Theory of self-oscillating neck propagation in polymers

Abstract

The theories describing self-oscillating neck propagation in polymers are compared with the experimental data. For the description of self-oscillating neck propagation in PET, the system of equations is proposed. This theory is based on the Toda equation for the thermal conductivity in the incoming flow, which takes into account heat release into the environment. Numerical solution demonstrates the existence of self-excited oscillations in the ascending branch of the strain rate dependence of postyield stress, and this result conflicts with the Davidenkov criterion but fully agrees with the experimental evidence. The Barenblatt model takes into account the limited compliance of the samples and provides further development of the Davidenkov model. Self-oscillating neck propagation in polymers is shown to be qualitatively different from relaxation oscillations (for example, periodic slippage of a load along a table) and from oscillations described by the first-order kinetic equations. Hence, the instability of the systems described by the equation of thermal conductivity and the system of kinetic equations appears to be principally different.