An elastic solution for adhesive stresses in multi-material cylindrical joints

The stress analysis of cylindrical adhesive joints is less frequently reported in the literature compared with that of flat geometries. Determination of shear and peel stresses in the adhesive layer is critical to the design of such multi-material joints. In this study, a theoretical framework is presented for the stress analysis of shaft-tube adhesive joints subjected to axial tensile loads. The axisymmetric assembly consists of similar or dissimilar isotropic or orthotropic adherends and a homogeneous adhesive layer. Adopting a generic stress function approach, stress fields are derived by enforcing the traction and traction-free boundary conditions as well as the stress continuity conditions at the interfaces. The principle of minimum complementary energy in conjunction with a variational method is used to obtain the governing differential equations in order to determine the stress-state in each of the constituents. Shear and peel stress distribution within the adhesive layer is presented to showcase the presence of stress concentration at the ends of the overlap. To verify the accuracy of the theoretical results, an identical axisymmetric finite element model is created and Finite Element (FE) analysis is performed. The stress fields obtained from the analytical model are in good agreement with the FE predictions. The influence of overlap length and stiffness mismatch between the adherends on peak adhesive stresses and their distribution are studied through a systematic parametric study. The findings of this study provides insight into the optimal design of multi-material adhesive joints.