  This paper presents a physics-based constitutive equation to predict the
thermo-chemical aging in elastomers. High-temperature oxidation in elastomers
is a complex phenomenon. The macromolecular network of elastomers'
microstructures undergoes chain scission and crosslinking under high
temperature and oxygen diffusion conditions. In this work, we modify the
network stiffness and the chain extensibility in the Arruda-Boyce well-known
eight-chain constitutive equation to incorporate the additional Helmholtz free
energy due to network changes in elastomers' microstructures. The effect of
network evolution due to aging in changing the shear modulus and the number of
chain monomers is considered. The modification is based on chemical
characterization tests, namely the equilibrium swelling experiment to measure
the crosslink density evolution. The developed constitutive equation predicts
the mechanical responses of thermo-chemically aged elastomers independent of
any mechanical tests on aged samples. The proposed constitutive equation is
validated with respect to a comprehensive set of experimental data available in
the literature that were designed to capture thermo-chemical aging effects in
elastomers. The comparison showed that the constitutive equation can accurately
predict the intermittent tensile tests based on crosslink density evolution
input. The developed constitutive equation is physics-based, simple, and
includes minimal material parameters.
