Linear viscoelastic flow elongational

The function F(t — t ) is related, as with the temporary network model of Green and Tobolsky (48) discussed earlier, to the survival probability of a tube segment for a time interval (f — t ) of the strain history (58,59). Finally, this Doi-Edwards model (Eq. 3.4-5) is for monodispersed polymers, and is capable of moderate predictive success in the non linear viscoelastic range. However, it is not capable of predicting strain hardening in elongational flows (Figs. 3.6 and 3.7). 

The experimental ranges of strain rates (or strains) are summarized in Table 2 for the various types of experiments. Time-temperatiire superposition was successfully applied on the various steady shear flow and transient shear flow data. The shift factors were foimd to be exactly the same as those obtained for the dynamic data in the linear viscoelastic domain. Moreover, these were found to be also applicable in the case of entrance pressure losses leading to an implicit appUcation to elongational values. 

Table 7 gives a summary of qualitative performances and problems encountered for simple shear and uniaxial elongational flows, using the Wagner and the Phan Thien Tanner equations or more simple models as special cases of the former. Additional information may also be found in papers by Tanner [46, 64]. All equations presented hereafter can be cast in the form of a linear Maxwell model in the small strain limit and therefore are suitable for the description of results of the linear viscoelasticity in the terminal zone of polymer melts. 

LDPE, and with polypropylene, PP, was studied In steady state shear, dynamic shear and uniaxial extenslonal fields. Interrelations between diverse rheological functions are discussed In terms of the linear viscoelastic behavior and Its modification by phase separation Into complex morphology. One of the more Important observations Is the difference In elongational flow behavior of LLDPE/PP blends from that of the other blends the strain hardening (Important for e.g. fllm blowing and wire coating) occurs In the latter ones but not In the former. 

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... 

Behavior of Entangled Polymer Melts and Solutions Transient Response. While the steady-state response of polymers in shear and elongational flows is of much interest, there are also many instances in which the transient response is important because not all processes attain steady state. There are two important transient responses in the nonlinear regime of behavior. These are the stress relaxation response in which the deformation is held constant and the stress evolution with time is followed. This was discussed above for the linear viscoelastic case. In addition, the response to a constant rate of deformation can be an important transient response to study. Also note that creep experiments are sometimes used to characterize the nonlinear response of polymeric fluids and these will also be discussed briefly. 

This modification of the convected Maxwell model contains one constant G (an elastic modulus) and the non-Newtonian viscosity function rj y). It describes the shear-rate dependence of the viscosity perfectly and the first normal stress coefficient rather well. In steady elongational flow it gives an infinite elongational viscosity, and does not simplify properly in the linear viscoelastic limit. Nonetheless it has been found to be useful in exploratory flow calculations aimed at assessing the interaction of shear thinning and memory. 

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