The order of stress singularity near the vertex in three-dimensional joints

Dissimilar materials are frequently used in industrial products, such as electronic devices, welded joints and composite materials. Many investigations on two-dimensional joints so far have been carried out theoretically and experimentally, although three-dimensional ones are rarely performed. In this paper, the order of stress singularity at the corner where four free surfaces and the interfaces of the three-dimensional joints meet is investigated by solving an eigenequation derived from a ®nite element formulation. The order of stress singularity for four typical joints, referred to as the 1/8±1/8, 1/8±1/4, 1/8±1/2 joints and a joint with various vertex angles, consisting of two blocks with di€erent properties is investigated. Dundursʹ composite parameters, a3D and b3D, for three-dimensional joints are newly introduced, and the order of stress singularity plotted on ordinary Dundursʹ parameters, the a and b plane, is rearranged on the a3D±b3D plane. The order of stress singularity at the vertex in the three-dimensional joints is larger than that in the two-dimensional joints, although, the zero boundary of stress singularity varies little on the a3D±b3D plane. Furthermore, it was shown that the order of stress singularity at a vertex, where some singular lines with di€erent orders meet, varies with the combination of material properties.