Theoretical model of adhesively bonded single lap joints with functionally graded adherends

• An analytical model is established for bonded joints with functionally graded adherends.
• Critical locations of stress concentration are identified.
• Methods to reduce stress concentrations are proposed.

Adhesively bonded joints with functionally graded (FG) adherends are of practical significance since tailoring material composition through the adherend thickness can lead to more uniform shear or peeling stress distributions in the adherends and the adhesive layer near the edges of the joint. Stresses at the free edges of the adhesive layer have been found to be critical to the integrity of the joint. To this end, an analytical model is proposed for an adhesively bonded single lap joint with FG adherends. In this model, the adhesive layer is modeled as a three parameter, elastic foundation, allowing for different peel stress values at the two adherend-adhesive interfaces. Closed-form expressions for interface stresses and internal forces in the adherends are obtained. The model is validated by its agreement with finite element analysis simulations. This model shows that the peel stresses are critical at the left edge of the upper adherend-adhesive interface and at the right edge of the lower adherend–adhesive interface, suggesting that the joint is vulnerable to delaminations along the upper adherend-adhesive interface at the left edge and along the lower adherend-adhesive interface at the right edge. Parametric studies reveal the effects of adhesive thickness, adhesive stiffness, and FGM configuration on the stresses within the single lap joint. Results show that stress concentrations can be reduced near the edges of the joint by increasing the thickness of the adhesive layer, reducing the Young’s modulus of the adhesive layer, and/or configuring the FG adherends so that the stiffer material is nearest the adhesive layer.