Recoverable shear

Polymers owe much of their attractiveness to their ease of processing. In many important teclmiques, such as injection moulding, fibre spinning and film fonnation, polymers are processed in the melt, so that their flow behaviour is of paramount importance. Because of the viscoelastic properties of polymers, their flow behaviour is much more complex than that of Newtonian liquids for which the viscosity is the only essential parameter. In polymer melts, the recoverable shear compliance, which relates to the elastic forces, is used in addition to the viscosity in the description of flow [48]. 

To add to this picture it should be realised that so far only the viscous component of behaviour has been referred to. Since plastics are viscoelastic there will also be an elastic component which will influence the behaviour of the fluid. This means that there will be a shear modulus, G, and, if the channel section is not uniform, a tensile modulus, , to consider. If yr and er are the recoverable shear and tensile strains respectively then... 

Note 5 Creep is sometimes described in terms of non-linear viscoelastic behaviour, leading, for example, to evaluation of recoverable shear and steady-state recoverable shear compliance. The definitions of such terms are outside the scope of this document. 

Mendelson (169) studied the effect of LCB on the flow properties of polyethylene melts, using two LDPE samples of closely similar M and Mw plus two blends of these. Both zero-shear viscosity and melt elasticity (elastic storage modulus and recoverable shear strain) decreased with increasing LCB, in this series. Non-Newtonian behaviour was studied and the shear rate at which the viscosity falls to 95% of the zero shear-rate value is given this increases with LCB from 0.3 sec"1 for the least branched to 20 sec"1 for the most branched (the text says that shear sensitivity increases with branching, but the numerical data show that it is this shear rate that increases). This comparison, unlike that made by Guillet, is at constant Mw, not at constant low shear-rate viscosity. 

Recoverable shear after steady-state deformation lim [yr/oo] oC... 

Philippoff, W., Gaskins,F.H., Brodnyan, J.G. Flow birefringence and stress. V. Correlation of recoverable shear strains with other rheological properties of polymer solutions. J. Appl. Phys. 28,1118-1123 (1957). 

L-100 (Mw — 1.4 0.1 x 10 , Mw/Mn — 2.2)4 in medicinal white oil as a rather high viscous solvent (1.50 poise at 25° C). In this figure the directly measured shear recovery (s ) (open triangles) is plotted against shear stress pzl of the preceding shear flow. From flow birefringence measurements (in a coaxial cylinder apparatus) and normal thrust measurements (in a cone-and-plate apparatus) values of normal stress difference (pn — p22) were calculated. These values were transformed with the aid of eq. (2.12) into recoverable shears s. The full circles (from... 

Fig. 2.3. "Recoverable shear" 5 vs. shear stress p21 for a 4.15 per cent solution of polyisobutylene L-100 in white oil at 25° C according to Philoppoff and Stratton (55). (A) shear recovery, ( ) calculated from flow birefringence, using eq. (2.12), (O) calculated from normal thrust measurements, using eq. (2.12)...

Recoverable shear strain measurements following the removal of shear stress after the sample has been sheared at a rate y0 collapse onto a single curve when the data are plotted against y0r [162],... 

In accordance with the experimental data (Ferry 1980), the shear modulus increases as the velocity gradient increases and the recoverable shear deformation A12 deviates from proportionality to the velocity gradient. 

Irec = recoverable shear or elastic shear deformation... 

Recoverable shear strain during steady shear flow... 

In Chap. 13 the creep recovery of a Burgers element was discussed and from Fig. 13.18 it becomes clear that the recoverable shear creep strain is in the present terms equal to... 

This recoverable shear strain shows up when the flow of a polymer melt in a capillary rheometer is suddenly stopped. The material that has just left the capillary rheometer will clearly recover to a certain extent, in principle equal to 1/2xi>i.o/(qVo)- Fig. 15.11 the various strains are shown after starting a steady shear flow at time f = 0 and stopping it at time fi. 

