A constitutive equation for the dynamic deformation behavior of polymers

Abstract

A constitutive equation based on the generalized concept of thermally activated flow units is developed to describe the stress–strain behavior of polymers as a function of temperature, strain-rate, and superposed hydrostatic pressure under conditions in which creep and long-term relaxation effects are negligible. The equation is shown to describe the principal features of the dynamic stress–strain behavior of polytetrafluoroethylene and, also, the yield stress of polymethylmethacrylate as a function of temperature and strain rate. A key feature of the model, not utilized in previous constitutive equation descriptions, is an inverse shear stress dependence of the shear activation volume. In contrast to metal deformation behavior, an enhanced strain hardening with increasing strain at higher strain rates and pressures is accounted for by an additional rate for immobilization of flow units. The influence of hydrostatic pressure enters through a pressure activation volume and also through the flow unit immobilization term. The thermal activation model is combined with a temperature dependent Maxwell–Weichert linear viscoelastic model that describes the initial small strain part of the stress strain curve.