Investigation of Through-Thickness Stresses in Composite Laminates Using Layerwise Theory

In this study, an analytical method is developed to exactly obtain the interlaminar stresses near the free edges of laminated composite plates under the bending moment based on the reduced form of elasticity displacement field for a long laminate. The analytical and numerical studies were performed based on the Reddy’s layerwise theory for the boundary layer stresses within cross-ply, symmetric, angle-ply, and general composite laminates. Finally, a variety of numerical results are presented for the interlaminar normal and shear stresses along the interfaces and through thickness of laminates near the free edges. The results showed high stress gradient of interlaminar normal and shear stresses near the edges of laminates. 1. Introduction Due to high specific strength and stiffness of fiber reinforced polymer composite, laminated composites have found augmented use in many industrial applications. In the boundary-layer regions, due to geometry and material discontinuities, the interlaminar stresses exhibit much higher values than those predicted by the classical lamination theory (CLT). These highly concentrated stresses cause delaminate failure in the laminates. However, no exact solution is found for elasticity equations because of inherent complexities involved in the problem of finding exact stress values in the edges. Hence, different analytical and numerical methods for finding the interlaminar stresses are used to describe the interlaminar stresses at the free edges of composite laminates. Complete literature surveys on this subject are available in review articles of Kant and Swaminathan [1] which obviously show the detailed path of development of methods. The first approximate analysis of interlaminar stresses was presented by Puppo and Evensen [2]. They studied interlaminar shear stresses in an idealized laminate consisting of orthotropic layers separated by isotropic shear layers with interlaminar normal stress being neglected through the laminate. Other approximate analytical methods utilized to examine the problem consist of the use of the higher-order plate theory by Pagano [3], the perturbation technique by Hsu and Herakovich [4], the boundary layer theory by Tang and Levy [5], and the approximate elasticity solutions by Pipes and Pagano [6]. An approximate theory is also employed by Pagano [7] based on the assumed inplane stresses and the use of Reissner’s variational principle. Wang and Choi [8] utilized Lekhnistskii’s stress potential and the theory of anisotropic elasticity for examining the free edge singularities. A variational