Method for calculating the interlaminar stresses in symmetric laminates containing a circular hole

Abstract

An efficient approximate solution for three-dimensional stress distributions around a circular hole in symmetric laminates under a set of far-field in-plane stresses is presented. Stress functions for each ply are assumed according to the boundary-layer equilibrium equations. In addition, all the boundary conditions for each ply and traction continuity at the ply interface are exactly satisfied. Eventually, the unknown parameters in stress functions are determined by the minimization of complementary energy of the whole laminate. Numerical examples are presented in comparison with given literature which shows that the present method is efficient. I. Introduction D UE to stiffness discontinuity between plies, it is easy to cause interlaminar stress concentrations near the freeedge region in composite laminates. Such stresses will commence delamination, matrix crackings, and failure of laminates, especially under fatigue loading. Since 1970, numerous investigations15 have used various methods to determine the interlaminar stresses at the straight free edge of composite laminates. Pipes and Pagano1 adopted the anisotropic elasticity theory in conjunction with the finite difference method to analyze a simple four-ply laminate. Wang and Crossman2 used a finite element approach to investigate this same problem. Wang and Choi3'4 derived an analytical solution based on Lekhnitskii's stress potentials and the theory of anisotropic elasticity to determine the exact order of stress singularity at the free edges of laminate. In an effort to develop an efficient method to deal with thick laminates (say 100 plies), Kassapoglou and Lagace5 used the force balance method in conjunction with the principle of minimum complementary energy to obtain an analytical solution for interlaminar stresses at straight free edges. Owing to the complicated geometry for the curved free edges as compared with the straight free edges, little work has been done for composite laminates with curved free edges. Basically, the analysis of straight free edge may be assumed as a problem with two-dimensional stress and strain variations. However, the curved free edge is a typical three-dimensional problem. This difference has rendered the analysis for the curved free edge more difficult than the straight free edge. A boundary-layer theory based on the perturbation technique for isotropic elastic plates with a circular hole developed by Reiss6 has been extended to composite laminates by Tang.7-8 This approach is based on identifying the boundary-layer problem as two equivalent problems, namely, a modified torsion problem and a modified plane strain problem. However, Tang's solution can only satisfy part of boundary conditions in an average sense, which may result in unreliable stress results near the free edges.9 In addition, Tang's solution will be very tedious for laminates with numerous plies. Zhang and Ueng10 proposed a simplified method to investigate the effect of the ratio of hole radius to laminate thickness on the interlaminar stress distributions around a hole in a (0/90 deg)s laminate under far-field tensile or shear stress; however, it is assumed that the order of stress singularity is prescribed and