Stress singularity analysis in three-dimensional bonded structure

Stress analysis for joints between two isotropic materials is performed using threedimensional boundary element method with Rongved’s fundamental solution [Rongved, L. (1955). Force interior to one of two joined semi-infinite solids. In Second Midwestern Conf. on Solid Mechanics, pp. l-131, which satisfies boundary conditions at the interface. The stress distribution around the vertex of the joint is precisely examined and the order of stress singularity obtained in three-dimensional analysis is compared with that in two-dimensional analysis. It is shown that the order of the stress singularity along the stress singularity line, which is the intersection of the interface with the free surface, varies from the value in plane strain to that in plane stress as the opposite side free-surface is approached. The order of stress singularity in the spherical coordinates centered at the vertex is next investigated. When singularity lines with a singularity order meet with each other at the vertex, the order of stress singularity is larger than that for plane strain and plane stress. When the vertex angle between two side free-surfaces is varied, the order of stress singularity is also altered. In particular, a bound at which singularity disappears at the c+/I plane for Dundurs’ composite parameters is examined for a cubic dissimilar material. It is demonstrated that the bound varies little in comparison with the one obtained from the two-dimensional theory. Copyright 0 1966 Elsevier Science Ltd