The Anisotropy of the Shear Moduli of Drawn Polyethylene

Abstract

Low density polyethylene was cold-drawn by simple tensile loading to produce transversely isotropic material. The elastic behaviour of such materials can, according to classical elasticity theory, be defined by five independent elastic constants. Three of these can be derived from Young's modulus measurements in various directions and the remaining two from shear moduli. The Young's modulus determinations have been previously reported, and the present paper concerns the determination of the shear moduli by means of torsional experiments (carried out at room temperature) on rectangular prisms of polyethylene. The draw ratios ranged from undrawn (isotropic) to draw ratio 4.6. The shear modulus governing torsion about the symmetry direction fell from 4.6 × 10⁸ dyn cm^-2 for the isotropic material to about one-third of this value for the highest draw ratio. The shear modulus for the other two principal directions increased over this range of draw ratios to about 3 times the isotropic value. All the experimentally determined shear moduli fell within the range calculated from the Young's moduli and the assumption that all deformations occurred at constant volume. Thus, although polyethylene is a viscoelastic material, for the small, elastic (completely recoverable with time) deformations here considered the well-established treatments of classical elasticity theory can be usefully employed. The five elastic compliances were calculated and, for the highly drawn polyethylene, showed a wider numerical range of values than most crystals and polymers previously reported. No molecular interpretation of these results can at present be suggested.