An adhesive zone model for polymeric interfaces

In this work we develop an adhesive zone model for polymeric interfaces, which describes the kinetics of dissociation and association of polymer chains bridging the interface. Compared with previous works on interfacial bond rupture, our adhesive zone model includes two novel features: possibility of bond reforming and a highly nonlinear force–extension relationship for the polymer chain motivated by previous experimental measurements. The absence of these two features was demonstrated in an earlier work to cause unphysical crack propagation under zero load as well as overextension of the chains beyond their full contour length. Using the rate dependent crack propagation in a double cantilever beam, which may be elastic or viscoelastic, as an example, the new adhesive zone model is shown to correct the unphysical results obtained earlier. Specifically, it leads to a significantly increased adhesive fracture energy, i.e., the energy per unit area required to rupture the chains on the interface, for slow crack propagation, owing to the ability to achieve a dynamic equilibrium of bond dissociation and association. Furthermore, the nonlinear chain model predicts a near-catastrophic decrease in chain density as the finite extensibility limit is approached. This results in an adhesive fracture energy which is orders of magnitude smaller than that predicted by the linear chain model for fast crack propagation. Although the adhesive zone model has only been applied to a double cantilever beam in this work, it is a generic model for polymeric interface, and can be implemented in finite element models to simulate fracture in bulk polymers in general.