Planar Elongation Research Articles

A Relationship Between the Single‐Jump Shear and Planar Elongational Strain Experiments

First Page

Polymer melt elongation—methods, results, and recent developments

AbstractFor film blowing of polyethylene it has been shown previously that melt elongation is very powerful for polymer characterization. With two types of rheometers, simple (also called “uniaxial”) elongational tests as well as creep tests can be performed homogeneously. In simple elongation, the melts of branched polyethylene show a remarkable strain hardening. With respect to their advantages and disadvantages, these rheometers complement each other. For multiaxial elongations the various modes of deformation can be performed by means of the rotary clamp technique. With the strain rate components ordered such that \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}11 ⩾ \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}22 ≥ \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}33, the ratio m = \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}22/\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document}11 characterizes the test mode. The Stephenson definition of the elongational viscosities makes use of the linear viscoelastic material equation and proves to be very efficient because the linear shear viscosity (t) (“stressing” viscosity) can act as the reference for the nonlinear behavior in elongation. Results are given for polyisobutylene measured not only in simple, equibiaxial, and planar elongations, but also in new test modes with a change of m during the deformation. This allows one to investigate the consequences of a deformation‐induced anisotropy of the rheological behavior.

EXPERIMENTAL ASPECTS IN POLYMER MELT ELONGATIONAL RHEOMETRY

After describing the present state-of-the-art, the open experimental problems are listed that prevent a broader application of elongational rheometry to more types of polymer melts. Small samples are preferable for the investigation of structure-properties relationships. Hints are given for the preparation of such samples and for the reduction, in simple elongation, of the error due to inhomogeneous deformations near the sample ends. Large elongations can be performed homogeneously with rotary clamps. However, it is important to characterize the quality of each test, because small errors in the strain rate lead to drastic changes in the stress-strain diagrams obtained for large strains, e.g. e > 4 (HENCKY strain) for melts of LDPE (low density polyethylene). For HDPE the main difficulty is the preparation of homogeneous samples, which requires a special cooling procedure after extrusion. The maximum elongations obtained so far are ϵmax = 5.5 for HDPE and ϵmax = 7 for LDPE. With modified rotary clamps, different modes of multiaxial elongational flows can be realized with polyisobutylene at room temperature. Eight such clamps in circular and rectangular arrangements are used for equibiaxial and planar elongations, respectively. Planar elongation gives two independent material responses. In presenting the test results, new definitions of the elongational viscosities concisely elucidate deviations from linear viscoelastic behavior. For other multiaxial flows the rotary-clamp-technique can also be applied, e.g. for flows with arbitrary ratios of the strain rate components and even with a variation of these ratios with time during an experiment. For a broader application, miniaturization of the rheomeler and operation at higher temperatures require further modifications

Extensional flows of oldroyd fluids

The complete equations for a general extensional flow of the eight-constant Oldroyd fluid are presented. The type of flow, described by a single parameter m, is fixed but the rate of strain and the stress components may vary with time. The conditions under which stresses reach steady values in stretching at constant rate of strain are investigated and specific results obtained for uniaxial, equibiaxial and planar elongation. Creep is discussed for a restricted (Maxwell-like) model, and the same critical value of a combination of parameters is obtained. The problem of possible loss of symmetry of the axisymmetric flows under certain conditions is discussed briefly.

Multiaxial elongational flows of polymer melts—classification and experimental realization

For the class of multiaxial elongational flows with constant strain rates, a new classification system is proposed. Ordering the main strain rates such that ∈ . 0  ∈ . 11 ⩾ ∈ . 22 ⩾ ∈ . 33, the constant ratio m  ∈ . 22/ ∈ . 11 characterizes the special type of flow, e.g. in simple elongation m = − 1/2, in equibiaxial elongation m = +1, and in planar elongation (“pure shear”) m=0. For the representation of the test results, three elongational viscosities μ i = A i σ i / ∈ . 0 are defined from the three normal stress differences σ i such that for the linear viscoelastic limit the time-dependent linear viscoelastic shear viscosity follows: μ i ( t)→ ▪ t. For the realization of such multiaxial elongational flows, rotary clamps are used. They are modified such that the force components along and normal to the direction of motion at the clamp can be measured separately. The investigation was performed with polyisobutylene in simple, equiviaxial, and planar elongations. The latter mode of testing is of special interest because two different elongational viscosities are determined simultaneously. The results show that for small deformations the material behaviour is linear viscoelastic. For larger deformations there are different deviations the character of which depends on m, i.e. the type of the elongational flow. From the general single-integral constitutive equation it follows that the predicted stress differences for the different m are very differently connected with the different parts of the equation, as in the case of the two normal stress differences in simple shear flow.