Examination of appearance conditions of singular stress fields at the vertex and along the side of interface in prismatic butt joint

Abstract

In this paper, we discuss the bad pair condition causing a singular stress at a vertex of the interface in three dimensional (3D) prismatic butt joints in comparison with the bad pair condition along the side. 3D finite element (FE) eigenanalysis is applied to obtain the singular index. We found that the bad pair condition at a vertex is slightly different from the well-known 2D bad pair condition α(α- 2β) > 0 , which can be expressed using Dundurs' parameter (α, β). It should be noted that in most cases the bad pair can be judged by (α, β) except for some cases where the bad pair depends on the material combination even under the same (α, β). To clarify the difference, the bad pair conditions are compared on the (α, β) diagram. For convenience, a simple expression for a bad pair is proposed on the basis of the theoretical consideration, and the validity is confirmed numerically. We also confirm that the bad pair condition along the side of the interface can be expressed using Dundurs' parameter as α(α- 2β) > 0 .