Shear strain recoverable

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. 

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). 

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],... 

Recoverable shear strain during steady shear flow... 

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... 

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. 

Normal stress differences generated in shear flow are common features of isotropic macromolecular fluids.. They are associated with fluid elasticity and are related to a number of phenomena such as elastic recoil, die swell, orientation, and melt fracture. In fact, the ratio, N /2o, is related to the ultimate recoverable shear strain which can be measured in a cone-and-plate device on cessation of flow. Liquid crystalline fluids also exhibit positive values of N (see Figure 9) and in some cases negative values of Vail... 

The permanent shear strain, is the non-recoverable shear strain resulting from a shear load. 

Spherulitic superstructures were formed at low shear strains and an oriented, row-nucleated stacked lamellar texture developed with increasing shear strain. At higher recoverable shear strain values, a fine surface roughness developed due to high melt elastic instabilities. 

An alternative expression relates die swell to the recoverable shear strain at the die wall (y ) which may be measured via creep experiments and the creep recovery function [4] ... 

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]...

Bagley, E. B. and Duffey, H. J., Recoverable shear strain and bams effect in polymer extmsion, Trans. Soc. Rheol. 14, 545-553 (1970). 

The above die swell model is based on the assumption that the polymer fluid behaves similarly to a rubber-Uke solid. However, it is difficult to measure recoverable shear strain under general conditions. 

To study the elastic response in the near-quiescent state we used a constant stress cone and plate rheometer to measure the recoverable shear strain after steady flow had been achieved. For an experimental liquid crystal polyester the elastic response at low stress is very large suggesting an elastic modulus of the order 400 N m —at least two orders of magnitude lower than a chemically similar polyester melt which does not exhibit liquid crystal phenomena (Fig. 3). However, at a shear stress of about 10 N —at which the conventional polyester is just starting to demonstrate significant elastic response—the high elasticity of the liquid crystal polyester collapses. 

---