Analytical comparison between cohesive crack modeling and finite fracture mechanics for mode-I loading conditions

In a context where adhesively bonded joints are increasingly used in many fields of engineering and applied science, prediction of interfacial failure mechanisms is an important issue to be treated theoretically and/or numerically. This work focuses on the prediction of mode-I debonding for a double cantilever beam (DCB). The specimen is considered as an assemblage of two sublaminates partly bonded together by an elastic interface with a continuous distribution of elastic springs acting along the normal direction. This generalizes the original idea suggested by [1]. Among the various modeling approaches, Cohesive Crack Modeling (CCM) and Finite Fracture Mechanics (FFM) are herein selected for the analytical investigation, due to their ability to join the stress- and energy-based approaches, as introduced in the literature by [2,3] among others. Based on a cohesive interface approach [4,5], it is assumed that, ahead of the physical crack tip, there exists a cohesive zone held by a cohesive traction separation law with linear softening. The local interfacial stresses and global load-displacement curves are determined in closed form considering the possible occurrence of structural instabilities. Furthermore, the length of the process zone (i.e. the zone where the energy is dissipated), and the ultimate load are derived both analytically and numerically. For numerical applications, linear finite elements are adopted, where a DCB interface is discretized with zero-thickness generalized contact elements. A good agreement is found between predictions from FFM and CCM as well as between analytical and numerical results. A final parametric investigation on the structural response of the DCB is performed for varying geometry and material properties, both in terms of debonding load, elastic stiffness and global load-displacement curve.