Modelling interfacial inclusions embedded between dissimilar solids

Abstract

In this paper, a generic model for interfacial inclusions embedded between dissimilar solids is proposed to address a wide range of problems in materials engineering. By virtue of the equivalent eigenstrain principle and line inclusion concept, the model is formulated in the framework of plane elasticity using the complex variable Green's function method. Explicit analytical solutions for the deformation field of the interfacial inclusions containing an internal eigenstrain distribution or subjected to far-field loading are derived. As a typical example, a lamellar semi-elliptical interfacial inclusion problem is analyzed, from which the robustness of the proposed interfacial inclusion model is validated through a direct FEM simulation. It is found that the internal eigenstrain distribution leads to a significant stress concentration in the vicinity of the endpoints of the major axis. Interfaces between an inclusion and substrates tends to debond due to the concentrated shear traction, while the bi-material interface outside the inclusion can detach as a result of the concentrated normal traction. The formulations established in this study provide a concise and convenient analytical solution for various interfacial inclusion problems encountered in material engineering.