# Delamination Effect on the Buckling Behaviour of Carbon-Epoxy Composite Typical Aeronautical Panels
## 1 Introduction  
Composite materials have been extensively used for decades for the production of both secondary and primary aircraft components. Nevertheless, there is still the need to study their damage behaviour because the weaknesses associated with composite materials continue to constrain their use, also limiting the benefits that could be gained from increasingly widespread application of these innovative materials [1; 2]. The scientific community is now well aware that one of the main weaknesses of composite materials comes from impact damage with foreign objects [3; 4; 5]. High-velocity impacts do not represent the real criticality, since, although very dangerous, they cause clearly visible and catastrophic damage [6; 7]. Low-velocity impacts, on the other hand, are extremely critical as they trigger non-visible surface damages, in particular delamination and matrix breakage [8; 9; 10]. In fact, low-velocity impacts have proven to be one of the primary causes of delamination in aircraft structures, which results in catastrophic damage, since their propagation significantly reduces the strength of the material, thus not allowing the structure's operating loads to be sustained. A significant background of the literature is present on delamination due to low-velocity impacts. For example, interlaminar and intralaminar damages due to low-velocity impact have been studied in [11] both experimentally and numerically. Different models have been investigated by varying the interlayer with cohesive contacts to assess the delaminated area for each interface. In [12], a methodology to predict impact-induced delamination was proposed. The work in [13] studied the interaction between matrix failure and delamination in carbon/epoxy laminates subjected to low-velocity impact. In [14], a review of the low-velocity impact responses of composite materials is presented. From the perspective of damage tolerance design, the study of damage propagation has become of primary importance. Particularly in the early design stages of aircraft structures,an appropriate compromise between geometric dimensions, weight and operational loads is essential. The use of numerical analyses becomes fundamental in this context, allowing a first design solution and thus reducing the excessive costs of the manufacturing and testing of demonstration structures [15; 16]. Many authors have performed numerical sensitivity analyses on composite components, considering the variation in various parameters, both with regard to geometry and loads. In [17], a composite tapered beam made of a glass/epoxy material system was analysed for the sensitivity of interlaminar normal stress and total strain energy release rate at the free edge, due to variations in taper angle and layer angle. The tapered beam was analysed in terms of both tension and bending. In [18], the effects of different sizes, shapes and positions of delamination and the stacking sequence of the sublaminate on the buckling load were studied. A sensitivity analysis to highlight the influence of the position and propagation of delaminations on the compressive behaviour of composite panels was carried out in [19]. Comparisons against experimental data available in the literature were performed to prove the effectiveness of the considered numerical techniques. In [20], the influence of interface ply orientation on delamination evolution was analysed in double cantilever beam and mixed-mode bending specimens both experimentally and numerically. In this manuscript, a typical stiffened aeronautical panel with embedded circular delamination, representing a typical low-velocity impact damage, was numerically examined. Specifically, the influence of delamination size and depth on the buckling behaviour of the structure was assessed. Indeed, composite aircraft components are typically relatively thin; hence, buckling instability can occur prior to the desired failure load when the structure is loaded under compression, particularly in the presence of damages or manufacturing flaws.