Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T _cr (near 100^∘C for natural rubber), its macromolecular structure undergoes time and temperature-dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (reduced stiffness) and permanent set on removal of the applied load.A new constitutive theory is used to study the influence of the changes of macromolecular structure on the torsion of an initially homogenous elastomeric cylinder. The cylinder is held at its initial length and given a fixed twist while at a temperature below T _cr. The twist is then held fixed and the temperature of the outer radial surface is increased above T _cr for a period of time and then returned to its original value. Assuming radial heat conduction, each material element undergoes a different chemical change. After enough time has elapsed such that the temperature field is again uniform and at its initial value, the cylinder properties are now inhomogeneous. Expressions for the time variation of the twisting moment and axial force are determined, and related to assumptions about material properties. Assuming the elastomeric networks to act as Mooney-Rivlin materials, expressions are developed for the permanent twist on release of torque, residual stress, and the new torsional stiffness in terms of the kinetics of the chemical changes.