Snap-back instability of double cantilever beam with bridging

Adhesive bonding community shows a continued interest in using bridging mechanisms to toughen the interface of secondary bonded joints, especially in the case of laminated composites. Due to snap-back instability that occurs during fracture, confusions may exist when identifying the toughening effect experimentally. The true toughening effect may be overestimated by lumping all energy contributions (kinetic energy included) in an overall effective toughness. Here, fundamentals for bridging to enhance fracture resistance are explored through the theoretical analysis of the delamination of a composite double cantilever beam (DCB) with bridging. Specifically, we establish a theoretical framework on the basis of Timoshenko beam theory and linear elastic fracture mechanics to solve the fracture response of DCB in the presence of discrete bridging phases. We elucidate the crack trapping and the snap-back instability in structural response during the crack propagation. We identify the contribution to the overall toughness observed numerically/experimentally of both the physical fracture energy and other types of dissipation. The associated toughening mechanisms are then unveiled. Furthermore, we study the effects of property of the bridging phases on the snap-back instability, based on which, we propose a dimensionless quantity that can be deployed as an indicator of the intensity of snap-back instability. Finally, we identify the role of geometrical properties, i.e. the substrate thickness and the arrangement spacing of the bridging phases, in the snap-back instability and the macroscopic fracture toughness of a DCB. This work provides, from a theoretical point of view, an essential insight into the physics related to the structural response of DCB with discrete toughening elements.