Application of two-state M-integral for analysis of adhesive lap joints

With the aid of the two-state M-integral and 7nite element analysis, the asymptotic solution in terms of the complete eigenfunction expansion is obtained for adhesive lap joints. The notch stress intensity is introduced to characterize the singular stress 7eld near the notch vertex of adhesive lap joints. The proposed scheme enables us to extract the intensity of each eigenfunction term from the far 7eld data without resort to special singular elements at the vertex. It turns out that a weak stress singularity is not negligible around the vertex when it exists in addition to the major singularity. For a thin adhesive layer, there exist two asymptotic solutions: one is the inner solution approaching the eigenfunction solution for the vertex at which the adherend meets with the adhesive and the other is intermediate solution represented by the eigenfunction series that would be obtained in the absence of the adhesive layer. An appropriate guideline for choosing the geometric parameters in designing the adhesive lap joints, particularly the overlap length or the size of the adhesive zone, is suggested from the viewpoint of minimizing the notch stress intensity.