Viscoelastic shear deformation

Fluids without any sohdlike elastic behavior do not undergo any reverse deformation when shear stress is removed, and are called purely viscous fluids. The shear stress depends only on the rate of deformation, and not on the extent of derormation (strain). Those which exhibit both viscous and elastic properties are called viscoelastic fluids. 

During the creep of PET and PpPTA fibres it has been observed that the sonic compliance decreases linearly with the creep strain, implying that the orientation distribution contracts [ 56,57]. Thus, the rotation of the chain axes during creep is caused by viscoelastic shear deformation. Hence, for a creep stress larger than the yield stress, Oy,the orientation angle is a decreasing function of the time. Consequently, we can write for the viscoelastic extension of the fibre... 

Fig. 63 The Eyring reduced time model involves the activated site model for plastic and viscoelastic shear deformation of adjacent chains...

Most pigmented systems are considered viscoelastic. At low shear rates and slow deformation, these systems are largely viscous. As the rate of deformation or shear rate increases, however, the viscous response cannot keep up, and the elasticity of the material increases. There is a certain amount of emphasis on viscoelastic behavior in connection with pigment dispersion as well as ink transportation and transformation processes in high-speed printing machines (see below). Under periodic strain, a viscoelastic material will behave as an elastic solid if the time scale of the experiment approaches the time required for the system to respond, i.e., the relaxation time. Elastic response can be visualized as a failure of the material to flow quickly enough to keep up with extremely short and fast stress/strain periods. 

For a more complete description of the time and the temperature dependence of the fibre strength a theoretical description of the viscoelastic and plastic tensile behaviour of polymer fibres has been developed. Baltussen (1996) has shown that the yielding phenomenon, the viscoelastic and plastic extension of a polymer fibre can be described by the Eyring reduced time model. This model uses an activated site model for the plastic and viscoelastic shear deformation of adjacent chains in the domain, in which the straining of the intermolecular bonding is now modelled as an activated shear transition between two states, separated by an energy barrier. It provides a relation between the lifetime, the creep load and the temperature of the fibre, which for PpPTA fibres has been confirmed for a range of temperatures (Northolt et al., 2005). 

In discussing shear deformation, it is convenient to distinguish between the initial elastic and viscoelastic response of the polymer to the applied load and the subsequent time-dependent response. However, the distinction is somewhat arbitrary and is not as fundamental as that between elastic volume response and crazing. Viscoelastic shear deformation continues throughout the period under load. The observed time-dependence of lateral strain reflects both generalized viscoelastic relaxation and shear band formation. Since crazing consists simply of displacement in the tensile stress direction, it makes no contribution to lateral strain therefore —e specifically measures deformation by shear processes. 

It should be emphasised that polymeric surfactants prevent the coalescence of water droplets in the multiple emulsion drops, as well as coalescence of the latter drops themselves. This is due to the interfacial rheology of the polymeric surfactant films. As a result of the strong lateral repulsion between the stabilising chains at the interface (PHS chains at the W/O interface and PEO chains at the O/W interface), these films resist deformation under shear and hence produce a viscoelastic film. On approach of the two droplets, this film prevents deformation of the interface so as to prevent coalescence. 

The word vixt oeUislic encompasses many fluids that exhibit both elasticity (solidlike behavior) and flow (liquid-like behavior) when sheared. Most concentrated pastes, emulsions, and gels are viscoelastic. Under small deformations, viscoelastic fluids literally behave as elastic solids under higher deformations they flow as liquids. 

When the solid feature dominates the mechanical response of a shear deformation, the shear stress cr is proportional to the shear strain y, and the proportionality coefficient is the shear modulus E. On the other hand, when the liquid feature dominates the response, the shear stress cr is proportional to the shear rate y, the proportionality coefficient is the shear viscosity 77. Maxwell equation of linear viscoelasticity can be applied to describe the continuous switching between the solid and the liquid (Maxwell 1867),... 

