A wedge of arbitrary angle interacting with a generalized singularity

Abstract

In this paper, the state of stress induced within a semi-infinite wedge of arbitrary angle by a generalized singularity is studied, and its analytical solution is derived. The wedge may, usefully, be a V-shaped notch if the internal wedge angle is larger than π, and the generalized singularity may represent either a concentrated force or an edge dislocation. Several scenarios are studied to validate the general solution. As an interaction example, the wedge interacting with an edge dislocation is considered, and the driving force on the dislocation is obtained in terms of the vector J-integral. The solutions developed in this study give basic information about the state of stress induced in the wedge, which, as well as representing crystalline defects, may be used as building blocks to model the damage at the V-notch root under complex load conditions, as well as to model elastic edge contacts. In addition, it is proved that the stress distribution behavior at the vertex of wedge is categorically determined by its open angle.