Effect of periodic lamellar inclusions on interface integrity

The bond strength between dissimilar solids is highly sensitive to defects near or within the interface. Interfacial inclusions, which are ubiquitous in materials engineering, play a critical role in determining the local and global integrity of materials or structures. In this article, we propose a theoretical model for periodic rectangular lamellar inclusions at the interface of dissimilar solids. In view of the concept of line inclusion, the Kolosov–Muskhelishvili complex potentials for the homogeneous periodic inclusion problem are derived based on the Green’s function method within the framework of plane elasticity. The explicit analytical solution of the stress field of the inhomogeneous periodic rectangular lamellar inclusion problem with arbitrary eigenstrain distribution is derived with the aid of the equivalent eigenstrain principle. A new stress concentration factor (SCF) is consequently defined to assess the interface strength. The influence of the size and material of rectangular lamellar inclusions on the SCF is analyzed. The accuracy of the theoretical results is further verified by finite element simulations. The analytical formulae established in this study offer a straightforward yet effective approach for various inhomogeneous and homogeneous interfacial inclusion problems encountered in engineering practice.