Substrate volume and stress gradient concepts in mechanical adhesion: analysis of single straight sections

The primary objective of this study was to optimize the geometry and volume of the substrate in lap, butt, and scarf adhesive joints under various loading and boundary conditions by finite element analysis. The finite element models are validated by evaluating for convergence and by calculating theoretical values using the strength of materials and applied elasticity. The results of this study are significant in optimizing mechanical adhesion because any real joint surface may contain a combination of the above model joints on a smaller scale. Studying the behavior of these basic models will help in optimizing the topography of surfaces to be bonded. As a novel approach for design purposes, new parameters involving stress times joint volume and stress divided by joint volume as well as stress gradients are considered. Finite element meshes of the basic lap, butt, and four scarf joints (30°, 45°, 60°, 75°) having 25.4 mm adhesive length are completed. Upon validation of these models, they arc subjected to various loading and boundary conditions and results obtained. A similar study is done by reducing the adhesive length by 50% in all the scarf joints to compare the trends with the original 25.4 mm adhesive length models. Also, several models are created to evaluate the effect of the volume of substrate in the lap and butt joints. Considering the fact that large strain gradients result in failure, this study focuses not only on the magnitudes, but also on the gradients of stresses and strains in optimizing the joint strength. This study has concluded that there exist significant differences in the interfacial stresses with respect to the scarf angle, considering lap and butt to be special cases of scarf with 0° and 90° angles, as well as with respect to the adhesive material properties, adhesive thickness, and loading conditions