Viscosity strain-rate-dependent

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

Fig. 9.12 (A) Time variation of elongational viscosity for PLA-based nanocomposite (MMT = 4wt%) melt at 170°C (B) Strain rate dependence of up-rising Hencky strain. Reprinted from [47], 2003 Wiley-VCH Verlag GmbH Co.

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

Using this formula it is possible to predict the viscosity of a macromolecu-lar solution knowing the shape factor of a macromolecule and its volume fraction. However, to do this we must hrst determine the shape factor. This equation also tells us that macromolecules with large shape factors have high viscosities and show increased strain-rate dependence of the viscous component of the stress in tissues. Therefore, we need to be able to evaluate the shape factor for different macromolecules. 

When failure does occur, the flow is frictional in nature and often is a weak function of strain rate, depending instead on shear strain. Prior to failure, the powder behaves as an elastic solid. In this sense, bulk powders do not nave a viscosity in the bulk state. 

Experimental verification of Eqs 7.94 indicated that the scaling relationships are valid, but the shape of experimental transient stress curves, after step-change of shear rate, did not agree with Doi-Ohta s theory [Takahashi et al., 1994]. Similar conclusions were reported for PA-66 blends with 25 wt% PET [Guenther and Baird, 1996]. For steady shear flow the agreement was poor, even when the strain-rate dependence of the component viscosities was incorporated. Similarly, the... 

The heuristic extension of the rheological state equation from Bingham to Casson materials is straightforward. It can be derived directly from Eqn. (7) by introducing a strain rate dependant viscosity 77(72) instead of Tjg... 

For an elastic solid, stress linear function of the applied strain e, and there is no strain-rate dependence. Elastic modulus E is the slope of the stress versus strain curve. An elastic material can be modeled as a spring, whereas viscous materials can be modeled as a dashpot. For a fluid (viscous material), stress is proportional to strain rate (de/dt) and unrelated to strain. Viscosity 17 is the slt of the stress versus strain rate curve. Figure 11.9 shows the stress/siiain relationship for elastic solids and the stress/strain-rate relationships for viscous liquids. 

The viscosity of a PP product is related to its M , and a good estimation of it at low shear rates can be obtained from the MFR test. This is only a single point test, and more information about the viscosity at different strain rates is needed to completely understand and characterize the processability of a product. The strain rate dependence of melt viscosity in PP is related to its molecular weight distribution, which is commonly described by the ratio of the to A/n... 

Most polymer processes are dominated by the shear strain rate. Consequently, the viscosity used to characterize the fluid is based on shear deformation measurement devices. The rheological models that are used for these types of flows are usually termed Generalized Newtonian Fluids (GNF). In a GNF model, the stress in a fluid is dependent on the second invariant of the stain rate tensor, which is approximated by the shear rate in most shear dominated flows. The temperature dependence of GNF fluids is generally included in the coefficients of the viscosity model. Various models are currently being used to represent the temperature and strain rate dependence of the viscosity. 

Numerous mathematical models exist that describe the strain rate dependence of viscosity (Carreau et al. 1997), but they are not important to the understanding of DMA. 

Kobayashi, M., Takahashi, T., Takimoto, J., Koyama, K., Influence of glass beads on the elongational viscosity of polyethylene with anomalous strain rate dependence of the strain-hardening. Polymer 37 (1996) 3745. 

In terms of the strain-hardening modulus, this has been developed by the use of Kuhn and Griin models and Kratky models to relate the development of molecular orientation and meehanical anisotropy (see Section 8.6.3). With regard to the strain rate sensitivity the strain rate-dependent viscosity has been developed by studies of creep and yield behaviour (see Sections 11.3 and 12.5.1). 

Fig. 7.15. PE under steady state shear flow at 150 °C Strain rate dependencies of the viscosity ry, the primary normal stress coefficient and the recoverable shear strain 7e. The dotted line represents Eq. (7.122). Results obtained by Laun [76]...

Thus for steady state uniaxial extensional flow, in contrast to steady state shearing flow, the second-order fluid result agrees with the UCM prediction only at small strain rates. The UCM, second-order fluid, and Newtonian fluid equations all differ in their predictions of the strain rate dependences of the extensional viscosity, though the strain rate dependences of the shear viscosity are the same for all three equations. This result typifies the usual finding that constitutive equations differ among themselves more strongly in their predictions of extensional viscosities than in their predictions of shear viscosities. 

In a fluid under stress, the ratio of the shear stress, r. to the rate of strain, y, is called the shear viscosity, rj, and is analogous to the modulus of a solid. In an ideal (Newtonian) fluid the viscosity is a material constant. However, for plastics the viscosity varies depending on the stress, strain rate, temperature etc. A typical relationship between shear stress and shear rate for a plastic is shown in Fig. 5.1. 

Fig. 53. Dependence of the critical strain-rate for chain scission (e ) on solvent viscosity (T)s) data from this work data from Ref. [109], where T)s was changed concomitantly with the solvent temperature -o- decalin at 7, 22 and 140°C -o- dioxane at 22 and 90 °C...

Equation (5.5) is known as Hooke s Law and simply states that in the elastic region, the stress and strain are related through a proportionality constant, E. Note the similarity in form to Newton s Law of Viscosity [Eq. (4.3)], where the shear stress, r, is proportional to the strain rate, y. The primary differences are that we are now describing a solid, not a fluid, the response is to a tensile force, not a shear force, and we do not (yet) consider time dependency in our tensile stress or strain. 

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