Finite Element Analysis (FEA) of multilayer structures using plates and shells is not able to quantify the singular stresses distribution, especially the local overstresses near the boundaries. This critical design parameter is taken into account by 3D FEA models, which are not used for systematic computations due to a very long calculation time. The software CLEOPS (Composites Local Effects Of Plates and Shells) is developed by MEDYSYS (MEchanics and DYnamics of SYStems) to address this problem for composite laminates and their bonded assemblies involved in aerospace or defense industry. It is used as a post-processor of Finite Element computations on plates and shells to calculate the 3D stresses within multilayer structures subjected to mechanical plane or bending loadings. The edge effects are computed at the mesoscale based on a semi-analytical asymptotic method with one-dimensional finite elements in the through-thickness direction. The software includes quadratic failure criteria in order to evaluate the delamination initiation and anticipate whether the laminates can withstand a fatigue load. The calculation of the stresses distribution near the edges of multilayer structures and the fatigue delamination are key issues developed in this article. Results provided by CLEOPS are compared to 3D FEA results.
composite, bonded assembly, edge effects, CLEOPS, delamination, FEA model
Brewer J.C., Lagace P.A. (1988). Quadratic stress criterion for initiation of delamination. Journal of Composite Materials, vol. 22, p. 1141-55.
Carrere N., Vandellos T., Martin E. (2009). Multilevel analysis of delamination initiated near the edges of composite structures, Proceedings of the 17th International Conference on Composite Materials (ICCM-17), Edinburgh.
Dumontet H. (1985). Boundary layers stresses in elastic composites. Studies in Applied Mechanics, vol. 12, p. 215-32.
Engrand D. (1981). A boundary layer approach to the calculation of transverse stresses along the free edges of a symmetric laminated plate of arbitrary width under in-plane loading. Ed. I.H. Marshall, Appl. Sc. Publishers, p. 247-61.
Engrand D. (1985). Local effects calculations in composite plates by a boundary layer method. Studies in Applied Mechanics, vol. 12, p. 199-214.
Esquej R., Castejon L., Lizaranzu M., Carrera M., Miravete A., Miralbes R. (2013). A new finite element approach applied to the free edge effect on composite materials. Composite Structures, vol. 98, p. 121-29.
Friedrichs K.O., Dressler R.F. (1961). A boundary layer theory for elastic plates. Communications on Pure and Applied Mathematics, vol. 14, p. 1-33.
Horvay G. (1953). The end problem of rectangular strips. Journal of Applied Mechanics, vol. 75, p. 87-94.
Lagunegrand L., Lorriot T., Harry R., Wargnier H., Quenisset J.M. (2006). Initiation of free-edge delamination in composite laminates. Composites Science and Technology, vol. 66, p. 1315-27.
Lécuyer F. (1991). Etudes des effets de bord dans les structures minces multicouches. Thèse de l’Université Pierre et Marie Curie, Paris 6.
Leguillon D., Marion G., Harry R., Lécuyer F. (2001). The onset of delamination at stress-free edges in angle-ply laminates - Analysis of two criteria. Composites Science and Technology, vol. 61, p. 377-82.
Lessard L.B., Schmidt A.S., Shokrieh M.M. (1996). Three-dimensional stress analysis of free-edge effects in a simple composite cross-ply laminate. International Journal of Solids and Structures, vol. 33, p. 2243-59.
Marion G. (2000). Etude expérimentale et théorique de l’amorçage du délaminage au bord de matériaux composites stratifiés. Thèse de l’Université Bordeaux 1.
Mittelstedt C., Becker W. (2007). Free-edge effects in composite laminates. Applied Mechanics Reviews, vol. 60, p. 217-45.
Nguyen V.T., Caron J.F. (2009). Finite element analysis of free-edge stresses in composite laminates under mechanical and thermal loading. Composites Science and Technology, vol. 69, p. 40-9.
Pécastaings F. (1985). On a method to evaluate edge effects in elastic plates. Studies in Applied Mechanics, vol. 12, p. 101-126.
Perret L., Lécuyer F., Allix O., Engrand D. (1991). Perforated composite plates - Effects of the curvature on three dimensional stress distributions around holes - Comparison between two different methods, Proceedings of the 7th International Conference on Composite Materials (ICCM-7), Honolulu.
Tang S. (1975). A boundary layer theory - Part I: Laminated composites in plane stress. Journal of Composite Materials, vol. 9, p. 33-41.
Weiss A. (2010). Comportement en fatigue des zones de reprises de plis. Thèse de l’Université de Toulouse.
Zhang C., Binienda W.K. (2014). A meso-scale finite element model for simulating free-edge effect in carbon/epoxy textile composite. Mechanics of Materials, vol. 76, p. 1-19.