Coupled thermal- and deformation-induced degradation in planar rubber membranes under radial loading

Abstract

Elastomers at elevated temperatures can undergo microstructural changes owing to the scission, re-coiling, and re-crosslinking in their macromolecular network. These result in chemically based stress relaxation and permanent set. In previous work, a constitutive equation was developed for the thermo-mechanical response of such elastomers that generalized the Tobolsky two-network theory and incorporated results from an experimental program. One experimental result was that the scission process appeared to be unaffected by stretch, to within moderate stretches. There are indications that larger deformations affect the scission process. The purpose of the present work is to modify the previously developed constitutive theory to allow for this. The constitutive theory contains material properties, representing the chemical kinetics of scission, re-coiling, and re-crosslinking, that are expressed in terms of activation energies. The premise considered here, motivated by the mechano-chemical discussion in the literature, is that an increasing deformation decreases the activation energy and results in faster chemical stress relaxation. A method for accounting for this is introduced. The resultant constitutive theory is then used in the simulation of the radial planar deformation of a planar annular sheet by tractions at its outer boundary. This particular geometry is chosen for two reasons: (1) its convenience for experimental study; (2) the stretch concentration near the inner circular boundary will cause faster chemically based stress relaxation there, which could be readily observable.