Two problems of fracture and deformation of metals are studied in this dissertation.

In the first problem, the growth of grain boundary cavities is examined using a mechanism proposed by Chuang and Rice in which atoms are driven by gradients in curvature along the surface of the cavity to the grain boundary. Atomic transport in the grain boundary is assumed to be fast compared to that along the cavity surface. Particular attention is given to following the time dependent shape evolution of an initially lenticular cavity, and in this respect the treatment differs from the Chuang-Rice approach in which a steady state crack-like configuration is assumed. Taking this approach allows for the determination of the effects of capillarity and transients on the growth process. A mathematical formulation of the time-dependent cavity growth problem is presented, but due to its complex nature, no attempt is made to find a closed form analytical solution. Rather, the cavity evolution is examined using a finite difference numerical scheme in which the displacements of discrete points on the cavity surface are followed in time.

For an isolated cavity on an infinite boundary, it is found that the Chuang-Rice treatment accurately describes cavity growth once the steady state is achieved. The effect of capillarity is manifested by an incubation period during which a "nose" protrudes from the tip of the cavity. Evidently, the nose which develops at the cavity tip behaves like the Chuang-Rice steady state crack. An array of cavities is studied to determine the effects of cavity interaction on the growth process and to define a criterion for fracture. The results of the investigation compare favorably with rupture data for silver containing artificially implanted grain boundary cavities.

The second problem examined deals with low temperature plastic deformation, and a dislocation dynamical model for low temperature plastic flow is developed from the Taylor-Orowan equation. It is shown that although the classical dynamical approach has been used in the past to model and predict flow phenomena in alkali halides and BCC metals, a direct extension of this modelling fails to predict certain flow behavior in FCC metals, particularly the strain rate sensitivity. This is largely due to the classical dynamical assumptions that the mobile dislocation density is a constant fraction of the total dislocation density and that dislocations are considered to be driven by the applied stress. It is argued that the mobile dislocation density can be a strong function of the applied stress and that dislocations are driven by an effective stress rather than the applied stress, and these factors are incorporated into the model. Dislocation link length arguments are used to develop the stress dependence of the mobile dislocation density, and a strain dependent long range back stress is used to define the effective stress. Including these considerations resolves the problems encountered in applying the dynamical method of FCC metals, and proper strain rate sensitivities as well as other flow behaviors are predicted. In addition, it is found that the differences in dislocation mobility between classes of materials give rise to their different mechanical properties, and a single dislocation dynamical model is capable of predicting low temperature plastic flow in a variety of materials.