A micro-mechanically motivated model for the oxidative ageing of elastomers

Abstract

Oxidative ageing of elastomers is an irreversible process brought about by chemical reactions occurring within the molecular structure of a polymer network. Such reactions are facilitated by oxygen and are characterised by two competing reactions; chain scission and chain cross-linking. On the macro scale, the chain scission reaction can be observed in a stress softening of the material as the supporting polymer chains in the network are broken. In contrast, the chain cross-linking reaction increases the cross-link density to result in an overall stiffening of the material and the complex, deformation history permanent set effect. The scission and cross-linking reactions may not occur at the same rate, leading to an asymmetry in the degrees of stress softening, stiffening and of permanent set.

The link between the micro- and macro-scales for the description of oxidative ageing is the main focus of this dissertation. Several models exist in the literature for the modelling of oxidative ageing, but a micro-mechanical basis is missing and they instead rely on a phenomenological approach. Such phenomenological models can produce non-physical results and rely on simple exponential type equations for capturing the oxidative degradation of polymer networks. A micro-mechanical approach has the benefit of gaining deeper insight into the main drivers behind oxidative ageing and involve physically motivated material parameters.

Exploiting the statistical mechanical relationship between the shear modulus and the cross-link density, a network dynamics model capturing the oxidative ageing reactions is derived. A distinction is made between active cross-links that can support a load, and inactive cross-links which are unable to support a load. This results in a set of coupled non-linear differential equations describing the rate at which cross-links are created and destroyed. Using the two-network concept, a split of the polymer network is made into primary and secondary networks. Here the primary network is only permitted to decay and the secondary network is created stress-free with respect to the deformation at the time of creation. The mechanical model is based on the well-known micro-sphere model with modifications to include network dynamics.

Using the network dynamics model, a novel mapping procedure is introduced to capture the degradation state in terms of a dimensionless parameter. This mapping allows both the primary network to degrade and the continual decay of secondary networks to be captured. Capturing the permanent set effect is arguably the greatest challenge as the permanent set effect arises from the stress-free post-curing and the tension between different stress-free states inside the polymer network. Intermediate configurations are introduced continuously as cross-links are created in a given deformation frame. The pull-back operator allows convenient accumulation of these stresses in the reference configuration through an integral formulation. This allows very efficient computation of the secondary network stress and ensures the material model satisfies axioms of constitutive modelling.

Numerical tests and experiments were performed to showcase the strengths of the modelling approach including simple uniaxial tests and finite element simulations. A comparison of the proposed model with the state-of-the-art model demonstrates clear improvements in the modelling fidelity.