Bridging effects for through-thickness reinforced laminates

The delamination growth resistance of laminates can be enhanced through bridging effects. Despite the potential to deliver improved mechanical performance, there are very few works that investigate bridging effects analytically, which could be used to facilitate the design and assessment of laminates. In this work, a novel analytical model is developed to assess the crack driving force (energy release rate, or J-integral) of a mode-I crack for z-pin-reinforced laminates using the double cantilever beam (DCB) configuration. To study bridging effects, a J-integral reduction factor and force enhancement are defined based on the developed model. Two critical conditions are established for the crack driving force being zero, namely, the crack’s complete closure, and zero crack-tip force balance. The analytical solutions are studied and validated for the cases of single-pinned and multiple-pinned DCB, showing excellent agreement with both numerical simulations and experiments. The developed theory can also be employed to study other types of through-thickness reinforcement and is readily applicable for assessment and design of laminate structures to improve their delamination growth resistance and fracture behavior.