Time dependent scission and cross-linking in an elastomeric cylinder undergoing circular shear and heat conduction

When an elastomeric material is at a sufficiently high temperature, there can be time-dependent scission of macromolecular network cross-links. The affected molecules can recoil and cross-link to form a new network in a new reference configuration. The material then consists of several molecular networks. This microstructural change affects the mechanical response and leads to permanent set. A constitutive equation is presented, based on the experimental work of Tobolsky (Properties and Structures of Polymers, Wiley, New York, 1960, pp. 223-265), which can account for the influence of this temperature-dependent microstructural change on the mechanical response. It is used to study an elastomeric cylinder undergoing circular shear and transient heat conduction.