Crack bridging by through-thickness reinforcement in delaminating curved structures

Abstract

The problem of how through-thickness reinforcement opposes the opening of delamination cracks in curved laminar structures is examined theoretically. Finite element calculations have been performed to show how the through-thickness reinforcement modifies the energy release rate of a delamination crack. Solutions are found for perfectly bonded and debonded cases. Energy conservation arguments are then used to define constitutive laws for equivalent continuous bridging springs acting on the delamination fracture surfaces. This step allows the immediate application of useful concepts from the literature on bridged cracks. Results are summarized for convenient use and trends are highlighted by relating the exact numerical results to analytical approximations for the perfectly bonded and debonded cases. Through-thickness reinforcement will be effective at modest volume fractions, provided the spacing of the discrete reinforcing elements is not much greater than the laminate thickness, in which case buckling between successive reinforcements facilitates delamination. With this provision, the present results confirm that simplistic linear constitutive laws used for bridging line springs in prior work are fairly accurate for most feasible values of geometrical and material parameters; and a minor amendment to the prior work, which is provided in analytic form, will lead to conservative design rules.