On the singularity of the stresses near the face of a thin elastic inclusion in a piecewise homogeneous plane

Abstract

The asymptotic behaviour of normal stresses near the tip of a thin elastic inclusion situated near a line weld joining two dissimilar elastic half-planes, is studied. It is established that apart from the well-known root-type singularity /1/ two additional terms of the asymptotic expression exist which must not be neglected. One of them is of the order of unity, and the other contains an “imaginary singularity” and makes a singificant contribution to the state of stress when the distances between the face of the inclusion and the line separating the materials are small.