Scaling of fracture energy in tensile debonding of viscoelastic films

The work done to separate viscoelastic adherends is often dominated by energy dissipation due to the bulk deformation that accompanies the intrinsic processes of interfacial separation. The inter-relationship between bulk and interfacial deformation processes is studied here by analyzing a one-dimensional model for steady-state crack propagation between a rigid substrate and a thin viscoelastic film when the latter is subjected to tensile loading and the former is fixed. The viscoelastic layer is represented by a standard linear solid and is connected to the rigid substrate via a Dugdale cohesive zone model. The principal result of the analysis is a prediction for the dependence of the total work of fracture on the rate of loading. A threshold crack-tip velocity that governs the onset of dissipation is determined as a function of the film thickness and the interfacial and viscoelastic parameters of the film. Based on the ratio of the crack-tip velocity to the threshold velocity, three velocity regimes are identified where the energy dissipation is low, high, or intermediate. These correspond, respectively, to the overlap of the cohesive zone with the film material that is completely relaxed, is completely unrelaxed, or is in the process of relaxation. An approximate solution for the scaling of fracture energy in these three regimes has been presented. Finally, the relevance of these results to a two-dimensional problem is discussed.