Analysis of singular regions in bonded joints

Singular regions in bonded joints with geometric and material stress singularities are studied by expressing the displacement and stress fields in the neighborhood of the singularity by means of eigenfunction expansions which are in terms of unknown coefficients. These coefficients are found by matching displacements with those from a finite element analysis at points remote from the singularity. Expressions for the eigenfunction expansions are given explicitly for bonded joints with and without fillets (closed and open wedges). The results are not limited to stress intensity factors at the point of singularity, but can include stress values at any point near the singularity. It was found that two singular terms exist in all cases, and that, for joints with adhesive fillets and E₁/E₂>7, failure is governed by the term associated with the second lowest eigenvalue, while the lowest eigenvalue controls the failure of joints without fillets. It was also found that the calculation of stresses using only the singular terms provided a good approximation to the actual stresses over a distance of about one-fifth the adhesive thickness. The method was also used in conjunction with the Erdogan-Sih maximum stress failure criterion to determine the initial angle of crack propagation for bonded joints with and without fillets. This revealed that the direction of the maximum principal stress in the adhesive, which is also the direction of crack propagation, for joints with fillets remains essentially constant beyond a very small region near the point of singularity, while for joints without fillets crack propagation always occurs in a direction parallel to the adhesive/adherend interface.