On the Modeling of Chemical Stress Relaxation of Elastomers

Chemical stress relaxation occurs when elastomers are exposed to high temperature and/or certain chemical environments.  The degradation mechanism may be chain scission, additional cross-linking or a combination of both.  Tobolsky’s two-network hypothesis has been used widely to interpret the test results when additional cross-linking accompanies the chemical stress relaxation.

In the two-network hypothesis, the original cross-links form the first network, and the additional crosslinks occurring at the deformed states in high temperatures or chemical environments form the second network.  The natural state (or stress free state) of the second network is the deformed state.  In the past, it was difficult to use the two-network hypothesis to calculate the long-term sealing performance of aged elastomers because of the difficulty of calculating the deformation of the second network relative to the deformed state.

Recently the multiplicative decomposition of the deformation gradient F = F_e·F_i (where F_e is the elastic part and F_i is the inelastic part of the deformation gradient) was used to implement viscoelastic constitutive equations such as the Bergstrom-Boyce (BB) model, the multi-network model and the Parallel Rheological Framework model.  The F_e·F_i decomposition enables the calculation of the second network in the two-network hypothesis.  This paper presents how the BB model can be extended to model the two-network hypothesis.  Also presented is a comparison of experimental results and the two-network hypothesis of a nitrile butadiene rubber (NBR).