A Two-Dimensional Approach of Single-Lap Adhesive Bonded Joints

Abstract

A general two-dimensional (2D) theoretical approach capable of providing an explicit closed-form solution is developed for the calculation of elastic stresses in single-lap adhesive bonded joints, assuming linear distribution of a longitudinal normal stress in the joint thickness direction. By treating the adhesive layer in the same way as the adherends, the two-dimensional stress and strain distributions at any point, and the tensile force, shearing and bending moment at any cross section can be predicted accurately, in both the adhesive and adherends. This makes it possible for the subsequent failure analysis of the bonded joints to predict all the main modes such as adherend failure, cohesive failure and adhesive failure. The analysis is based on a two-dimensional elasticity theory that both includes the complete stress-strain and the complete strain-displacement relationships for the adhesive and adherends. Then, through the use of the displacement continuity conditions at the interfaces between the adhesive and adherends, four coupled, fifth-order ordinary differential equations with constant coefficients for the determination of the stresses are developed. The proposed method is capable of satisfying all the boundary stress conditions of the joint, including the stress-free surface condition at the ends of the bondline. The calibration of the new theoretical approach was verified by comparing it with the previously theoretical solutions, and the 2D geometrically nonlinear finite element models with the rotation and non-rotation boundary conditions. It is indicated that the present solution can provide a good prediction for the stress and strain distributions in the adhesive and adherends. A different approach is also established for determining bending moment factor of the short joints wherein the consideration of overall joint moment equilibrium is emphasized. It was shown that when the proposed bending moment factor is adopted instead of the original one, the classical solution by Goland and Reissner (1944) [4] might still remain applicable to the adherends and adhesive even with the parameter E3t1 /( E 1t3 ) > 0.1.