Flow and Elasticity

As a melt is subjected to a fixed stress or strain, the deformation versus time curve will show an initial rapid deformation followed by a continuous flow. Elasticity and strain are compared in Fig. 8-9 that provides (a) basic deformation vs. time curve, (b) stress-strain deformation vs. time with the creep effect, (c) stress-strain deformation vs. time with the stress-relaxation effect, (d) material exhibiting elasticity, and (e) material exhibiting 

Deformation contributes significantly to process-flow defects. Melts with only small deformation have proportional stress-strain behavior. As the stress on a melt is increased, the recoverable strain tends to reach a limiting value. It is in the high stress range, near the elastic limit, that processes operate. 

Molecular weight, temperature, and pressure have little effect on elasticity the main controlling factor is MWD. Practical elasticity phenomena often exhibit little concern for the actual values of the modulus and viscosity. Although MW and temperature influence the modulus only slightly, these parameters have a great effect on viscosity and thus can alter the balance of a process. 

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Deformation is the relative displacement of points of a body. It can be divided into two types flow and elasticity. Flow is irreversible deformation when the stress is removed, the material does not revert to its original form. This means that work is converted to heat. Elasticity is reversible deformation the deformed body recovers its original shape, and the appHed work is largely recoverable. Viscoelastic materials show both flow and elasticity. A good example is SiEy Putty, which bounces like a mbber ball when dropped, but slowly flows when allowed to stand. Viscoelastic materials provide special challenges in terms of modeling behavior and devising measurement techniques. 

The study of flow and elasticity dates to antiquity. Practical rheology existed for centuries before Hooke and Newton proposed the basic laws of elastic response and simple viscous flow, respectively, in the seventeenth century. Further advances in understanding came in the mid-nineteenth century with models for viscous flow in round tubes. The introduction of the first practical rotational viscometer by Couette in 1890 (1,2) was another milestone. 

As reviewed thermoplastics (TPs) being viscoelastic materials respond to induced stress by two mechanisms viscous flow and elastic deformation. Viscous flow ultimately dissipates the applied mechanical energy as frictional heat and results in permanent material deformation. Elastic deformation stores the applied mechanical energy as completely recoverable material deformation. The extent to which one or the other of these mechanisms dominates the overall response of the material is determined by the temperature and by the duration and magnitude of the stress or strain. The higher the temperature, the most freedom of movement of the individual plastic molecules that comprise the... 

There are three important phenomena seen is polymeric liquids that make them different from simple fluids a non-Newtonian viscosity, normal stresses in shear flow, and elastic effects. All these effect are a result of the complex molecular structure of polymer macromolecules. 

The temporary network model predicts many qualitative features of viscoelastic stresses, including a positive first normal stress difference in shear, gradual stress relaxation after cessation of flow, and elastic recovery of strain after removal of stress. It predicts that the time-dependent extensional viscosity rj rises steeply whenever the elongation rate, s, exceeds 1/2ti, where x is the longest relaxation time. This prediction is accurate for some melts, namely ones with multiple long side branches (see Fig. 3-10). (For melts composed of unbranched molecules, the rise in rj is much less dramatic, as shown in Fig. 3-39.) However, even for branched melts, the temporary network model is unrealistic in that it predicts that rj rises to infinity, whereas the data must level eventually off. A hint of this leveling off can be seen in the data of Fig. 3-10. A more realistic version of the temporary network model... 

There are three main rheological properties of materials viscous flow, plastic flow, and elastic deformation. The stress deformation behavior of elastic materials is represented by a straight line through the origin. However, in this case, the... 

Equation (6-94) has been found to be valid for a number of filled systems up to a value of f of about 0.3, whereas (6-95) and (6-96c) can be used at somewhat higher concentrations. These equations were first used to describe the viscosity of liquids with suspended solid particles. In fact equation (6-94) was derived using basic hydrodynamic principles. Equations of this type have been "borrowed" to be used for the elasticity of filled elastomers, based on the analogy between steady viscous flow and elastic deformation as described in equations (3-4) and (2-14), respectively. Certainly an additional justification... 

