Stresses in Adhesively Bonded Joints: A Closed-Form Solution

Abstract

In this paper the general plane strain problem of adhesively bonded struc tures which consist of two different orthotropic adherends is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. Also, assuming that the thickness of the adhesive is small compared to that of the adherends, the thickness variation of the stresses in the adhesive layer is neglected. However, the transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into ac count. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stif fened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory and to give some idea about the validity of the plate assumption itself, a sample pro blem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. It is found that the plate theory used in the analysis not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results. The solution is ob tained by assuming linear stress-strain relations for the adhesive. In the Ap pendix the problem is formulated by using a nonlinear material for the adhesive and by following two different approaches.