Special 2-D and 3-D Geometrically Nonlinear Finite Elements for Analysis of Adhesively Bonded Joints

Abstract

Finite element models have been successfully used to analyze adhesive bonds in actual structures, but this takes a considerable amount of time and a high computational cost. The objective of this study is to develop a simple and cost-effective finite element model for adhesively bonded joints which could be used in industry. Stress and durability analyses of crack patch geometries are possible applications of this finite element model. For example, the lifetime of aging aircraft can be economically extended by the application of patches bonded over the flaws located in the wings or the fuselage.

Special two and three- dimensional adhesive elements have been developed for stress and displacement analyses in adhesively bonded joints. Both the 2-D and 3-D elements are used to model the whole adhesive system: adherends and adhesive layer. In the 2-D elements, adherends are represented by Bernoulli beam elements with axial deformation and the adhesive layer by plane stress or plane strain elements. The nodes of the plane stress-strain elements that lie in the adherend-adhesive interface are rigidly linked with the nodes of the beam elements. The 3-D elements consist of shell elements that represent the adherends and solid brick elements to model the adhesive. This technique results in smaller models with faster convergence than ordinary finite element models. The resulting mesh can represent arbitrary geometries of the adhesive layer and include cracks. Since large displacements are often observed in adhesively bonded joints, geometric nonlinearity is modeled.

2-D and 3-D stress analyses of single lap joints are presented. Important 3-D effects can be appreciated. Fracture mechanics parameters are computed for both cases. A stress analysis of a crack patch geometry is presented. A numerical simulation of the debonding of the patch is also included.