Mechanics of dislocations in multilayered materials

Abstract

This thesis reports an investigation into the mechanics of anisotropic multilayered materials embedded with dislocations. An image technique is developed for solving the problems of infinite bilayers, film-substrates and general N-layer composites. The key contributions are: (1) the development of an image decomposition scheme which is instrumental to the accuracy of the complete solution, and (2) the elimination of singularities from the governing integral equations using certain H and I transforms. Numerical investigations reveal that many factors, e.g., elastic anisotropy and layer inhomogeneity, will significantly influence the image forces acting on the dislocation. Furthermore, a single-ended discrete dislocation pileup model is developed and used to show that the shear strength dependence on layer thickness obeys the Hall-Petch relation quite well for sufficiently thick layers while image forces result in a deviation of the relation for very thin layers. The numerical predictions are in good agreement with a comprehensive set of experimental data for metallic multilayer systems.