Instabilities in stress corrosion and the transition to brittle failure

Abstract

Studies on the dissolution of stressed crystals have shown that stress corrosion can lead to roughening of interfaces. The corrosion pattern develops due to gradients in elastic energy along a free crystal surface with an initial roughness. Dissolution will cause further increase in elastic energy, which in turn will speed up dissolution, the so-called Asaro-Tiller-Grinfeld instability. We present a numerical model in order to study the effect of stress corrosion that is observed in physical experiments of interface roughening of brittle salt crystals. In the simulations a salt crystal that is immersed in saturated brine is stressed and dissolution patterns develop. Stress corrosion can lead to an Asaro-Tiller-Grinfeld instability that develops into cusp instabilities and crack-like structures or anti-cracks. The system breaks its symmetry and produces a secondary instability where the number of growing anti-cracks is reduced. This coarsening of the surface roughness is due to stress-shielding effects of growing anti-cracks. Finally, one single anti-crack remains on each side of an initial hole as a "superstructure". The large anti-crack grows at an almost constant speed and eventually leads to brittle failure of the crystal. This mechanism may be important not only for dissolution-precipitation creep but also other phase-transitions and may lead to large scale brittle failure that can be associated with earthquakes.