An high order Mixed Interpolation Tensorial Components (MITC) shell element approach for modeling the buckling behavior of delaminated composites Marco Gaiotti a , Cesare M. Rizzo a,⇑ , Kim Branner b , Peter Berring b a Università degli Studi di Genova, Scuola Politecnica – DITEN, Via Montallegro 1, Genova, Italy b Technical University of Denmark, Department of Wind Energy, Frederiksborgvej 399, Roskilde, Denmark article info Article history: Available online 15 October 2013 Keywords: Composites Buckling Tests FEM modeling Delamination abstract This paper describes the experimental and numerical studies carried out on delaminated fiberglass epoxy resin laminates made-up by different fabrication methods, namely by vacuum infusion and prepreg. While the tested specimens were originally intended for the assessment of buckling behavior of compos- ite laminates of wind turbine blades, results were found valuable for the marine industry as well, because similar laminates are used for the hull shell and stiffeners. Systematic calculations were carried out to assess the effects of an embedded delamination on the buckling load, varying the size and through thick- ness position of the delamination. Different finite element modeling strategies were considered and val- idated against the experimental results. The one applying the 9 nodes MITC shell elements was found matching the experimental data despite failure modes were different for the two fabrication methods. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Delaminations in multilayered laminates: overview The marine industry has been applying fiber reinforced plastics for decades, particularly in the field of small recreational boats. However, fiber reinforced plastics are now used in larger and larger structures such as airplanes, wind turbine blades as well as marine structures, such as mine-hunters. For wind turbine blades and air- plane structures fiber reinforced plastics is considered to provide light, slender and sufficiently robust structures, able to reduce the total structural weight while being cost effective at the same time. For mine-hunters fiber reinforced plastics is considered as large displacements are allowed before failure enhancing the blast loads resistance of the structure and low signature is achieved. In a multilayered composite laminate, the delamination can be defined as an area which lack bonding between two adjacent lay- ers: previous works, like e.g. [1], established that due to marine environmental loads composite ships’ structures are prone to delamination because of the limited inter-laminar shear strength of these materials. Also, delamination may originate from impact loads such as slamming, whose amplitude may give rise to high peaks of local stresses as shown e.g. in [2], but stress concentrations in way of structural discontinuities and stress con- dition along free edges may cause delaminations too. Delaminations may also be generated in the composite fabrica- tion process due to lack of impregnability of the fibers, or to ther- mal and chemical shrinkage of composite components during the matrix polymerization [3]. As reported by several authors [4,5], delamination is usually the most critical type of damage that composite and sandwich struc- tures experience under compressive loads. Two stochastic models for the distribution of delaminations in wind turbine blades are analyzed in [6]. The reliability is estimated for a generic wind turbine blade model both with and without del- aminations. It is found that the probability of failure for this partic- ular blade and analysis assumptions increases 5-11 times when delaminations are included. When a delaminated panel is under compression, depending on delamination size and position, different behaviors can be ob- served. When the critical load limit is reached, the panel starts buckling and may show two possible conditions: the global mode buckling, where the sub-laminates on both sides of the delamina- tion move towards the same side, and the local buckling where the sub laminates move towards opposite directions as shown in Fig. 1. In [5,7] it is observed that the bending moment introduced in the laminate due to elastic instability after reaching the critical buckling load results in a reduced failure load. A large amount of numerical and experimental work has al- ready been carried out to determine the ultimate strength of dela- minated panels; in particular remarkable analyses are reported in 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.10.003 ⇑ Corresponding author. Address: Via Montallegro 1, I-16145 Genova, Italy. Tel.: +39 010 353 2272; fax: +39 010 353 2127. E-mail addresses: marco.gaiotti@unige.com (M. Gaiotti), cesare.rizzo@unige.it (C.M. Rizzo), kibr@dtu.dk (K. Branner), pber@dtu.dk (P. Berring). Composite Structures 108 (2014) 657–666 Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct