A CONSTITUTIVE LAW FOR LARGE DEFORMATIONS OF POLYMERS AT HIGH-TEMPERATURES

The model of crosslinks and sliplinks of Ball et al. [(1981) Elasticit y of entangled networks. Polymer 22, 1010-1018] was shown in a previou s paper to return the appropriate behaviour of necking and strain hard ening observed in many polymers. Stress-strain experiments on the stre tching of polypropylene at 150 degrees C show that there is an initial stiff response preceding necking, which begins at a lower strain than that predicted by the model of Ball et al. We have introduced a modif ication such that, as deformation proceeds, the number of sliplinks de creases. In the modified model, necking can begin at strains comparabl e with those observed experimentally. The proposed model is of an elas tic, but not hyperelastic, material. An alternative explanation of the observed early onset of necking in terms of rate-dependent plasticity is explored and found to be inadequate, suggesting that the observed effect is an inherent property of the network. Superficially similar p roposals for the modelling of glassy polymers, which also involve a ch anging number of chain interactions, are compared, and found to be ess entially different; the effects modelled by these theories can be equa lly well modelled by the unmodified Ball et al. approach. We demonstra te the applicability of the present proposal by incorporating it into a finite element scheme and modelling a uniaxially stressed necking sp ecimen of polypropylene. Copyright (C) 1996 Elsevier Science Ltd