At low viscosities, glass forming melts usually behave as Newtonian liquids which immediately relax to relieve an applied stress. At extremely high viscosities, however, these liquids respond to the rapid application of a stress as if they were actually elastic materials. It follows that there must exist an intermediate range of viscosities where the response of these melts to application of a stress is intermediate between the behavior of a pure liquid and that of an elastic solid. Since this behavior has aspects of both viscous flow and elastic response, it is known as viscoelasticity, or viscoelastic behavior. 

The word rheology comes from the Greek Rheos which means flow. Rheology smdies the deformation and flow of materials in response to the action of a force. It describes the interrelationship between force, deformation,and time and provides information on the consistency of materials, by their viscosity—which is simply the resistance to flow—and elasticity, i.e. structure and/or adhesion. 

However, various combinations of eiastic and viscous elements have been used to approximate the material behavior of polymer melts. Some models are combinations of springs and dashpots to represent the elastic and viscous responses, respectively. The most common ones being the Maxwell model for a polymer melt and the Kelvin or Voight model for a solid. One model that represents shear thinning behavior, normal stresses in shear flow and elastic behavior of certain polymer melts is the K-BKZ model [28-29]. 

Fiber-forming PP melts behave Uke non-Newtonian viscoelastic liquids having drop of viscosity with increasing share rate. The declination from a Newtonian flow and elasticity of PP melt are essentially higher comparing with polyamides and polyesters. Typical values of melt viscosity at processing conditions are 150-450 Pa s [4]. 

Rheology is concerned with the flow and deformation of matter. Viscoelastic properties are more concerned with the flow and elasticity of matter. 

The study of polymer viscoelasticity treats the interrelationships among elasticity, flow, and molecular motion. In reality, no liquid exhibits pure Newtonian viscosity, and no solid exhibits pure elastic behavior, although it is convenient to assume so for some simple problems. Rather, all deformation of real bodies includes some elements of both flow and elasticity. Because of the long-chain nature of polymeric materials, their visco-elastic characteristics come to the forefront. This is especially true when the times for molecular relaxation are of the same order of magnitude as an imposed mechanical stress. 

In lubrication applications the fluid inertia is usually not important. Thus the form for both Che elastic deformation equations and Che fluid velocity equations are Che same however, the meaning of the dependent variables is different. Buckholz [1] applied a singularity superposition method to solve the coupled flow and elastic deformation equations Che method was applied to squeeze film journal bearings. Singularity superposition methods of solution for Stokes flows are discussed by Chwang and Wu [5]. 

Marenduzzo, D., Orlandini, E. and Yeomans, J. M., (2004). Interplay between shear flow and elastic deformations in liquid crystals. /. Chem. Phys., Vol. 121, pp. 582-591... 

Theoretical treatments of liquid crystals such as nematics have proved a great challenge since the early models by Onsager and the influential theory of Maier and Saupe [34] mentioned before. Many people have worked on the problems involved and on the development of the continuum theory, the statistical mechanical approaches of the mean field theory and the role of repulsive, as well as attractive forces. The contributions of many theoreticians, physical scientists, and mathematicians over the years has been great - notably of de Gennes (for example, the Landau-de Gennes theory of phase transitions), McMillan (the nematic-smectic A transition), Leslie (viscosity coefficients, flow, and elasticity). Cotter (hard rod models), Luckhurst (extensions of the Maier-Saupe theory and the role of flexibility in real molecules), and Chandrasekhar, Madhusudana, and Shashidhar (pre-transitional effects and near-neighbor correlations), to mention but some. The devel-... 

Rubber and plastic melts can be considered, to a first approximation, as extremely high-viscosity fluids. This is only an approximation and it must be remembered that polymers generally show viscoelastic properties—a combination of viscous flow and elastic recovery. Viscosity, in turn, is the quantitative measure of resistance to flow under a given set of circumstances. The Greek letter that usually designates viscosity is Tj. For an ideal, Newtonian fluid, viscosity is simply the ratio between Shear Stress (t), the pressure placed on the fluid to create flow, and the Shear Rate (y), the rate of flow over time as seen in Equation 16C.1 ... 

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