In order to elucidate the correlation method it may be recalled that the viscosity 77 approaches asymptotically to the constant value r c with decreasing shear rate q. Similarly, the characteristic time t approaches a constant value xQ and the shear modulus G has a limiting value G0 at low shear rates. Bueche already proposed that the relationship between 77 and q be expressed in a dimensionless form by plotting 77/r]0 as a function of qx. According to Vinogradov, also the ratio t/tq is a function of qxQ. If the zero shear rate viscosity and first normal stress are determined, then a time constant x0 may be calculated with the aid of Eqs. (15.60). This time constant is sometimes used as relaxation time, in order to be able to produce general correlations between viscosity, shear modulus and recoverable shear strain as functions of shear rate. 

According to Eq. (15.80) recoverable shear strain is proportional to the elastic shear compliance, J°. The elastic shear compliance depends on the molecular-weight distribution in the following way... 

Accordingly, the recoverable shear strain is for polymers with a broad MWD larger than for a polymer with a narrow MWD with the same Mw and thus the extrudate swell ratio will be higher for the "broad" polymer. This is in agreement with Fig. 15.37. Eq. (15.107) proved to be quite successful in describing data on extrudate swell, as long as it only concerns molecular-weight distribution. 

Finally, it has to be mentioned that die swell is also dependent on the kind of convergence of the flow. Fig. 15.38 shows the relationships between swelling and recoverable shear strain as derived by Cogswell (1970) for long capillaries and slit dies BER represents the swelling ratio in capillaries Bsh and Bst that in slit dies in the thickness direction and transverse direction, respectively. Fig. 15.39 shows the analogous relationships for very... 

FIG. 15.38 Relationship between swelling ratio and recoverable shear strain for long capillary and slit dies. After Powell (1974). 

Recommended values for group contributions to standard molar volume, 87 Recoverable shear, 531,551 Recoverable shear strain, 551 Recrystallisation, 703 Rectilinear flow, 527 Redox doping, 341 Reduced... 

The technological importance of xanthan gum rests principally on its unusual and distinctive properties25 28 29 49,116,251,257-260 in aqueous solution. Some of these properties are (1) remarkable emulsion-stabilizing and particle-suspension ability, (2) low concentrations yield high viscosities, (3) recoverable shear-thinning (extremely large shear dependence of viscosity), (4) little variation in viscosity with temperature under normal conditions of industrial utilization, and (5) gel formation when mixed with certain other, nongelling polysaccharides. 

When the stress is suddenly removed at D, the pattern consists of an elastic recovery (D-E) followed by a retarded elastic recovery (E-F). Because bonds between structural units are broken in region C-D, a part of the structure is not recovered. For values of time after the applied stress is removed, the recovered strain approaches a maximum value, 5r, called recoverable shear (Dealy, 1982) ... 

In addition to elongation flow, material can also exhibit elastic behavior. Two parameters that have been proposed " to quantify this property are (1) recoverable shear RS and (2) compliance C. These can be derived from ... 

Extrudate swell, B, has been used to calculate the recoverable shear strain, Yj, for single-phase materials [Utracki et ah, 1975]. Introduction of the interface negates the basic theoretical assumptions on which the calculation of Yj was based. In addition, presence of the yield stress, frequently observed in multiphase systems, prevents B from reaching its equilibrium value required to calculate Yr and then N. Nevertheless, B is used as a qualitative measure of blend elasticity. 

If a system is to possess elasticity, it must possess a physical mechanism for storing energy. In flow, droplet distortion causes an increase in surface free energy (aAA) which is released on cessation of flow, manifesting as, for example, recoverable shear compliance. The magnitude of the (dimensionless) droplet distortion is proportional to the Weber number, We, which is the ratio of the deforming stress (n y) to the restoring Laplace stress (4(j/dd). Thus, the drop Weber number based on drop radius is defined as ... 

FIGURE 5.17 Logarithmic presentation of the recoverable shear compliance, Jr(t), of Epon 100 IF as a function of the logarithm of time I at nine temperatures as indicated. Dramatic loss of long-time viscoelastic mechanisms is evident when temperature is decreased toward Tg. 

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