Contact stresses in adhesive joints due to differential thermal expansion with the adherends

The contact stresses in a bonded joint due to differential thermal expansions are calculated by considering the adhesive as an elastic rectangle confined by plates representing the adherends. The interface is cohesive in type, so that the contact area is a perfectly adherent region surrounded by cohesive areas where slip occurs at constant shear-stress. The problem is formulated in terms of Papkovich-Fadle eigenfunctions, which satisfy the boundary conditions on the stress free edges. The resulting integral equations are solved with the Jacobi integration formula. The size of the cohesive zone, which is determined by imposing the finiteness of the contact stresses at the frontier with the bonded region, depends upon the length and height of the joint. In very long joints the result tends to the technical rule of thumb traditionally employed to design such joints, but for intermediate lengths the elastic solution is quite different.