Antiplane strain problem of diamond inclusion

Abstract

In this paper, the singular stress fields created by an antiplane deformation at an inclusion corner are studied. It is shown that these singular stress fields can be separated into two independent types: a symmetric type with the stress singularity of 1/Υ ^1−λ1 and a skew-symmetric type with the stress singularity of 1/Υ ^1−λ2. These two types of the singular stress field can not occur simultaneously at the corner. If G ₂<G ₁, there exists only the singularity of the skew-symmetric type, and if G ₂>G ₁, there exists only the singularity of the symmetric type. A general expression of stress fields in the vicinity of the corner is presented. In the expression the singular stress fields for the symmetric type and the skew-symmetric type are defined in terms of the constants K _III, λ₁ and K _III, λ₂, respectively. K _III, λ₂ and K _III, λ₂ have to be determined from the complete boundary conditions of the given problem. For the problem of an infinite plate containing a diamond inclusion and subjected to a uniform longitudinal shear stress at infinity, the values of K _III, λ₁ and K _III, λ₂ are obtained by body force method. In the body force method, the investigated stresses are simulated by the superposition of the fundamental stress fields due to point forces. In order to obtain accurate solutions, the basic density functions of the distributed point forces are used, so that the stress singularities at the corner tip can be simulated by the point forces.