Influence of thermally induced scission and crosslinking on the post-scission inflation of circular elastomeric membranes

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T_cr (near 100 °C for natural rubber), macromolecular chains and crosslinks undergo scission, recoiling and re-crosslinking. The process depends on time and temperature and 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 constitutive theory that accounts for these changes in macromolecular structure is used to simulate an experiment involving the inflation of an initially flat circular membrane. The membrane is initially at a temperature T < T_cr. A prescribed volume of fluid inflates the membrane to a surface of revolution. The temperature of the fluid and membrane is increased above T_cr for some period of time. Attention is restricted to the case when scission is independent of the deformation of the membrane. It is shown that the time dependence of the pressure in the inflating fluid must satisfy a specific relation involving a time dependent property measured during scission under uniaxial extension. This result provides a useful experimental means for determining when scission is independent of deformation in biaxial deformations.The temperature is returned to its original value and the pressure is gradually removed. It is shown that compressive stresses may develop as the pressure is reduced. If the membrane is removed from its support, it will have developed a permanently curved shape. Results of a numerical simulation are presented that compares the initial inflated shape to the permanently curved shape.