Approximate Nonlinear Analysis Method for Debonding of Skin/Stringer Composite Assemblies Enzo Cosentino * Airbus UK, Ltd., Bristol, England BS99 7AR, United Kingdom and Paul M. Weaver † University of Bristol, Bristol, England BS8 1TR, United Kingdom DOI: 10.2514/1.31914 A nonlinear approach is developed and used to predict crack initiation in discretely assembled composite panels made from skin and stringers. Particular emphasis is given to stringer run outs within a stiffened panel for the optimization of novel composite wing configurations. The nonlinear structural behavior is obtained by means of the von Karman formulation for moderately large deflections in plates; three-dimensional assemblies are schematized and the effect of eccentricity is included in the simulation. Solutions are calculated by means of a Rayleigh–Ritz approach based on Galerkin’s orthogonal eigenfunctions, and a linear elastic fracture mechanics-based model is used to simulate the crack initiation in the critical regions. Numerical results obtained by means of the present method are validated against tests reported in the literature and compared with advanced nonlinear finite element analysis. Limits of applicability and further potential exploitations are discussed. A validation study showed fairly good correlation with reported experimental data. Nomenclature A, D = laminate in-plane and transverse stiffness matrices A 0 , D 0 = laminate in-plane and transverse compliance matrices A  = matrix of in-plane flexibility in partially inverted laminate constitutive equations a = crack length B = laminate coupling stiffness matrix B 0 = laminate coupling compliance matrix B  = coupling matrix in partially inverted laminate constitutive equations D  = matrix of reduced flexural stiffness matrices in partially inverted laminate constitutive equations e = neutral-plane function e i = generalized coordinates of the neutral-plane function l x , l y = length and width of panel N, M = stress, bending moment resultant vectors N x , N y , N xy = external in-plane load per unit width N x;o , N y;o , N xy;o = internal in-plane load per unit width U = internal elastic potential energy u, v = in-plane displacement in x and y directions w = out-of-plane displacement w i = generalized coordinates of the displacement function X, Y = beam eigenfunctions  i = panel eigenfunctions  N = potential of external in-plane loads  Q = potential of external transverse loads I. Introduction T HE use of cocured or cobonded structures (Fig. 1) in aerospace potentially offers significant weight reduction over conven- tional fasteners. Continuous fiber reinforced polymer matrix composites have been gaining wide acceptance as structural materials. Unfortunately, the vulnerability of such structures to through-thickness stresses is well known. This weakness is particularly exacerbated in critical areas such as the skin/stringer overlap in cocured or cobonded stiffened panels or thick sectioned run-out regions, for which the necessity to terminate stiffeners contrasts with the allowable strain requirements. Skin/stringer interface or run-out tips are vulnerable areas due to geometrical effects and mechanical load paths. Despite their high level of performance in specific areas, such as weight, durability, and through-life costs, composites are often used at relatively low strain levels in primary structures due, in part, to poor through-thickness failure characteristics. This has lead to relatively slow take up within primary flight structures. This delay is mostly due to a reduced understanding of the failure mechanisms and their behavior when damaged. The widespread lack of knowledge and know how often leads to oversized structures, which are in contrast to the lightweight philosophy characterizing new design solutions. In cocured skin/ stringer panels, failure often occurs due to delamination and/or debonding at the stiffener foot tip rather than to overall strain limitations. Other critical locations are the core (noodle) and the corner radius, as shown in Fig. 2 Several test programs have shown that the critical load condition that leads the noodle to failure is the out-of-plane load on the stiffener web [1] (Fig. 3a). Nevertheless, tip failure (Figs. 3b and 3c) is the most important failure mode, because it is related to several load conditions. Several studies [2–5] have shown that the onset of debonding may be caused by the differential stiffness at the interface between the skin and the cocured/cobonded surface. Skin deflection causes the onset of peeling moments and tractions that trigger the first and the second crack opening modes. Furthermore, stress concentration and free edge effect due to material anisotropy can exacerbate the failure Received 2 May 2007; revision received 5 October 2007; accepted for publication 19 November 2007. Copyright © 2007 by Enzo Cosentino and Paul Weaver. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/08 $10.00 in correspondence with the CCC. * Composite Stress Analysis, Composite Structures Development Centre; enzo.cosentino@airbus.com. † Reader, Advanced Composite Centre for Innovation and Science, Department of Aerospace Engineering, Queens Building 2.39, University Walk. Member AIAA. AIAA JOURNAL Vol. 46, No. 5, May 2008 1144