Simulation of the elastic field of an interfacial dislocation in an anisotropic medium: Fourier series approach

Abstract

Interfacial dislocation networks, located at the interface between two crystals, significantly influence the mechanical, thermal and electrical behaviors of materials. Despite their importance, these phenomena have received relatively little attention in the scientific literature. This gap can be mainly explained by the difficulty of analyzing these complex systems under realistic experimental conditions, particularly using advanced techniques, which take into account the anisotropy of materials.  This study focuses on the simulation of the elastic field (stresses and displacements) of a dislocation located at the interface of two infinite anisotropic media. Based on previous work in anisotropic elasticity, an analytical formulation based on Fourier series was used to numerically solve a system of 12 equations with 12 unknowns. The results obtained show the equistress curves for different crystalline systems (Al/Al, Cu/Cu and Al/Cu) considering both anisotropic and quasi-isotropic cases. The study highlights more pronounced stress dispersion in copper due to its hardness, as well as notable differences between isotropic and anisotropic cases, especially for heterogeneous materials such as Al/Cu. The conclusions highlight the importance of material heterogeneity in stress distribution and the relevance of the results for modeling crystal interfaces. This work offers promising perspectives for the optimization of materials in industrial fields such as aeronautics, electronics and renewable energies. It also provides a robust methodological framework for the study of complex crystalline materials.