Geometrically Non-Linear Analysis of Adhesively Bonded Double Containment Corner Joints

In cases where adhesively bonded joints may experience large displacements and rotations whilst the strains remain small, although all joint members behave elastically the small strain-small displacement (SSSD) theory cannot correctly predict the stresses and deformations in the adhesive joint members. Previous studies have shown that the small strain-large displacement theory considering the non-linear effects of the large displacements in the stresses and deformations has to be used in the analysis of adhesively bonded joints. In this study, the geometrical non-linear analysis of an adhesively bonded double containment corner joint was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The objective of the study was to determine the effects of the large displacements on the adhesive and adherend stresses of the corner joint. Therefore, the corner joint was analysed for two different loading conditions; a compressive applied load, P_x, at the free end of the horizontal plate and one normal to the plane of the horizontal plate, P_y. The plates, support and adhesive layer were assumed to have elastic properties. In practice, the adhesive accumulations, called spew fillets, arising around the adhesive free ends were taken into account in the analysis since their presence results in a considerable decrease in the peak stresses around the free ends of the adhesive. The SSLD and SSSD analyses showed that the stress concentrations occurred around the free end of the adhesive, thus at the adherend (slot) corners inside the right vertical and the lower horizontal adhesive fillets, and inside the left vertical and the upper horizontal adhesive fillets for the loading conditions P_x and P_y, respectively. In addition, the plate regions around the adherend (slot) free ends along the outer fibres of the vertical and horizontal plates undergo very high stress concentrations. The SSLD analysis predicted a non-linear effect in the displacement and stress variations at the critical adhesive and plate locations, whereas the SSSD analysis showed their variations were lower and proportional to the applied incremental load. This non-linear effect became more evident for the loading condition P_x, whereas both analyses predicted very close displacement and stress variations in the adhesive fillets and in the horizontal plate for the loading condition P_y. As a result, the geometrical non-linear behaviour of the corner joint is strictly dependent on the loading condition and the large displacements affect the stress and deformation states in the joint members, and result in higher stresses than those predicted by the SSSD theory.