Influence of angle between side surface on singular stress field in 3D joints under a tensile loading

Abstract

Characteristics of singular stress field at the vertexes of two interfaces in three-dimensional joints with three layers are investigated using eigen analysis formulated by FEM and BEM using fundamental solutions for two-phase materials. Angle between two side surfaces at the vertex is varied from 30° to 150°. An expression for stress field near the vertex on the interface is firstly derived from the result of eigen analysis. The order of stress singularity decreases with the increase of the angle. Angular functions corresponding to stress components are deduced from eigen analysis. A coefficient in the power law term of distance from a side surface in the angular function is a function of an angle between two side surfaces, and the value of coefficient increases with the increase of the angle. A coefficient of power law term in a stress distribution for the distance from the vertex has an extremum at 90° of the angle between side surfaces. It was found that stress singularity field at the vertex with a weaker singularity is affected largely by that at the vertex with a stronger singularity. There are two factors, which define the singular stress filed near the vertex; 1) the intensity of singularity defined by the distance from the vertex, 2) an angular function defined by the distance from stress singularity lines. The intensity of singularity at the vertex of interface was defined considering those factors. The value of the intensity of singularity at the vertex increases with the increase of the angle between side surfaces.