Viscoelasticity stationary stress

Pyshnograi GV (1996) An initial approximation in the theory of viscoelasticity of linear polymers and non-linear effects. J Appl Mech Techn Phys 37(1) 123—128 Pyshnograi GV (1997) The structure approach in the theory of flow of solutions and melts of linear polymers. J Appl Mech Techn Phys 38(3) 122—130 Pyshnograi GV, Pokrovskii VN (1988) Stress dependence of stationary shear viscosity of linear polymers in the molecular field theory. Polym Sci USSR 30 2624—2629 Pyshnograi GV, Pokrovskii VN, Yanovsky YuG, Karnet YuN, Obraztsov IF (1994) Constitutive equation on non-linear viscoelastic (polymer) media in zeroth approximation by parameter of molecular theory and conclusions for shear and extension. Phys — Doklady 39(12) 889-892... 

Viscoelasticity was introduced in Section 11.5. A polymer example may be useful by way of reeapitulalion. Imagine a polymer melt or solution confined in the aperture between two parallel plates to which it adheres. One plate is rotated at a constant rate, while the other is held stationary. Figure 11-3la shows the time dependence of the shear stress after the rotation has been stopped, r decays immediately to zero for an inelastic fluid but the decrease in stress is much more gradual if the material is viscoelastic. In some cases, the residual stresses may... 

In EME the polymer is sheared between two plates, one stationary and one rotating. The extruder makes use of the viscoelastic properties of polymer melts. When a viscoelastic fluid is sheared, the normal stresses develop in the fluid, trying to push the shearing plates apart. Thus, leaving a hole in the center of the stationary plate makes it possible for the melt to flow continuously from the rim toward the center then out [Maxwell and Scalora, 1959 Blyler, 1966 Eritz, 1968, 1971 ... 

The oscillatory deep-channel rheometer described by Nagarajan and Wasan (227) can be used to examine the rheological behavior of liquid/liquid interfaces. The method is based on monitoring the motion of tracer particles at an interface contained in a channel formed by two concentric rings, which is subjected to a well-defined flow field. The middle liquid/liquid interface and upper gas/liquid interface are both plane horizon tal layers sandwiched between the adjacent bulk phase. The walls are stationary while the base moves. In the instrument described for dynamic studies of viscoelastic interfaces the base oscillates sinusoidally. This move ment induces shear stresses in the bottom liquid that are transmitted to the interface. The interfaces are viewed from above through a microscope attached to a rotary micrometer stage which is coaxial to the cylinders. 

Here was adopted for simplicity that a = 1/2 and a 1 (the latter inequality is satisfied for bubbles with Ro > >1 mkm). Phase plot of diis equation is presented in Figure 7.2.2. It is seen that for k = -1 (collapsing cavity) z —>Zi as t —> if Zq > Zj. The stationary point z = Zj is unstable. The rate of die cavity collapse z = Zj in the asymptotic regime satisfies inequality Zp < Z < (f where Zp = -RCp is equal to the collapse rate of the cavity in a pure viscous fluid with viscosity of polymeric solution ii. It means diat the cavity closure in viscoelastic solution of polymer at asymptotic stage is slower dian in a viscous liquid with the same equilibrium viscosity. On the contrary, die expansion under the same conditions is faster at k = 1 Zp cavity expansion in a pure solvent widi die viscosity (1- P)q. Tliis result is explained by different behavior of the stress tensor component controlling the fluid rheology effect on the cav-... 

For this result to be valid in the viscoelastic case, it is necessary that the boundary conditions outside the contact region be of the stress only type, that the contact region be receding but also either stationary or contracting and that (2.10.1) hold for all contours in the region covered by both bodies. 

We will show in Sect. 4.4 that a stationary crack may be open even when/ (0 < 0, which does not happen in elastic theory. It follows that in viscoelastic theory, the stress intensity factor K may be zero or negative. In elastic theory, it may be zero but not negative. 

Validity of the linear stress-optical rule points at the dominant role of the network forces in pol3mier melts. The Lodge equation of state can be interpreted on this basis. We introduced the equation empirically, as an ap>-propriate combination of properties of rubbers with those of viscous liquids. It is possible to associate the equation with a microscopic model. Since the entanglement network, although temporary in its microscopic structure, leads under steady state conditions to stationary viscoelastic properties, we have to assume a continuous destruction and creation of stress-bearing chain sequences. This implies that at any time the network will consist of sequences of different ages. As long as a sequence exists, it can follow all imposed deformations. 

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