Elongation, uniaxial

The uniaxially elongated NR vulcanizate with a = 4.0 formed line stmctures with several micrometers in width along the strain direction, as shown in Figure 21.12. It was evident from the series of observations with different a that there was a strong dependence of a on line-width change (data not... 

FIGURE 21.12 Tapping-mode topographic image of uniaxially elongated NR vulcanizate. The elongation ratio was about 4. The scan size was 20 p,m. 

In the present paper, we describe how photodegradation of low density polyethylene films was enhanced by uniaxial elongation. An explanation of the enhancement process is given based on the photooxidation and deformation mechanisms, and the photodegradation products. 

Note 2 From the definition of general homogeneous flow (Definition 1.5) G X = GX = constant) in the particular case of steady uniaxial elongation flow... 

The same line shapes are observed in deuterium NMR of uniaxially elongated crosslinked rubbers118). On the basis of quadrupole effects (taking into account that... 

For uniform uniaxial elongational deformation along axis 1, the tensor of the velocity gradients, taking into account the condition of incompressibility, can be written in the form... 

Figure 15.5 Spectra simulated with a phantom network, in which each chain is elongated, and thus oriented, along its end-to-end vector. A gaussian distribution of the end-to-end vectors is assumed, a relaxed (isotropic) state b uniaxially elongated state (deformation ratio A, = 2.5). Affine displacement of junctions is assumed. No...

The jump from uniaxial elongation to uniform compression is a simple one in terms of defining all the stresses and strains. The final modulus we wish to define, the shear modulus., r, is a little different and you have to pay... 

Schweizer T (2000) The uniaxial elongational rheometer RME - six years of experience. Rheol Acta 39 428-43. 

Venerus DC, Zhu S-H and Ottinger HC (1999) Stress and birefringence measurements during the uniaxial elongation of polystyrene melts. J Rheol 43 795-813. 

Segmental orientation in a material submitted to uniaxial elongation may be conveniently described by the average of the second Legendre polynomial ... 

The aim of the present work has been to establish correlations between bulk macroscopic response of polymer melts under flow and the behaviour at a molecular level as seen by SANS, and to discuss the results in the frame of molecular theories. Two simple and well defined geometries of deformation have been investigated uniaxial elongation and simple shear. The... 

The aim of this section is to perform comparisons between the predictions of some constitutive equations and experimental results in simple shear and uniaxial elongation on three polyethylenes. In addition, this is expected to provide well-defined sets of material parameters to be used in the model equations for the computation of complex flows. 

Part 2 presents a summary of the theoretical considerations and basic assumptions that lead to the model equations. Part 3 discusses some experimental aspects and focuses on the measmements in various shear and uniaxial elongational flow situations. Part 4 and 5 are devoted to the comparisons between experimental and predicted rheological functions. Problems encountered in the choice of correct sets of parameters or related to the use of each type of equation will be discussed in view of discrepancies between model and data. 

The mathematical form of the function can be derived simply from a fit of the experimental h(y) as obtained in step shear strain for example. However, the problem is further complicated if one now takes into account flows where the two invariants differ from each other as, for example, in uniaxial elongational flows where ... 

In its form, the model of equation (27) is very useful since using a proper damping function enables a correct description of various shear or uniaxial elongational basic experiments. 

Provided that a suitable Y function is chosen, this is claimed to give a correct picture of many phenomena displayed in simple shear and uniaxial elongational flows. One should note that the original model of Phan-Thien and Tanner uses the non-af ne derivative together with nonlinear stress term. 

This latter method can also be used in uniaxial elongation using the transient elongational stress (OE(t,e) = Xii(t,e) - T (t,e)) ... 

This section presents different results obtained using the Wagner equation with the form of the damping function of equation (33) together with the generalized invariant of equation (25). It is primarily devoted to comparisons between predictions and experimental results in shear and uniaxial elongational flows described in paragraph 3 for LD. 

The previous set of comparisons shows that the Wagner model enables a good description of the experimental data in various experiments in simple shear and uniaxial elongation. However, it is worth pointing out that in most cases, there is a major difficulty concerning the determination of the parameters of the damping function. 

Figures 15 to 18 show the predictions of the model for LD at 160°C in steady state and some transient flows in shear and uniaxial elongation.

At least, using the complete Phan Thien Tanner equation, with non-affine motion and modified kinetics enables a correct description of the data in shear and in elongation. However, the parameters that can be determined for this model are bound to be some compromise. This is necessary in order to minimize the deviation to the Lodge-Meissner rule, due to the use of the Gordon-Schowalter derivative. This is also required to give adequate description of both the shear and uniaxial elongational behaviour. Additional undesirable phenomena in some flows have also been pointed out such as oscillations in transient flows. 

Two different constitutive equations, namely the Wagner model and the Phan Thien Tanner model, both based on network theories, have been investigated as far as their response to simple shear flow and uniaxial elongational flow is concerned. This work was primarily devoted to the determination of representative sets of parameters, that enable a correct description of the experimental data for three polyethylenes, to be used in numerical calculation in complex flows. Additionally, advantages and problems related to the use of these equations have been reviewed. 

Though the Wagner and Phan Thien Tanner equations seem to give adequate description of the observed behaviour either in shear or in uniaxial elongation, it is worth mentioning some peculiarities and key points that should keep the attention of the user to avoid misleading conclusions. 

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. 

M.H.Wagner, A constitutive analysis of uniaxial elongational flow data of a low density polyethylene melt, J. of Non-Newt. Fluid Mech. 1 (1978), 39-55. 

---