| In this dissertation, a variational approach, which can incorporate a wide range of thermodynamic forces and mass transport mechanisms, has been applied to study stress induced structural evolution. The approach combines driving forces, kinetic laws and the free energy variations associated with virtual structural change. A program with an embedded stress field solver, using Boundary Element Method (BEM), is developed. By using the program developed, thin film morphology evolution in elastically stressed solid due to surface diffusion and/or evaporation/condensation is simulated first. The similarity and difference between surface diffusion and evaporation-condensation induced surface grooving and the effect of the mobility ratio of two processes are explored. Special attention is paid on the effect of the initial profile of the surface. Simulations show that if the initial surface contains many sharp cracks or notches, the surface may take longer time to develop deep cusps and break into islands than the relatively flatter initial surfaces. In the second part of this work, stress relaxation due to grain boundary diffusion is considered. A set of stress relaxation processes are simulated under different surface and grain boundary energy ratio to explore the effect of surface profile on stress relaxation. It is found that when the stress relaxation is limited by the rate of surface diffusion, the dihedral angle at the surface-grain boundary junction plays a significant role. In addition, the simulation result on stress relaxation process that is limited by grain boundary diffusion is used to determine the grain boundary diffusivity by being compared with the experimental results. Finally, the numerical scheme is extended to 3D axi-symmetric model to study the evolution of a cylinder under stress by surface diffusion. Under a periodic perturbation, it is found that the stressed fiber is not always stable even its perturbation wavelength is smaller than its circumference. It can still stay stable, or develop grooves first then approach to a steady state shape, or develop cusps and break into particles. These two critical stresses that are corresponding to initial stability and the transition from steady state to unstable state are estimated by using numerical simulation. |
