Anisotropic Elastic Field of 3D Prismatic Dislocation Loops in Bounded and Voided Single Crystal Films

Dislocations in a finite medium bring about image stresses. These image stresses play important roles in the dislocation behavior in finite sized systems such as thin films. Since the ratio of surface to volume is higher for thin films than for bulk materials, dislocation behaviors in thin films are greatly different from those in a corresponding infinite medium, which make it necessary to take into account the effects of free surfaces on the evolution of dislocations in thin films. In the investigations[4, 5], image stresses in an elastic cylinder and thin films are calculated by employing a Fourier transform (FFT) approach and isotropically elastic fields due to dislocations are adopted in their formulation. However, most crystals are anisotropic, and the anisotropic ratio changes with environment physical parameters, such as the temperature, moisture, electron field, magnetic field. A theorem based on anisotropic Stroh’s formula for calculating the image stress of infinite straight dislocations in anisotropic bicrystals has been developed by Barnett and Lothe[6]. Wu et al.[3] recently also make use of the FFT technique to investigate the general dislocation image stresses of cubic thin films, thus extending the formalism by Weinberger et al.[4,5] from isotropic to anisotropic thin films. It is clear that for the assumed in-plane elastic fields to be periodically defined within an unbounded region is an essential and indispensable prerequisite for the above FFT-based approach to be effectively implemented, thus ruling out the possibility of its being employed to analyse image stresses in bounded and/or voided thin cubic films. Our motivation here is then to make an further extension by first calculating the anisotropic elastic fields of dislocation loops in an unbounded thin film with cavities and then invoking FEM and the principle of superposition to seek the image stress solution.