Solution of the Displacement Boundary Value Problem of an Interface Between Two Dissimilar Half-Planes and a Rigid Elliptic Inclusion at the Interface

Abstract

The displacement boundary value problem of a bimaterial interface is solved using the complex stress function technique. A rational mapping function is used to map the two half-planes into unit circles and analysis is carried out in the mapped plane. The symmetric bimaterial problem is considered and the particular case of a rigid elliptic inclusion at the interface is solved. Uniform remote tensions both along and normal to the interface are considered. Stress distributions on the inclusion boundary are shown. Stress concentration factors at the inclusion tips are obtained and are expressed in terms of the radius of curvature using an approximate form of a general expression. These results are used to predict the likelihood of debonding/cracking at the tips. Also, stress concentration factors at the tips of an elliptic inclusion and elliptic void are compared. Stress intensity factors at the tips of a thin rigid elliptic inclusion are also determined.