Singularities near three-dimensional corners in composite laminates

Abstract

The high interlaminar stresses, which appear in laminated composites due to the boundary layer effect near the free edge, play an important role in the analysis and design of advanced structures. Moreover, they are also the dominant effect causing delamination. Even if the singular behavior of such structures is investigated in many works, most of them deal either with 2D, or with pseudo-3D problems, i.e. problems of two variables in a three-dimensional space. However, some numerical and experimental findings indicate that laminated plates exhibit a tendency to delaminate at corners, an effect impossible to be determined by a two-dimensional analysis. The aim of the present paper is to investigate stress singularities in a laminated composite wedge under consideration of real three-dimensional corner effects. A weak formulation, as well as a finite element approximation technique introduced in the past for isotropic problems is extended here to cover anisotropic material properties. This formulation leads to a quadratic eigenvalue problem, which is solved iteratively using the Arnoldi method. The first singular terms in the asymptotical expansion of the linear-elastic solution near the vertex of the wedge are obtained as eigenpairs of this eigenvalue problem. The order and mode of singularity are reported for all wedge angles and different fiber orientations for angle and cross-ply laminates. All calculations are based on a typical for some high modulus graphite-epoxy systems orthotropic material model.