Three-parameter viscoelastic foundation model of adhesively bonded single-lap joints with functionally graded adherends

Functionally graded (FG) adherends are beneficial to adhesively bonded joints, as different material composition through the adherend thickness can manipulate the interfacial stress distribution. It is a fact that both shear and peeling stresses along the adhesive/adherend interface at the free edges play important roles in the structural integrity of a joint. Previous studies have shown that both shear and peeling stresses can be uniformly distributed near the edges of a joint with FG adherends if the right adherend composition is selected through the adherends' thickness. However, the effect of the viscoelastic behavior of the adhesive layer has been neglected in those studies. This study establishes a viscoelastic analytical model for adhesively bonded single-lap joints with FG adherends. In this model, the adhesive layer is simulated as a three-parameter viscoelastic foundation using a standard linear solid (SLS) model to account for both creep and relaxation behaviors in the adhesive. This model satisfies the zero-shear-stress boundary at the free edges of the adhesive and predicts different peel stresses along two adherend/adhesive interfaces. Excellent agreement with finite element analysis (FEA) has been achieved by the present model, confirming the accuracy of the model. The viscoelastic behavior of the adhesive layer affects stress concentration near the edges of a joint at early ages, suggesting that the present model can properly capture the stress relaxation in adhesively bonded joints with FG adherends. The parametric studies show that FG material configuration and the mechanical properties of adhesive layers play an important role in the uniformity of shear stress distribution along the length of single-lap joints with FG adherends. The present viscoelastic solution can predict more uniform stress distribution and is a valuable tool in design optimization of joints with FG adherends.