Linear coupled bending and extension of an unbalanced bonded repair

An unbalanced repair is a composite patch bonded to one side of a cracked structure for the purpose of preventing or reducing damage growth in the substrate. A single-sided repair offsets the load path within the structure, inducing out-ofplane bending. This bending increases the stress intensity in the underlying crack and causes adhesive peel stresses and bending of the repair which can, relative to a repair that is restrained against bending, lead to early failure. In this article the authors correct the analysis of Wang and Rose [Wang, C.H., Rose, L.R.F., 1997. On the design of bonded patches for one-sided repair. In: Proceedings of the 11th International Conference on Composite materials, Gold Coast, Australia, vol. 5, pp. 347–356] developed by using an energy analysis of a single-sided or unbalanced repair applied to a very long-crack, to comply with Maxwell’s reciprocal theorem and to account for transverse normal and shear stresses at the crack tip and the accompanying shear deflections. The authors then develop closed-form equations useful for bonded composite repair design and damage tolerance assessment of cracks of arbitrary length by developing a new method for interpolation between this long-crack limit and a short-crack limit based on the stress intensity and crack face displacements for an unreinforced crack. The interpolation method is then tested against an advanced line-spring model that has been created by using a 6th order generalized plane strain plate formulation in extension and a new 8th order formulation in bending, thus allowing for the inclusion of transverse shear and normal stresses. The closed-form equations are found to be accurate when compared to the line-spring model, and to provide reasonable results when compared to a three-dimensional finite element model of a bonded repair. Inaccuracies are shown to exist principally in the determination of the nominal stresses in the vicinity of the crack.