On the prediction of the stress field in adhesive joints using a combined analytical-numerical method

In this paper, the stress field in adhesively bonded joints is predicted by employing an analytical approach together with the finite element method (FEM). To accomplish this, the adhesive joint is considered as a bi-material notch. Then, a unified analytical formulation for the in-plane stress and displacement field of bi-material notches is presented in the form of asymptotic series. Subsequently, a numerical procedure based on an over-determined system of equations is used to obtain the coefficients of the series solution for various types of adhesive joints including single lap joint (SLJ), single fillet lap joint (SFLJ), butt joint (BJ), scarf joint (SJ), and single lap joint with an inside taper and adhesive fillet (SLJ-ITAF). By comparing the results obtained from the analytical stress field with the numerical results, the accuracy of the calculated coefficients is evaluated. It is shown that by using the proposed approach one can obtain the stress field within the adhesive layer by using the stress or displacement fields of the adherend. The obtained results also show that neglecting the higher-order terms can result in significant errors while considering the first three non-singular stress terms besides the singular term reveals very good results.