Bending analysis of a laminated composite patch considering the free-edge effect using a stress-based equivalent single-layer composite model

The interlaminar stresses of a laminated composite patch, which is made up of reinforcing fibers (carbon/graphite) and epoxy matrix are analyzed using a stress-based equivalent single-layer model under a bending load. The composite patch is frequently used as reinforcement for a metallic adherend of mechanical/aerospace structures (i.e., aluminum alloy, etc) by attaching the film- or paste-type adhesive (i.e., epoxy, BMI, etc). To calculate the adhesive stresses transferred from the substrate, an interlayer model is introduced. The adhesive stresses are obtained by solving the equilibrium equations. The stress fields of the patch are determined by assuming certain stress functions. To satisfy the equilibrium state of the patch, the stress functions are divided into homogeneous and particular parts. The adhesive stresses act as prescribed stress boundary conditions of the laminated composite patch. The stress functions are substituted into a complementary virtual work principle, and from this, two coupled ordinary differential equations are obtained. General eigenvalue problems are derived to solve the coupled governing equations. To demonstrate the validity and efficiency of the proposed method, cross-ply, angle-ply and quasi-isotropic laminated composite patches are studied. From the observations made, the authors found that the stress function-based approach is suitable for solving the stress prescribed boundary value problem with accuracy and efficiency compared to a displacement-based approach such as the finite element method. The proposed method can be used as an efficient tool in the initial design stage of structural components when it is necessary to consider the free-edge effect.