Morphological stability and evolution of stressed solids and films.

Abstract

The morphological stability and evolution of solids and films depend upon the forces to which the material is subject and the physical kinetic processes that lead to matter transport. In this thesis, we considered the cases where the driving forces for morphological change are associated with surface/interfacial energy and applied stresses, and the physical mechanism of matter transport is surface diffusion. Since the morphological stability and evolution of stressed solids and films generally involve nontrivial morphology evolution, the computational methods are employed within this thesis to investigate (a) the morphological stability of holes in stressed films and misfitting island on substrate and (b) the surface morphology evolution in stressed solids driven by surface diffusion. We have developed a computer model that incorporates several novel methods within the framework of boundary element analysis for elasticity and finite element analysis for matter transport kinetics. We analyze the stability of misfitting islands on a substrate. We demonstrate that, unlike in the stress-free case, the equilibrium strained island aspect ratio is a function of the volume of material in the island. We examine the stability of a hole in a stressed film. Combination of the elastic analysis with an analysis of the interfacial energies also defines conditions under which the stressed film will be stable (i.e., holes will shrink) and for which the film will be unstable (i.e., holes will grow). We present the results of a numerical study of the full nonlinear surface morphology evolution driven by stress-assisted surface diffusion. Ours results demonstrate that a nominally flat surface profile bounding an elastic stressed solid can rapidly evolve into a crack-like morphology, with smooth tops and sharp, deep grooves. These grooves continue to sharpen and accelerate as they grow. We demonstrate that when the groove depth reaches a critical length, it becomes the mechanical equivalent of an unstable crack. We further show the stress-driven surface instability maps formally onto classical fracture mechanics. Unlike in classical fracture mechanics, which starts by assuming a crack exists, the present analysis accounts for crack nucleation and propagation based upon a single unified theory. These results constitute a consistent view of crack nucleation and growth which yields the Griffith criteria in one limit as a natural by-product of the full morphology evolution.