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

Abstract

In the present paper, the order of stress singularity at the corner where four free surfaces and interface in the three-dimensional joints meet are investigated by solving an eigen equation derived from a finite element formulation. The order of stress singularity for three typical joints, refered to as 1/8-1/8 joint, 1/8-1/4 one and 1/8-1/2 one, consisted of two rectanglar blocks with different properties is investigated and compared with that for two-dimensional joints with the same cross section of three-dimensional joints. Dundurs'composite parameters, α3D, and β3D, for three-dimensional joints are newly intoduced and the order of stress singularity plotted on the ordinal Dundurs' parameters, α and β plane, is rearranged on 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 bound vanishing the stress singularity little varies on the α3D-β3D plane. Furthermore, it was shown that the order of stress singularity at a vertex gathering some singular lines with different orders varies depending on a combination of material properties.