Thermal activation based constitutive equations for polymers

Abstract
Minimal assumptions are used in deriving constitutive equations for polymers based on the theory of thermal activation. With a shear volume of activation inversely proportional to the flow stress, the general structure of the constitutive equation as a function of temperature, pressure, and strain rate may be elucidated without regard to the details of the underlying flow mechanisms. Strain hardening or softening is described by a differential equation relating the hardening rate to creation or destruction of flow units. While many polymers are, strictly speaking, nonlinearly viscoelastic materials, over a limited time and temperature range they may be considered to exhibit unrecoverable, though not necessarily volume conserving, strains and treated as viscoplastic. The equations have been applied to the yield stress of glassy PMMA, showing the excellent result that may be obtained with the assumed inverse dependence of the shear volume of activation upon the flow stress, and to the dynamic deformation behavior of semicrystalline PTFE, showing a reasonably good reproduction of the stress-strain behavior as a function of temperature, pressure, and strain rate. The yield stress results for PMMA are used to describe its ductile-brittle transition properties.