Self-driven propagation of crack arrays: A stationary two-dimensional model

Heat or mass transfer across crack surfaces can generate localized shrinkage causing internal stresses which drive crack propagation. We present experiments suggesting the existence of such a diffusion controlled directional self-cracking. Ne formulate a simple two-dimensional stationary model of straight, evenly spaced, parallel cracks for this process, which takes into account the heat transfer across the crack surfaces and the interaction of neighboring cracks. The governing equations are solved numerically using finite elements. Crack spacing and velocity can be predicted utilizing a stability argument combined with simple ideas about the formation of the crack array. The selected solution is marginally stable with minimal values for crack spacing and velocity. The results are compared with predictions from a simpler model by Yakobson.