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

Heat or mass transfer across crack surfaces can generate localized shrinkag e causing internal stresses which drive crack propagation. We present exper iments suggesting the existence of such a diffusion controlled directional self-cracking. Ne formulate a simple two-dimensional stationary model of st raight, evenly spaced, parallel cracks for this process, which takes into a ccount the heat transfer across the crack surfaces and the interaction of n eighboring cracks. The governing equations are solved numerically using fin ite elements. Crack spacing and velocity can be predicted utilizing a stabi lity argument combined with simple ideas about the formation of the crack a rray. The selected solution is marginally stable with minimal values for cr ack spacing and velocity. The results are compared with predictions from a simpler model by Yakobson.