Emergence of cracks by mass transport in elastic crystals stressed at high temperatures

Single crystals are used under high temperatures and high stresses in hostile environments (usually gases). A void produced in the fabrication process can change shape and volume, as atoms migrate under various thermodynamic forces. A small void under low stress remains rounded in shape, but a large void under high stress evolves to a crack. The material fractures catastrophically when the crack becomes sufficiently large. In this article three kinetic processes are analyzed : diffusion along the void surface, diffusion in a low melting point second phase inside the void, and surface reaction with the gases. An approximate evolution path is simulated, with the void evolving as a sequence of spheroids, from a sphere to a pennyshaped crack. The free energy is calculated as a functional of void shape, from which the instability conditions are determined. The evolution rate is calculated by using variational principles derived from the balance of the reduction in the free energy and the dissipation in the kinetic processes. Crystalline anisotropy and surface heterogeneity can be readily incorporated in this energetic framework. Comparisons are made with experimental strength data for sapphire fibers measured at various strain rates.