More recently Christie [5] has developed a finite-element simulation package, SimForm, using transversely anisotropic, hyperelastic discrete ply deformation as a first step to simulate the viscoelastic shear response discussed earlier in this section. The program employs three-dimensional continuum elements to describe deformations in each ply, while a contact procedure couples the motion of neighbouring plies to simulate the interply slip process. Interply slip is given a linear velocity-dependent... 

FIG. 2-1. Creep compliance plotted logarithmically for eight typical polymer systems viscoelastic liquids on left, viscoelastic solids on right, identified by numbers as described in the text. Deformation is shear, J t), except for curves VI and Vlll, which are for simple extension, D t). The dashed curves represent the compliance after subtraction of the flow contribution t/rjo- The solvent for the dilute solution, example I, is also shown as a dashed line. 

For a viscoelastic liquid in shear, the ratio oz t)/y in equations 56 to 58 is sometimes treated as a time-dependent viscosity J (r) which increases monoton-ically (provided the viscoelasticity is linear) to approach the steady-state viscosity Meissner has pointed out that, in an experiment involving deformation at constant strain rate followed by stress relaxation at constant deformation, viscoelastic information can be obtained without imposing the restriction in equation 11 of Chapter 1 that the loading interval is small compared with the time elapsed at the first experimental stress measurement. ... 

At small deformations, viscoelastic information can in principle be obtained from stress-strain measurements at a constant strain rate, as shown for shear deformations in equations S6 to S9 of Chapter 3. Such experiments are often made in simple extension, but the deformations can become rather large so there are marked deviations from linear viscoelastic behavior. The most commonly used instrument is the Instron tester other carefully designed devices have been described. - The sample is usually a dumbbell or a ring. In the former case, the strain in the narrow section as checked by separations of several fiducial marks can be calculated from the separation between the clamps by a suitable multiplication factor. In... 

Abrasive wear in polyethylene occurs when the surfaee of a sample is removed by contact with a counterface with which it is in relative motion. The surfaces of the polymer and the counterface are always rough to some extent, either by design or due to the inescapable consequences of fabrication. Thus there are always asperities that protrude above the level of the surrounding surface. It is these asperities that make contact and are sites for ductile tearing failure. Asperities may be sharp and incisive, as in the case of those found on inorganic counterfaces, such as stainless steel and emery paper, or rounded and deformable, as in the case of those found on polymer surfaces. Sharp asperities cut and scour surfaces smooth ones act by adhesion to viscoelastically shear the surface. 

Material parameters defined by Equations (1.11) and (1.12) arise from anisotropy (i.e. direction dependency) of the microstructure of long-chain polymers subjected to liigh shear deformations. Generalized Newtonian constitutive equations cannot predict any normal stress acting along the direction perpendicular to the shearing surface in a viscometric flow. Thus the primary and secondary normal stress coefficients are only used in conjunction with viscoelastic constitutive models. 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

Many industrially important fluids cannot be described in simple terms. Viscoelastic fluids are prominent offenders. These fluids exhibit memory, flowing when subjected to a stress, but recovering part of their deformation when the stress is removed. Polymer melts and flour dough are typical examples. Both the shear stresses and the normal stresses depend on the history of the fluid. Even the simplest constitutive equations are complex, as exemplified by the Oldroyd expression for shear stress at low shear rates ... 

Figure 36 is representative of creep and recovery curves for viscoelastic fluids. Such a curve is obtained when a stress is placed on the specimen and the deformation is monitored as a function of time. During the experiment the stress is removed, and the specimen, if it can, is free to recover. The slope of the linear portion of the creep curve gives the shear rate, and the viscosity is the appHed stress divided by the slope. A steep slope indicates a low viscosity, and a gradual slope a high viscosity. The recovery part of Figure 36 shows that the specimen was viscoelastic because relaxation took place and some of the strain was recovered. A purely viscous material would not have shown any recovery, as shown in Figure 16b. 

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