Elongational stress growth

Lodge rubberlike liquid (3.3-15) Constant = constant l/2 = 0 No predicts elongational stress growth rj1 (l, k) Yes... 

Figure 16. Compositional dependence of the Initial slope of the elongational stress growth function for LPX-30/LLDPE 10 (top) and LPX-30/LDFE (bottom). The broken lines were computed assuming miscibility.

The material functions tii and rji depend on both t and 8q, and of course on the parameter b that specifies the type of shear-free flow. For elongational flow, with b = 0 and Sq positive, rj becomes rj, the elongational stress growth function. This quantity has been measured for a number of polymer melts. Further information on elongational properties can be found in several extensive... 

Small-amplitude oscillatory shear Uniaxial steady elongation Biaxial steady elongation Planar steady elongation Elongational stress growth... 

M.H.Wagner, Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt, Rheol. Acta 12 (1976), 136-142. 

Although this experimentally observed scaling behavior is correctly predicted by the Doi-Ohta theory, the shape of the transient response curve—in particular, the overshoot and undershoot in the shear stress—are not predicted. This implies that the relaxation expressions chosen by Doi and Ohta, Eqs. (9-46) and (9-47), are inaccurate. This is not very surprising, since Eqs. (9-46) and (9-47) were chosen rather arbitrarily from many possible forms that satisfy the scaling relationship. Optical microscopy suggests that the overshoot and undershoot are caused by elongation of droplets followed by their breakup (Takahashi and Noda 1995). Vinckier et al. (1997) have shown that the stress growth after start-up or... 

Figure 13. Stress growth function for blends of linear low density polyethylene, LLDPE, with (left) another type of LLDPE (miscible, Series-I) and (right) with low density polyethylene (immiscible. Series II). Broken lines experimental data in elongation triangles experimental data in steady state shearing at y - O.Ols". Solid lines were computed from the frequency relaxation spectrum. (Adapted from ref. 14.)...

Stress Growth at Inception of Steady Elongational Flow... 

Fig. 9. Stress growth in elongational flow as calculated from Eq. (18.9)...

Stress growth at inception of steady elongational flow... 

In stress growth at inception of steady elongational flow, both the rigid dumbbells and elastic dumbbells give expressions for... 

Thus, once the four parameters of Eq 7.42 are known, the relaxation spectrum, and then any linear viscoelastic function can be calculated. For example, the experimental data of the dynamic storage and loss shear moduli, respectively G and G , or the linear viscoelastic stress growth function in shear or uniaxial elongation can be computed from the dependencies [Utracki and Schlund, 1987] ... 

Blends of LLDPE/PP = 50 50, with or without compatibilizing ethylene-propylene copolymer, EPR, were studied by Dumouhn et al. [1984]. In spite of the expected immiscibihty, the blends showed additivity of properties with good superposition of the stress growth functions in shear and elongation, as well as with the zero deformation rate Trouton ratio, Rj, = 1. In earlier work, blends of medium density PE (MDPE) with small quantities of ultra-high molecular weight polyethylene (UHMWPE) were studied in shear and extension. Again, SH and Rj, = 1 were observed. 

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

As shown in Figure 2.11, the stress growth function in elongation has three zones ... 

Figure 2.11 Stress growth function in elongation at constant Hencky strain rate, e, for linear and nonlinear viscoelastic melt - the latter shows the strain hardening (SH) see text.

The time dependence of stress under conditions of constant strain rate has been discussed for the case of linear viscoelasticity in Section FI of Chapter 3. For uniaxial extension at constant strain rate ei = (l/ ) d /dt), the time-dependent tensile stress ffriO is often expressed in terms of a time-dependent viscosity = An example of the stress growth in such elongational flow from... 

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