A Pressurized Spherical Elastomeric Membrane Undergoing Temperature Induced Scission and Crosslinking

Abstract

When an elastomeric material is held at a fixed state of stretch at a sufficiently high temperature, macromolecular network junctions undergo time-dependent scission and the applied force relaxes with time. The affected molecules recoil and crosslink to form a new network that is stress-free in a new reference configuration. A constitutive equation that accounts for this process as the elastomer undergoes a time-dependent deformation has been presented elsewhere. This constitutive equation is used to study the response of a pressurized spherical elastomeric membrane at a temperature high enough for the scission-crosslinking process to occur. It is shown that the membrane diameter increases with time. Moreover, there can be a finite time when the membrane diameter increases at an infinite rate, i.e. there is “runaway inflation”. This event depends on the elastic properties of the molecular networks, the rate of scission, the rate of formation of new networks, and the history of the increase in the membrane diameter. Numerical results are presented that illustrate these phenomena.