Phase-Field Modeling of Strain-Induced Crystallization of Elastomer

Natural rubber and more generally elastomer present a unique physical property that is very important for many engineering applications: strain-induced crystallization. Indeed, the formation of crystallites in a polymer network induces a strengthening of this material under strain. The dynamic of crystallization of natural rubber (NR) is the key to fully understand the mechanical response of the system under strain. Numerous attempts to develop a model able to describe the strain-induced crystallization of polymer networks have been made (Flory’s model, the phantom network model …), but these models are usually based on static considerations. Nevertheless, these models introduce important physical concepts of polymer networks. In this study we develop a new physical approach (a Phase-field model) for crystal growth under strain taking into account interface energies and the coupling between the thermodynamics of crystallization and the local stress. The challenge is to model the dynamics of the strain-induced crystallization of elastomer in particular in natural rubber. The main idea of this approach is to use a local thermodynamic potential to describe the coexisting phases and their interfaces, and to add the local stress contribution to this functional. Dynamic equations are obtained based on conservation considerations. The resulting model is solved numerically to predict the morphology of the crystallites.

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