Strain hardening of thermoplastics

Most of the published stress--strain curves for thermoplastics are of limited theoretical interest as the test piece does not deform uniformly. However, over the last 20 years, several methods have been developed which enable true stress--strain curves to be obtained. This can be done either by using a polymer which is capable of uniform deformation or by confining the measurement to a small volume of the test piece in which uniform deformation may be assumed. The results so obtained can be interpreted by means of a spring and dashpot model in which the spring defines a strain hardening process according to the theories of high elasticity. When conventional Gaussian chain statistics are employed to represent the spring, the plastic deformation is represented by the equation sigma sub True = Y + G sub p ( lambda exp 2 --1/ lambda ) (eq 1) where sigma sub True is the true stress, Y the extrapolated yield stress, G sub p a strain hardening modulus, and lambda the extension ratio lambda = extended length (l)/original length (l sub o ). Most crystalline polymers obey this relation at temperature significantly below their melting point (T sub m ). In some cases, this agreement extends to very high values of lambda , as with high-density polyethylene where the equation has been followed up to lambda values of 12. With glassy polymers, difficulties may arise when a true strain softening effect occurs at the beginning of the extension process. Sometimes, as with PVC, this effect disappears at low strains and eq 1 is obeyed above lambda approx 1.2, but with polycarbonate the strain softening extends to high values of lambda and appears to distort the whole stress--strain relation. It is proposed that the modulus G sub p is determined by the sum of the restraints imposed by a mesh of uncrossable polymer chains. Attempts to interpret G sub p in terms of a conventional entanglement molecular weight give generally unacceptable results except in the case of polyethylene. Polymers with an extended chain conformation (high values of the Kuhn length) have high values of G sub p . A ratio of Y/G sub p / = 3 corresponds to the Considere condition for necking and gives a good indication of plastic instability.