Shear polymers under

The example shows that Eq. (2.24) successfully describes the behavior of this polymer under shear over more than two orders of magnitude. 

It has already been mentioned that polymer melts are non-Newtonian and are in fact under normal circumstances pseudoplastic. This appears to arise from the elastic nature of the melt which will be touched on only briefly here. In essence, under shear, polymers tend to be oriented. At low shear rates Brownian motion of the segments occurs so polymers can coil up at a faster rate than they are oriented and to some extent disentangled. At high shear rates such re-entangling rates are slower than the orientation rates and the polymer is hence apparently less viscous. 

PEs, as other polymers, exhibit nonlinear behavior in their viscous and elastic properties under practical processing conditions, i.e., at high-shear stresses. The MFI value is, therefore, of little importance in polymer processing as it is determined at a fixed low-shear rate and does not provide information on melt elasticity [38,39]. In order to understand the processing behavior of polymers, studies on melt viscosity are done in the high-shear rate range viz. 100-1000 s . Additionally, it is important to measure the elastic property of a polymer under similar conditions to achieve consistent product quality in terms of residual stress and/or dimensional accuracy of the processed product. 

It is well known that LCB has a pronounced effect on the flow behavior of polymers under shear and extensional flow. Increasing LCB will increase elasticity and the shear rate sensitivity of the melt viscosity ( ). Environmental stress cracking and low-temperature brittleness can be strongly influenced by the LCB. Thus, the ability to measure long chain branching and its molecular weight distribution is critical in order to tailor product performance. 

Director Reorientation of Liquid Crystalline Polymers Under Shear and... 

As an example of such applications, consider the dynamics of a hexible polymer under a shear how [88]. A shear how may be imposed by using Lees-Edwards boundary conditions to produce a steady shear how y = u/Ly, where Ly is the length of the system along v and u is the magnitude of the velocities of the boundary planes along the x-direction. An important parameter in these studies is the Weissenberg number, Wi = Ti y, the product of the longest... 

Chakrabarti, S. Guillot, D. Rondelez, F. "Gelation of Hydroxypropylguar Under Simple Shear", Polymer Preprints 27(1), 247(April, 1986). 

Equimolar quantities of 2,4-diamino-l,5-benzenediol dihydrochloride and isophthalic acid were mixed in fresh poly (phosphoric acid) using a high-shear stirrer under a slow stream of nitrogen gas. The system was heated at 40°C for 6 hours, at CG°C for 18 hours, at 120°C for 6 hours, at 160°C for 8 hours, and at 220°C for 24 hours. The resultant mixture was dark brown. The polymer was precipitated from water. After filtration and washing with water and methanol, the solid product was then dissolved in methane-sulfonic acid, filtered and precipitated by the addition of methanol. The solid was washed with concentrated ammonium hydroxide, water, methanol, methanol/benzene mixtures (with a volume ratio of 1/1), and finally benzene. The final product was dark brown. 

Fig. E5.6 Rate of melting of a 2 x 2-in block of HDPE on a hot rotating drum, (a) Drum temperature at 154°C. (b) Drum temperature at 168°C. Rate of melting measured in volume of displaced solid. [Reprinted by permission from D. H. Sundstrom and C. Young, Melting Rates of Crystalline Polymers under Shear Conditions, Polym. Eng. Sci., 12, 59 (1972).]...

D. H. Sundstrom and Chi-Chang Young, Melting Rates of Crystalline Polymers under Shear Conditions, Polym. Eng. Sci., 12, 59-63 (1972). 

The anisotropy itself may be linear or circular, or a combination of both. In linear anisotropy the refractive index depends on the direction of polarised light. It is found in solid polymers under tension and in viscous polymeric liquids during flow (shear and elongation). The refractive index can also depend on the chirality of polarised light in this case one speaks of circular or elliptic anisotropy. Thus the so-called "optical activity" is circular birefringence its extinction analogue is circular dichroism. 

Shear rate Under idealised conditions, the polymer melt subjected to simple shear is contained between two (infinitely extending) parallel walls, one of which is translated parallel to the other at a constant distance. The result of the shear stress (moving wall per unit of surface area) is a velocity gradient in the melt in a direction perpendicular to the wall. If the velocity increases linearly from the one plate to the other one, then the flow is rectilinear. In that case, the velocity gradient is constant (see Fig. 15.1) ... 

Ductile Failure of Brittle Polymers under Compressive Shear Stresses... 

Tphe literature is replete with examples showing that the application of hydrostatic pressure enhances the ductile behavior of strained amorphous polymers. In this paper we present a possible explanation of this effect and two experiments demonstrating the enhanced ductility of polymers under compressive shear stresses applied orthogonally to the plane of shear. 

In a final chapter a closely related phenomenon, the formation of shear bands in semi-crystalline polymers under compressive load will be described. It is attempted to discuss under which conditions shear bands are formed in semi-crystalline materials and how they interact with each other or with certain microstructural features, finally leading to crack initiation and shear fracture of the bulk polymer. 

The formation of shear bands under compression is found in crystalline polymers when loaded at temperatures lower than 0.75 T. Under such a condition the shear bands interact with certain morphological features such as spherulite boundaries or lamellar arrangements inside the spherulites. The band initiation stress, ct, increases and the strain at break, Cp, decreases with decreasing temperature and increasing stiffness of the tested polymer, i.e. increasing degree of crystallinity. 

For macroscopically isotropic polymers, the Tresca and von Mises yield criteria take very simple analytical forms when expressed in terms of the principal stresses cji, form surfaces in the principal stress space. The shear yield surface for the pressure-dependent von Mises criterion [Eqs (14.10) and (14.12)] is a tapering cylinder centered on the applied pressure increases. The shear yield surface of the pressure-dependent Tresca criterion [Eqs (14.8) and (14.12)] is a hexagonal pyramid. To determine which of the two criteria is the most appropriate for a particular polymer it is necessary to determine the yield behavior of the polymer under different states of stress. This is done by working in plane stress (ct3 = 0) and obtaining yield stresses for simple uniaxial tension and compression, pure shear (di = —CT2), and biaxial tension (cti, 0-2 > 0). Figure 14.9 shows the experimental results for glassy polystyrene (13), where the... 

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