Utilizing Fourier transforms, the elastic field of 3-dimensional dislocation loops in anisotropic multilayer materials was developed. Green's functions and their derivatives, obtained first in the Fourier domain and then in the real domain by numerical inversion, were used in integrals to determine the elastic field of dislocation loops. The interaction forces between dislocations and free surfaces or interfaces in multilayer thin films were then investigated. The developed method was based on rigorous elasticity solutions for dislocations approaching to within one to two atomic planes from the interface. For a dislocation in one layer, the interface image force was determined mainly by the elastic moduli and thicknesses of neighbouring layers. When a dislocation approaches an interface between two layers, within 10-20 atomic planes, the image force changes rapidly. Interaction forces were then kept constant up to the interface. The model showed that, when a dislocation crosses an interface from a soft to a hard layer, additional external forces must be applied to overcome an elastic mismatch barrier. The developed method extends the concept of the Kohler barrier in 2D, and showed that the interface force barrier not only depends on the relative ratio of the elastic moduli of neighbouring layers, but also on the 3D shape of the dislocation, the number of interacting adjacent layers, and on layer thicknesses.

Stress Field and Interaction Forces of Dislocations in Anisotropic Multilayer Thin Films. X.Han, N.M.Ghoniem: Philosophical Magazine, 2005, 85[11], 1205-25