Mesh-independent proportional method to obtain ISSF and singularity index at the interface corner of three-dimensional dissimilar structures

Abstract

An efficient analysis method is proposed for the intensity of singular stress field (ISSF) as well as the singularity index (SI) at the interface corner of three dimensional (3D) bonded joints by using the finite element method (FEM). By varying the minimum mesh size $e_{min}$, the FEM stresses ${\sigma }_{\mathrm{FEM}}$ obtained from the FEM are investigated around the corner singular point. Then, mesh-independent expressions such as ${\sigma }_{\mathrm{FEM}}\left(r\right)·{\left(e_{min}\right)}^{1-\lambda }=const.$ are derived for ISSF and SI based on the proportional stress fields in prismatic joints having similar FEM mesh pattern. Previously analyzed results coincide with the present mesh-independent results to the three digits for ISSF and SI in 3D corners. The experimental results show that the critical singular stress distributions causing debonding are almost identical at the interface corner and at the interface edge independent of the adhesive thickness. This is confirmed for the ABA joint denoting the 3D prismatic butt joints whose similar adherends A are bonded by resin B. Under a constant load, the ABC joint whose dissimilar adherends A and C are bonded by resin B has larger ISSF than the ABA joints. This ISSF difference increases with decreasing the adhesive thickness $h$, and this ISSF difference is more remarkable at the interface corner than at the interface edge. The debonding failure criterion is discussed by using the previous experiment conducted for ABA-, ABC-butt joints and ABA-, ABC- three step lap joints. It is found that the adhesive strength of the ABC joint can be expressed as a constant critical ISSF at the interface corner and the constant value coincides with the value of the 3D ABA joints. Those new findings show that the proposed 3D mesh-independent proportional method is especially useful for evaluating the debonding strength of the adhesive ABC joints.