Accurate determination of stress distributions in adhesively bonded homogeneous and heterogeneous double-lap joints

In this paper, within the displacement field of the full layerwise theory (FLWT), an analytical method is developed for stress analysis of symmetric adhesively bonded homogeneous and heterogeneous double-lap joints (DLJs). The joints with fixed-free end conditions subjected to uniaxial tension and bending moment are considered to investigate stress distributions at the adhesive bond-line. Moreover, the effects of inhomogeneity of the adherends on distributions of interfacial peel and shear stresses along the length and through the thickness of the bonding regions are studied. The joints are divided into a large number of mathematical sub-layers through the thickness in order to obtain accurate results from the layerwise theory. Furthermore, each joint is divided into three regions along the length. The governing equations of equilibrium for each region are obtained using the principle of minimum total potential energy. The interlaminar stresses are obtained along the length of the two bonding interfaces and the mid-surface of the adhesive layer as well as through the adhesive thickness to investigate how they change through the adhesive length and thickness and particularly near the end-points. It is found that the present theory can predict accurately the stresses in the interior and near the ends of adhesive layer, where the stress fields can be significantly influenced by the edge effects. The results presented in this paper can be introduced as the benchmark solutions to evaluate the credibility of other solutions.

► Interfacial stresses in double-lap joints are determined using the full layerwise theory.
► Actual nonlinear through-thickness variations of stresses in adhesive are obtained.
► Edge effects, inhomogeneity of adherends, and different loadings are investigated.
► Convergence study is provided, and it is shown that the results converge very fast.
► Great agreement exists except near the edges, where the stress singularity exists.