Investigation of the free-edge stresses in composite laminates using three-dimensional hierarchic finite elements

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Abstract

Due to their exceptional mechanical and chemical properties, fibre reinforced polymer composites are used in a variety of industrial applications. The successive staking of unidirectional fibrous layers in combination with polymer matrix is used for the manufacturing of composites structures. The choice of fibre orientation in an individual layer or ply provides designers with enormous flexibility to tailor the material properties in the desired direction. On the other hand, discontinuity/mismatch in the material properties across these layers leading to very large inter-laminar stresses, especially on approaching the free edges. In literature ([3]), this is referred as free-edge or boundary-layer effect. The classical laminate theory cannot predict these stresses. Due to very low inter-laminar normal and shear strengths, the free-edge effect can lead to the initiation of delamination and subsequent failure of composite laminates. Therefore, accurate calculations of the inter-laminar stresses are essential for the optimum design of composite structures.This paper presents a hierarchic finite element-based computational framework for the efficient and accurate investigation of inter-laminar stresses and displacements in composite laminates of finite width subjected to a variety of loading scenarios. As compared to the standard finite elements, hierarchic finite elements allow to change the order of approximation locally or globally without changing the underlying finite element mesh leading to very accurate results for relatively coarse meshes [1]. In the case of hierarchic finite elements, high order shape functions are calculated from low order shape functions recursively and therefore maintain the continuity in the shape functions across the elements in the case of localised p-refinement. A variety of laminates including cross-ply [90/0]s, angle-ply [±45]s and quasi-isotropic [90/0/−45/45]s are considered as test cases. The effective or homogenised material properties for each layer are calculated using the computational homogenisation [5, 4, 6]. Tetrahedral elements are used for the discretisation of composite laminates. The problem domain is divided into several blocks and the computational framework allows to change the approximation order independently within each block. As compared to the rest of the problem domain, higher approximation order is used near the free edges. With increasing approximation order near the free edges, the computational framework is able to capture the complex profiles of inter-laminar stresses and displacements very accurately. Results are compared with reference results from the literature and found in a very good agreement. The computational model is implemented in the finite element software library Mesh-Oriented Finite Element Method (MOFEM) [2]. The computational framework has additional flexibly of high-performance computing and makes use of the state-of-the-art computational libraries including Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Mesh-Oriented datABase (MOAB).REFERENCES[1]M. Ainsworth and J. Coyle. Hierarchic finite element bases on unstructured tetrahedral meshes. International Journal for Numerical Methods in Engineering, 58(14):2103–2130, 2003.[2]Ł. Kaczmarczyk, Z. Ullah, K. Lewandowski, X. Meng, X. Y. Zhou, and C. J. Pearce. MoFEM (Mesh Oriented Finite Element Method): http://doi.org/10.5281/zenodo.438712, 2019.[3]C. Mittelstedt and W. Becker. Interlaminar stress concentrations in layered structures: Part I A selective literature survey on the free-edge effect since 1967. Journal of Composite Materials, 38(12):1037–1062, 2004.[4]Z. Ullah, Ł. Kaczmarczyk, S.A. Grammatikos, M.C. Evernden, and C.J. Pearce. Multi-scale computational homogenisation to predict the long-term durability of composite structures. Computers & Structures, 181:21–31, 2017.[5]Z. Ullah, Ł. Kaczmarczyk, and C.J. Pearce. Three-dimensional nonlinear micro/meso-mechanical response of the fibre-reinforced polymer composites. Composite Structures, 161:204–214, 2017.[6]Z. Ullah, X.-Y. Zhou, Ł. Kaczmarczyk, E. Archer, A. McIlhagger, and E. Harkin-Jones. A unified framework for the multi-scale computational homogenisation of 3D-textile composites. 
Original languageEnglish
Publication statusPublished - 22 Jun 2020
Event19th European Conference on Composite Materials - Nantes, France
Duration: 22 Jun 202026 Jun 2020

Conference

Conference19th European Conference on Composite Materials
CountryFrance
CityNantes
Period22/06/202026/06/2020

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    Ullah, Z. (2020). Investigation of the free-edge stresses in composite laminates using three-dimensional hierarchic finite elements. Paper presented at 19th European Conference on Composite Materials, Nantes, France.