Theory of bubble growth in crystals under stress

Abstract

In a previous paper, the theory of bubble growth in crystals was extended to include an analysis of the interaction that occurs between the diffusion mechanism that supplies gas to the bubble and the concurrent material displacement that accommodates its growth. A novel mechanism of gas supply was also identified that derives from the accommodation process itself. As material near to the bubble is diffusively consumed, the gas dissolved within it must be deposited into the bubble. A critical gas concentration was predicted, at which the gas supplied by this mechanism can lead to self-sustained bubble growth without the need for any diffusive supply through the crystal. In the present paper, these ideas are extended to cases in which external stresses are applied to the material. For bubbles in the lattice, only hydrostatic stress is important. External pressure is shown to inhibit self-sustained growth mechanism. For grain boundary bubbles, normal stresses at the boundary can dominate. Tensile stresses augment the self-sustained growth process, while compressive stresses inhibit it. If the stress drives diffusional creep, the diffusive removal of material from boundaries under compression must lead to the deposition of its gas content at these boundaries. The unusual possibility then emerges that enhanced bubble growth might occur on boundaries under compressive stress. Since these bubbles give rise to a component of strain in the compressive direction, it is anticipated that an effective ‘Poisson ratio’ for creep should exist, with a value exceeding unity: that is, the material becomes fatter as it elongates.