Viscoelastic analysis of stress distribution in balanced and unbalanced adhesively bonded single-lap joints with functionally graded adherends under the Reddy model

In this study, shear and peel stress distributions in the viscoelastic adhesive layer of a single-lap joint (SLJ) with functionally graded (FG) adherends are investigated. The study focuses on the effect of different adherend profiles and material composition on the time-dependent stress concentration/distribution in balanced and unbalanced SLJs. For this purpose, the Reddy model is applied to the FG adherends and a three-parameter solid viscoelastic model is used to simulate the adhesive layer behavior. Using the first-order shear deformation theory for the FG adherends, the governing differential equations are derived and then transformed into the Laplace domain. A finite element model of the joint was also developed to further backup the numerical solution. The numerical inverse Laplace transform method was used to extract the desired results that were then compared with those of finite element method (FEM) findings. Very good agreements were observed between the results of both methods. Results show that the geometric and mechanical properties of the FG adherends have an essential role in reducing the shear and peel stress concentrations as well as the uniformity of shear stress distribution in the overlap region. Results also show that either method (finite element or the proposed semi-analytical method) can be utilized with confidence for prediction of stress relaxation in the adhesively bonded SLJs with FG adherends.