Initiation of mode I degradation in sodium-beta alumina electrolytes

Abstract

The extension of initial surface cracks by the focusing of the ionic current in beta alumina electrolytes (Mode I degradation) is discussed in terms of existing models. Focusing for an ion current impinging on an elliptic-cylindrical flaw is calculated by solving for the electric potential with suitable boundary conditions. The current density distribution along the crack is used to calculate the sodium flow velocity and Poiseuille pressure inside the flaw. Calculated critical current densities using aKlc criterion are several orders of magnitude higher than measured average critical current densities. This implies a lower effectiveKlc for electrolytic degradation than for mechanical testing. Current density enhancement around insulating barriers, such as non-wetted surface areas, is also calculated using elliptic-cylindrical coordinates. Significant current density enhancements are found, but they are localized in very small regions. Crack growth would occur within these regions, but should be arrested once the flaw extends past the high current density zone. A plausible mechanism for decreasingKlc in the electrolytic case is discussed.