Non-linear adhesive bonded joint design analyses

Abstract

The general plane strain problem of adhesively bonded structures which consist of two different adherends is considered. The adhesive joint is modelled as an adherend-adhesive sandwich allowing the application of any combination of tensile, shear and moment loading at the adherend ends. The adherends are assumed to behave as linearly elastic cylindrically bent plates with the adhesive forming a non-linear interlayer between them. The deformation theory of plasticity is used to model the stress-strain characteristics of the adhesive, with the stress-strain curve itself being approximated by any continuous mathematical function. In this case both a Ramberg-Osgood curve and a hyperbolic tangent approximation were used. Unlike some approaches to this problem both the adhesive shear and the transverse direct stresses contribute to the yield of the adhesive, and the non-linear response of both is modelled. The adhesive yield can be modelled using either a simple or modified von Mises yield criterion. The latter is formulated for adhesives taking into account hydrostatic stresses as well as deviatoric stresses. Force and moment balance equations for an elemental length of sandwich overlap are presented. Simple adherend bending is assumed and the differential deformations in the upper and lower adherends in both the shear and transverse directions are related to the corresponding strains in the adhesive layer. The problem is then reduced to a set of six first-order non-linear differential equations, which, in conjunction with the chosen stress-strain properties of the adhesive, are solved using a boundary-value finite-difference method. Both the stress and strain results in the shear and transverse directions for various load cases have been compared with the results of a non-linear finite element analysis and agree favourably, even for high levels of adhesive non-linearity. Finally the analysis has been used to study the effect of adhesive thickness on lap joint strength and it is shown that this effect can only be modelled using a non-linear analysis.