Rate dependent fracture of a double cantilever beam with combined bulk and interfacial dissipation

The energy required to fracture viscoelastic media is known to depend on the rate of crack propagation. In this work, crack propagation, driven by applied moments¸ in an idealized model of a viscoelastic double cantilever beam (DCB) is studied. Rate dependency is taken into account through a standard linear solid viscoelastic model for the bulk material, and an adhesive zone model describing bond rupture kinetics for the polymer chains which bridge the interface. Attractive van der Waals (vdW) forces are also taken into account within the adhesive zone. The apparent energy release rate consists of two parts: the energy to overcome adhesion on the interface as well as viscous dissipation in the bulk. The adhesive energy in rupturing polymer chains increases as crack propagation speed increases. Relaxation of the bulk material causes viscous dissipation as stored strain energy is lost. For a beam of fixed length this dissipation was found to be negligible at high and low rates of crack propagation. Between these two limits there is a critical crack propagation speed where viscous dissipation is maximized.