Effect of geometrical non-linearity on the stress and deformation states of adhesive joints

Abstract

When an adhesively bonded joint is subjected to reasonably high loads a non-linearity arises because of significant changes in the geometry of the bonded joint although the adhesive and adherends are still elastic. This is called geometrical non-linearity. In this case the linear elastic analysis may be misleading in predicting the stress and deformation states of the adhesive and adherends. Since the displacements and rotations may become large, so equilibrium equations must be written for the deformed configuration rather than for the original configuration. In this study the small strain-large displacement theory was recalled for the analysis of the adhesively bonded joints, and its application to the incremental finite element method was reviewed. Therefore, the material non-linearity in the adhesive and adherends was not considered. This non-linear finite element method was used to analyze the two-dimensional stress distributions in an adhesively bonded T-joint with a single support plus an angled reinforcement. The T-joint configurations bonded to a rigid base and a flexible base were considered. For each case the linear and non-linear stress analyses of the adhesive T-joint were compared for the different plate end conditions which cause substantial changes (large displacements and rotations) in the joint geometry. The geometrical nonlinear analysis showed that the large displacements had considerable effects on the stress and deformation states of the adhesive and adherends. In addition, the effects of the support length and the angled reinforcement length on the peak stresses were investigated; increasing these dimensions resulted in an evident decrease in the peak stresses until a specific support or angled reinforcement length/joint length ratio.