Crack nucleation on an elastic polycrystal surface in a corrosive environment: Low dimensional dynamical models

Abstract

This paper analyses a process of crack nucleation on the surface of a ceramic subject to a stress parallel to the surface, in an environment where the ceramic evaporates slowly and deforms elastically. We formulate dynamical models of one or two degrees of freedom by combining an existing elasticity solution and a variational approach. Both grain boundary tension and elastic stress concentration cause the surface to groove along its intersections with the grain boundaries. Two behaviors are identified. If the applied stress is small, the grooves approach an invariant shape, and the ceramic erodes by gross mass loss. If the applied stress is large, the grooves sharpen into crack fronts, and the ceramic breaks by decohesion. The models relate crack nucleation threshold and time to the applied stress, surface and grain boundary tensions, chemical free energy, grain size, and kinetic parameters. Surface self-diffusion is also included in the analysis.