Mode-I debonding of a double cantilever beam: A comparison between cohesive crack modeling and Finite Fracture Mechanics

In this paper we focus on the prediction of mode-I debonding for a double cantilever beam (DCB). Among the various modeling approaches available, the Cohesive Crack Model (CCM) and Finite Fracture Mechanics (FFM) are selected for the analytical investigation, due to their ability to reconcile the stress- and energy-based approaches. The specimen is considered as an assemblage of two identical beams partly bonded together by an initially elastic interface. After the elastic stage, according to the CCM approach, it is assumed that, ahead of the physical crack tip, there exists a cohesive zone where the interface behavior is described by a stress-separation law. The interfacial stresses and length of the process zone are determined in closed form, along with the global load-displacement response. The method is first compared to the simple beam theory (SBT) and the enhanced beam theory (EBT) approaches, which are found to provide larger values of the debonding load; the difference between predictions of CCM and SBT/EBT is more pronounced for less brittle interfaces, i.e. for larger process zones. Then the analytical solution obtained by means of FFM is presented, which, despite being simply based on the elastic foundation model, closely matches the CCM results. Finally a numerical solution is achieved by a finite element analysis where generalized zero-thickness contact interface elements are adopted. An excellent agreement with these results confirms the good performance of the proposed CCM and FFM approaches.