Physics and chemistry-based phase-field constitutive framework for thermo-chemically aged elastomer

We propose a physics and chemistry-based constitutive framework to predict the stress and brittle failure responses of thermo-chemically aged elastomers. High-temperature aging in the presence of oxygen causes chemical reactions inducing significant changes in the elastomer macromolecular network. Experimental studies agree that the increase in effective chemical crosslinks is dominant, leading to increased material stiffness and ultimately causing brittle failure of aged elastomers. The main novelty of this work relies on directly connecting the evolution of the effective crosslink density to the mechanical properties which control stress and failure response of thermo-chemically aged elastomers. We equip the Arruda-Boyce hyperelastic constitutive equations to predict the stress-strain response until failure with phase-field to capture the induced brittle failure via a strain-based criterion for fracture. Four material properties associated with the stress and failure responses evolve to capture the detrimental effects of thermo-chemical aging. The evolution of the four material properties is characterized by the change in the effective crosslink density, obtained based on chemical characterization tests, for any given aging temperature and duration. The established constitutive framework is first solved analytically for the case of uniaxial tension in a homogeneous bar to highlight the interconnection between the four material properties. Then, the framework is numerically implemented within a finite element (FE) context via a user-element subroutine (UEL) in the commercial FE software Abaqus. The framework is validated versus a set of experimental results available in the literature. The comparison confirms that the proposed constitutive framework can accurately predict the stress-strain and failure responses of thermochemically aged elastomers. Further numerical examples are provided to demonstrate the effects of evolving material properties on the response of specimens containing pre-existing cracks exploiting the capabilities of the phase-field approach.