Analysis for Stress Singularity Field at a Vertex in Three-Dimensional Bonded Structures.

In the present paper, the order of stress singularity at the corner where four free surfaces and interfaces in three-dimensional joints meets is investigated by solving an eigenequation derived from a finite element formulation. The order of stress singularity for three typical joints, referred to as the 1/8 - 1/8, 1/8 - 1/4 and 1/8 - 1/2 joints, between two rectangular blocks with different properties is investigated and compared with that of two-dimensional joints with the same cross section as that of the three-dimensional joints. Dundurs' composite parameters, α3D and β3D for three-dimensional joints are newly introduced and the order of stress singularity plotted on ordinal Dundurs' parameters, the α and β plane, is rearranged on the α3D - β3D plane. The order of stress singularity at the vertex in the three-dimensional joints is larger than that in the two-dimensional ones, although, the boundary at which the stress singularity vanishes varies little on the α3D - β3D plane. Furthermore, it is shown that the order of stress singularity at a vertex, where some singular lines with different orders meet, varies with the combination of material properties.