Shear rate plastic

Traditionally the kinetic relation of the plastic-shearing rate yP has been given in the form below, where the probability of reverse transformations is not negligible ... 

As suggested above, the character of atomic environments can be changed by athermal mixing in which the LL environment fraction can increase with plastic shear rate yP in proportion to the availability of the SL environments, i.e., 1 — as... 

We develop first the considerations related to shear response in a ID context of plastic-shear flow to state the basic kinetic response of the solid, where s stands for an applied shear stress, t stands for a threshold plastic-shear resistance, and y is taken to be the plastic-shear strain yP. As a useful simplification, we first consider the material to be rigid on the basis that the plastic-shear increments are large, in comparison with the elastic-strain increments. At temperatures T > OK, for which the elastic moduli of the solid are significantly lower than at 0 K, we expect that the rate-independent plastic-shear resistance z temperature dependence as the elastic-shear modulus (Chapter 4). Then, where the plastic response in a rate-independent manner is initiated when s = z(T), under conditions of s < z T), a plastic response is still possible by thermal assistanee and occurs at a (plastic) shear rate of (Argon 1973)... 

Of the models Hsted in Table 1, the Newtonian is the simplest. It fits water, solvents, and many polymer solutions over a wide strain rate range. The plastic or Bingham body model predicts constant plastic viscosity above a yield stress. This model works for a number of dispersions, including some pigment pastes. Yield stress, Tq, and plastic (Bingham) viscosity, = (t — Tq )/7, may be determined from the intercept and the slope beyond the intercept, respectively, of a shear stress vs shear rate plot. 

Fig. 10. Viscosity vs shear rate for solutions of a styrene—butadiene—styrene block copolymer (42). A represents cyclohexanone, where c = 0.248 g/cm (9-xylene, where c = 0.246 g/cm C, toluene, where c = 0.248 g/cm. Courtesy of the Society of Plastics Engineers, Inc.

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

Power consumption for impellers in pseudoplastic, Bingham plastic, and dilatant nonnewtonian fluids may be calculated by using the correlating lines of Fig. 18-17 if viscosity is obtained from viscosity-shear rate cuiwes as described here. For a pseudoplastic fluid, viscosity decreases as shear rate increases. A Bingham plastic is similar to a pseudoplastic fluid but requires that a minimum shear stress be exceeded for any flow to occur. For a dilatant fluid, viscosity increases as shear rate increases. 

Viscosity has been replaced by a generahzed form of plastic deformation controlled by a yield stress which may be determined by compression e)meriments. Compare with Eq. (20-48). The critical shear rate describing complete granule rupture defines St , whereas the onset of deformation and the beginning of granule breakdown defines an additional critical value SVh... 

If the maximum resolved shear stress r and the plastic shear strain rate y are defined according to (it is assumed that the Xj and Xj directions are equivalent)... 

Steady-propagating plastic waves [20]-[22] also give some useful information on the micromechanics of high-rate plastic deformation. Of particular interest is the universality of the dependence of total strain rate on peak longitudinal stress [21]. This can also be expressed in terms of a relationship between maximum shear stress and average plastic shear strain rate in the plastic wave... 

The melt viscosity is highly non-Newtonian in that the apparent viscosity drops considerably with increasing shear rate. Melt viscosities are about the average encountered with plastics materials but there is a considerable variation between grades. 

The rate of mastication, as measured by changes in plasticity or viscosity, is a complex function of temperature (Figure 11.16) with the rate going through a minimum at about 105°C. Below this temperature the increasing viscosity of the rubber causes increased shearing stresses at constant shearing rates and this... 

In practice there are a number of other factors to be taken into account. For example, the above analysis assumes that this plastic is Newtonian, ie that it has a constant viscosity, r). In reality the plastic melt is non-Newtonian so that the viscosity will change with the different shear rates in each of the three runner sections analysed. In addition, the melt flow into the mould will not be isothermal - the plastic melt immediately in contact with the mould will solidify. This will continuously reduce the effective runner cross-section for the melt coming along behind. The effects of non-Newtonian and non-isothermal behaviour are dealt with in Chapter 5. 

