A fibre composite model of drawn crystalline polymers

Abstract

The two-phase fibre composite model proposed by us elsewhere [Barham and Arridge (1977)] is used to explain the behaviour of polyethylene and polypropylene on drawing to very high draw ratios. The basis of the theory is that, after necking, there exists a uniform distribution of aligned needle-like elements of near perfect crystallinity in a less-perfect matrix. On further drawing these reinforcing elements are supposed to elongate in a homogeneous deformation while contracting laterally. The resultant change in their aspect ratio is sufficient, using short fibre reinforcement theory, to account for the increase in the modulus on drawing. The Young's modulus of the drawn fibre is given by the expression: E f=cE c 1− tanh x x +(1−C)E m where c is the concentration of elements, E c the modulus of the crystalline elements and E m that of the matrix while x, derived from shear-lag theory, depends upon the aspect ratio of the elements and the moduli of the two phases. For both polyethylene and polypropylene it is found that x ∝ t 3 2 , where t is the post-neck draw ratio. The model is applied (1) to the explanation of the observed relation between Young's modulus and draw ratio, (2) to explain the temperature dependence of drawing behaviour, (3) to postulate a mechanism far non-linear viscoelasticity and creep behaviour and (4) to explain the self-stiffening after annealing under constraint [Arridge, Barham and Keller (1977)].