Abstract
Based on linear superposition rules and fast discrete Fourier transformation, a semi-analytical solution is developed for calculating the elastic fields induced by dislocation loops in an isotropic thin film-substrate system. The elastic field problem of thin film-substrate system is decomposed into two sub-problems: bulk stress due to a dislocation loop in an infinite space, and correction stress induced by free surface and interface of the film-substrate system. Correction elastic field is linearly superimposed onto bulk elastic field to produce continuous displacement and traction stress across the interface plane of the perfectly-bounded film-substrate system. Firstly, calculation examples of dislocation loops in Cu-Nb film-substrate system are performed to demonstrate the calculation efficiency of the developed semi-analytical approach. Then, elastic fields of dislocation loops within Cu film and Nb substrate of the Cu-Nb film-substrate system are analyzed. Finally, effects of film thickness, loop positions are investigated, and it is found that the elastic fields of dislocation loop are influenced remarkably by these two factors.
Highlights
Film-substrate structures and systems composed of thin film of finite thickness and substrate of infinite thickness are widely used in micro-chips, smart electronics, micro-sensors and manipulators, protective coatings, etc
Solutions to the elasticity field induced by dislocations within film-substrate system are important, because the elasticity solution provides a direct means of determining the Peach-Koehler force acting on dislocations, which is of direct relevance in understanding the microstructure evolution and mechanical behaviors of these filmsubstrate systems
Making use of the solution of an edge dislocation in half-plane and that of the reversed traction force prescribed on the interface plane, Weeks et al [4] presented an exact analysis for the elastic field and the Peach-Kohler force due to an edge dislocation within the substrate medium of film-substrate system
Summary
Film-substrate structures and systems composed of thin film of finite thickness and substrate of infinite thickness are widely used in micro-chips, smart electronics, micro-sensors and manipulators, protective coatings, etc. Study of the collective dynamic behaviors of dislocations embedded in thin film-substrate system are of great interest to researchers and engineers, which are of critical importance for understanding the microstructure evolution, plastic deformation process of thin filmsubstrate systems. Solutions to the elasticity field induced by dislocations within film-substrate system are important, because the elasticity solution provides a direct means of determining the Peach-Koehler force acting on dislocations, which is of direct relevance in understanding the microstructure evolution and mechanical behaviors of these filmsubstrate systems. Et al [7] studied the stress field induced by an edge dislocation of arbitrary orientation in both the surface layer and substrate medium of the layer-substrate system, and the solution can be employed for deriving the solution of crack problems, together with the Peach-Koehler force.
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