The plastic has a viscosity of 200 Ns/m. Calculate also the shear rate in the metering zone. 

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. 

In this apparatus the plastic to be tested is heated in a barrel and then forced through a capillary die as shown in Fig. 5.16, Normally the ram moves at a constant velocity to give a constant volume flow rate, Q. From this it is conventional to calculate the shear rate from the Newtonian flow expression. 

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. 

Elastomer-plastic blends without vulcanization were prepared either in a two roll mill or Banbury mixer. Depending on the nature of plastic and rubber the mixing temperature was changed. Usually the plastic was fed into the two roll mill or an internal mixer after preheating the mixer to a temperature above the melting temperature of the plastic phase. The plastic phase was then added and the required melt viscosity was attained by applying a mechanical shear. The rubber phase was then added and the mixture was then melt mixed for an additional 1 to 3 min when other rubber additives, such as filler, activator, and lubricants or softeners, were added. Mixing was then carried out with controlled shear rate... 

Bingham-plastic slurries require a shear stress diagram showing shear rate vs. shear stress for the slurry in order to determine the coefficient of rigidity, T], which is the slope of the plot at a particular concentration. This is laboratory data requiring a rheometer. These are usually fine solids at high concentrations. 

For Newtonian fluids the dynamic viscosity is constant (Equation 2-57), for power-law fluids the dynamic viscosity varies with shear rate (Equation 2-58), and for Bingham plastic fluids flow occurs only after some minimum shear stress, called the yield stress, is imposed (Equation 2-59). 

Figure 4-185. Shear stress-shear rate diagram, (a) Newtonian fluid, (b) Bingham plastic fluid, (c) Power iaw fiuid. (d) Herschei-Buckiey fiuid.

In order to complete the discussion of methodical problems, we should mention two more methods of determining yield stress. Figure 6 shows that for plastic disperse systems with low-molecular dispersion medium, when a constant rate of deformation, Y = const., is given, the dependence x on time t passes through a maximum rm before a stationary value of shear stress ts is reached. We may assume that the value of the maximal shear stress xm is the maximum strength of the structure which must be destroyed so that the flow can occur. Here xm as well as ts do not depend or depend weakly on y, like Y. The difference between tm and xs takes into account the difference between maximum stress and yield stress. For filled polymer melts at low shear rates Tm Ts> i,e- fhese quantities can be identified with Y. 

The high shear rate produces two other effects that significantly affect product performance. The plastics molecules become... 

The operating pressures and shear rates in the extrusion process are considerably lower than they are in molding. As it exits the die, but not necessarily when it leaves the process, the material is in an essentially stress-free condition. Depending on the wall thickness of the material and the particular material, there is orientation of the plastic to a greater or lesser controllable degree. Thin walls produce higher orientation in materials such as PP, that is a highly crystalline polyolefin, and which orients much more than materials such as PVC. 

The melt index (MI) or melt flow index (MFT) is an inverse measure of viscosity. High MI implies low viscosity and low MI means high viscosity. Plastics are shear thinning, which means that their resistance to flow decreases as the shear rate increases. This is due to molecular alignments in the direction of flow and disentanglements. 

The Ml test equipment is easy to operate, provides repeatable results, and low cost to operate. It is widely used for quality control and for distinguishing between members of a single family of plastics. Specifically, this MI makes a single-point test that provides information on resistance to flow at only a single shear rate. Because variations in branching or MWD can alter the shape of the viscosity curve, the MI may give a false ranking of plastics in terms of their shear rate resistance to flow. To overcome this problem, extrusion rates are sometimes measured for two loads, or other modifications are made. 

Viscosity, apparent Defined as the ratio between shear stress and shear rate over a narrow range for a plastic melt. It is a constant for Newtonian materials but a variable for plastics that are non-Newtonian materials. 

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