A novel approach to construct a thickness-independent bridging law for large scale bridging in type I delamination of composites

Large-scale fiber bridging plays a crucial role in enhancing the toughness of composite structures during delamination, typically analyzed through the R-curve and the bridging traction-separation law. These metrics, however, are influenced by the specimen's thickness, necessitating separate experimental evaluations for each thickness variation. Recent research indicates that this thickness-dependency originates from the varying bending stiffness across structures of different thicknesses. By incorporating the crack opening angle, a thickness-independent traction-separation and angle relationship was developed. Existing methods for establishing this relationship require embedding optical fibers to gauge the internal strain, complicating the experimental procedure. This study introduced an elastic restraint beam model to get analytical solution of the double cantilever beam (DCB) test, based on which the pre-crack tip opening displacement and deflection angle were derived. These equations, combined with the J-integral method, formed a thickness-independent bridging traction-separation and angle relationship. Experimental validation confirmed the thickness-independence of the derived bridging law. Furthermore, an iterative method was proposed to inversely calculate the R-curves and bridging traction-separation laws for any thickness based on data from a single thickness DCB experiment. Experiments on carbon fiber/epoxy resin and aramid fiber/epoxy resin composite laminates of varying thicknesses demonstrated the accuracy of the inversely deduced curves compared to direct measurements. The present method is based on an analytical model and requires only the measurement of load-displacement curves, avoiding the need to measure crack length and conduct multiple experiments with different thicknesses. This simplifies the experimental process and provides a powerful tool for characterizing the performance of composite material structures.