Investigation of elastic stresses in an adhesively bonded single lap joint with functionally graded adherends in tension

Abstract

In this study three-dimensional elastic stress state of an adhesively bonded single lap joint with functionally graded adherends in tension was investigated. The adherends compose of a functionally gradient layer between a pure ceramic (Al 2O 3) layer and a pure metal (Ni) layer. Stress concentrations are observed along the free edges of the adhesive layer and through the corresponding zones in the upper and lower adherends. The adhesive layer experiences stress concentrations along the left and right free edges in the horizontal plane, and the normal stresses and the shear stress σ xy are critical. Whereas the middle overlap region has a uniform low stress distribution the zones in the upper adherend corresponding to the left free edge of the adhesive layer and the zones in the lower adherend corresponding to the right free edge of the adhesive layer are subjected to higher stresses. The normal stress σ xx among the normal stresses and the shear stress σ xy among the shear stresses are dominant in both upper and lower adherends. The normal stress σ xx changes uniformly from compression in the ceramic layer to tension in the metal layer through the upper plate-thickness and from tension in the ceramic layer to compression in the metal layer through the lower plate-thickness. In the adhesive layer, the normal stress σ yy becomes peak at the left free edge of the upper adherend–adhesive interface and at the right free edge of the lower adherend–adhesive interface and then decreases uniformly across the adhesive layer towards the other adherend–adhesive interface. The functionally gradient region across the adherend thickness was modelled using the layers with the mechanical properties calculated based on the power law. However, a layer number larger than 20 has a minor effect on the through-thickness profiles and magnitudes of von Mises and normal stresses in both the adherends and the adhesive. In addition, increasing the ceramic phase in the material composition (compositional gradient exponent n) of the functionally gradient region does not affect the through-thickness profiles of von Mises and normal stresses in the adherends and adhesive whereas their magnitudes in the ceramic rich layer of both adherends and along the adherend–adhesive interfaces increase considerably. On the contrary, the layer number and compositional gradient exponent have an evident effect on the through-thickness profiles and magnitudes of the critical stress components in the adherends and adhesive layer of the functionally graded adhesively bonded joints.