The application of a Gauss-Eyring model to predict the behavior of thermoplastics in tensile experiments

The Gaussian expression for the isothermal tensile deformation of thermoplastics including the proposed strain hardening constant G_p, has been combined with the Eyring flow equation to provide a new relation describing the rate of strain of a thermoplastic in terms of the true stress and the extension ratio under isothermal conditions. In conventional mechanical tests this model can be used to quantify the tendency to strain localization, to predict the natural draw ratio and the inversion point where the true engineering stress passes through a minimum. The latter is expected to correlate with the value of the extension ratio where crazes do not propagate under tension. The equation is most easily demonstrated in constant load experiments where they agree well with published work. However, for a more precise evaluation of the theory the constant G_p should be measured separately and the calculated results compared with other tests on the same material. Where necking occurs it is possible to use a simplified plug flow model to calculate neck profiles. These show that no special assumptions are required to account for necking which results directly from the interaction of geometric thinning and strain hardening, even where true strain softening is absent. The procedure makes it possible to illustrate the way in which the form of the neck can be affected by the rate of extension or in a constant load experiment by the applied load. ©1995 John Wiley & Sons, Inc.