Multiaxial elongational flows of polymer melts—classification and experimental realization

Abstract

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.