New theories on fracture and metal oxidation in an elastic solid

In this dissertation, we have two objectives. The first one is to develop a new theory for fracturing of solids. Long-range intermolecular forces are incorporated into the immediate neighborhood of the fracture surface, since the material behavior of the immediate neighborhood of the surface is different from the bulk material behavior.; We use the descriptions of bulk material behavior within the interfacial region. The effects of the long-range intermolecular forces within the interfacial region are taken into account by surface excess properties such as surface mass density and surface energy, assigned to a dividing surface. A singular perturbation analysis with the strength of the intermolecular force as a perturbation parameter is employed to solve boundary value problems. From this analysis, it is clear that stress singularity at the crack tip is removed and that the shape of the crack tip is sharp. A new criterion of the energy release rate for a quasi-static fracture is derived using the surface energy and the surface Gibbs free energy.; The second objective is to obtain stresses developed during the oxidation of a metal. We determine the stress developed during the oxidation of titanium by combining mass conservation with conservation of linear momentum with special attention given to the choice of reference configurations. The key differences between this comprehensive approach to stress analysis during oxidation in metals and existing approaches based on thermoelasticity are thoroughly discussed.; Based on the diffusion of oxygen, the metal oxidation for planar and cylindrical geometries is analyzed using a regular perturbation method. We investigate the dependence of the reaction rate, the oxygen diffusion, the volume ratio, etc, on the oxide thickness. The oxide film thickness predicted by the perturbation analysis is compared to the thickness experimentally measured and the thickness numerically calculated. Stress distributions for both metal and oxide are given as functions of position and oxidation time.