Viscosity tensile

If, on the other hand, the channel section changes then tensile stresses will also be set up in the fluid and it is often necessary to determine the tensile viscosity, k, for use in flow calculations. If the tensile stress is a and the tensile strain rate is s then... 

For many polymeric melts the tensile viscosity is fairly constant and at low stresses is approximately three times the shear viscosity. 

From this relatively simple test, therefore, it is possible to obtain complete flow data on the material as shown in Fig. 5.3. Note that shear rates similar to those experienced in processing equipment can be achieved. Variations in melt temperature and hypostatic pressure also have an effect on the shear and tensile viscosities of the melt. An increase in temperature causes a decrease in viscosity and an increase in hydrostatic pressure causes an increase in viscosity. Topically, for low density polyethlyene an increase in temperature of 40°C causes a vertical shift of the viscosity curve by a factor of about 3. Since the plastic will be subjected to a temperature rise when it is forced through the die, it is usually worthwhile to check (by means of Equation 5.64) whether or not this is signiflcant. Fig. 5.2 shows the effect of temperature on the viscosity of polypropylene. 

For tensile creep, TJ would be the tensile viscosity. When the viscosity is high (e.g., when working at relatively low temperatures or with very high-molecular-weight polymers) it can be difficult to determine tl-x accurately, so creep recovery measurements are made. Here the load is released after a given creep time and the strain is followed as the specimen shrinks back toward its new equilibrium dimensions. 

Kalyanasundaram, Kumar, and Kuloor (K2) found the influence of dispersed phase viscosity on drop formation to be quite appreciable at high rates of flow. The increase in pd results in an increase in drop volume. To account for this, the earlier model was modified by adding an extra resisting force due to the tensile viscosity of the dispersed phase. The tensile viscosity is taken as thrice the shear viscosity of the dispersed phase, in analogy with the extension of an elastic strip where the tensile elastic modulus is represented by thrice the shear elastic modulus for an incompressible material. The actual force resulting from the above is given by 3nRpd v. 

Flow Viscosity. The additional tensile viscosity that a polymer chain of Z elementary units imparts upon its solvent is given by (P) ... 

Extensional viscometers are useful to measure tensile viscosity in processes such as stretch orientation. 

In other words, independently of the viscoelastic history in the linear region, the tensile compliance function can readily be obtained from both the shear and bulk compliance functions. For viscoelastic solids and liquids above the glass transition temperature, the following relationships hold when t oo J t) t/T[ [Eq. (5.16)], D t) = y Jt [Eq. (5.21)], and D t)J t)/ >. These relations lead to r 3t that is, the elongational viscosity is three times the shear viscosity. It is noteworthy that the relatively high value of tensile viscosity facilitates film processing. 

The viscosity emphasized in this chapter, called elongational or extensional viscosity, was originally designated (34) tensile viscosity. When this bulk-phase parameter is near the interface, its two-dimensional equivalent is called the surface dilational viscosity. The importance of this parameter in the foaming of coatings, which arises from differences in surfactant structures, has been discussed (35). In cosmetic applications, foam and gel structures are important and probably reflect the reason the hydrophobically modified acrylic acid polymers were emphasized in the last section of Ghapter 7. 

Another term sometimes used is the dynamic tensile viscosity, rj = E"/oj. Using Equation 3.80, Equation 3.84, and Equation 3.86, one further obtains... 

The only way to generate data for this type of unsteady biaxial tensile flow is to instrument a blown film machine. The tensile viscosity, defined by Eq. (5.16), hardly changes with the tensile strain rate. Figure 5.15 shows data for the uniaxial stretching of an LDPE and an HDPE. The apparent tensile viscosity increases with strain rate for the more elastic LDPE, in contrast with the non-Newtonian reduction in viscosity in shear flows. 

For a length L = 0.2 m, a density p = 750kgm and g = 9.8 ms , the stress a = 1.5 kPa. To avoid significant stretching, the tensile strain rate must be less than 0.2 s , which means that the tensile viscosity must exceed 7500Nsm. When these two conditions are imposed on a typical shear flow curve in Fig. 5.18, it is clear that the melt must be highly non-Newtonian. A similar process cannot be used for Newtonian silicate glasses... 

Prom the comparison of Eqs. (5.65) and (5.73), we see that the tensile viscosity is three times the shear viscosity. This is Trouton s well-known rule, which is analogous to the relation of Young s modulus being three times the shear modulus for an isotropic incompressible material. 

For film blowing, strain-hardening, namely, the tensile viscosity improves with the tension rate, is preferred for a stable process line. To obtain the goal, long branches were introduced into the PBS polymer chain. 

Elongational or tensile viscosity Biaxial extensional viscosity Biaxial stress growth coefficient Biaxial stress decay coefficient Scattering angle... 

Extensiometer n. A rheometer for measuring the extensional flow properties of molten polymers. In one early form, the Cogswell rheometer, useful at tensile viscosities over lO Pa/s, unidirectional tensile force was exerted on a polymer rod by a dead-weight acting through a cam and pulley. As the cam rotated, the moment arm exerted... 

Formulas for linear viscoelastic models can be apphed to tensile deformation as well as shear deformation by replacing the shear stress x with tensile stress o, shear strain y with tensile strain e, shear modulus G with Young s tensile modulus E, and newtonian shear viscosity T with Trouton s tensile viscosity iig [11—13]. 

If aji tends to a constant value as stretching proceeds, will also approach a limiting value this is termed either the elongational, extensional, or tensile viscosity, The exten-sional viscosity is a true material property, and is independent both of the technique of measurement and of any assumptions concerning the constitutive behavior of the polymer. For homogeneous materials, its numerical value can be a function of the stretch rate and of the temperature at which the measurement is made. 

Fig. 10 Dependence of the steady-state tensile viscosity tf-g, on the tensile stress at 150°C for a LDPE and two metallocene samples. C4 P1 represents branched mPE and Clb P5 represents linear mPE. Curves are fitted to the data points to guide the eye. Reprinted from [120], with kind permission from American Chemical Society...

Equations 36 to 41 are written for simple shear. Analogous relations hold for simple extension with all 7 s replaced by D s and the shear viscosity r]o replaced by the tensile viscosity o, which is defined as cr/e in steady flow (see Section F below). 

Elongational Viscosity n (extensional viscosity, Trouton viscosity) The viscosity that characterizes an element undergoing Elongational Flow (above). It is equal to the tensile stress divided by the rate of elongation and for polymers it depends on the rate, but may increase with rate, unlike the usual reduction of shear viscosity with rate. Tensile viscosities are apt to be many times larger than shear viscosities for the same resin, temperature, and deformation rate. Values in the range of 10 -10 Pa s have been reported. For Newtonian liquids, the elongation viscosity is three times the shear viscosity (at the same temperature). 

FIG. 26 Comparison of steady-state or plateau elongational viscosities of polyethylene melts from homogeneous isothermal elongation tests (unfilled s mibols) and transient tensile viscosities evaluated from converging flow (filled symbols). Unfilled symbols with tick denote tensile creep measurements. T = 150°C. 

From the extensional material function data shown in Chapters 2 and 4, we know that extensional response can differ very much from shear. For example, at low extension rate tensile viscosity typically obeys Trouton s rule, but at higher extension rates it shows very little of the thinning so common for shear viscosity (Figure 2.1.3). Sometimes even thickening is observed (Figures 4.2.5-4.2.7). Such behavior is not unexpected from structural theories for rodlike suspensions (Chapter 10) and for polymers (Chapter 11). 

Where t is the tensile viscosity, V and Vf are the total volume and free volume of the system respectively, and A and B are constants. 

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