber types. Phenomenological theory of linear viscoelasticity of semicrystalline polymers has been tested with creep measurements performed on textile fibers (18). From these works one can readily appreciate that creep behavior is affected by many factors on both practical and theoretical levels. 

In Figure 5.8d an intermediate behavior, called viscoelastic, is depicted such a relation is often called a creep curve, and the time-dependent value of the strain over the stress applied is called creep compliance. On application of the stress, the material at first deforms elastically, i.e., instantaneously, but then it starts to deform with time. After some time the material thus exhibits flow for some materials, the strain can even linearly increase with time (as depicted). When the stress is released, the material instantaneously loses some of it deformation (which is called elastic recovery), and then the deformation decreases ever slower (delayed elasticity), until a constant value is obtained. Part of the deformation is thus permanent and viscous. The material has some memory of its original shape but tends to forget more of it as time passes. 

Figure 1.11 Temporal behavior of a step-like stress, (Tq. applied between t and ti (a), and of the corresponding y i) (b) for a Newtonian liquid (red line), a Hookean solid (blue line) and a viscoelastic material (continuous black curve) showing a creep-recovery dynamics. The anelastic component to the viscoelastic response is also shown (green line).

The line connected by data points in Fig. 34.15 represents the experimental data while the continuous curve relates to the numerically simulated behavior based on the four parameter Burgers model for viscoelasticity. The load history consists of repeatedly loading for 24 h followed by 24 h of recovery. 

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. 

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