Spacing of crack patterns driven by steady-state cooling or drying and influenced by a solidification boundary

Regular columnar joints that originate from networklike crack patterns can be observed in basalt and, on a much smaller scale, in dried starch slurry. Here, the basalt columns are idealized by a periodic array of parallel cracks driven by steady-state cooling. By means of a bifurcation analysis, the minimal possible crack spacing for sustained propagation of the crack array is calculated. It can be shown qualitatively that the minimal possible crack spacing for sustained propagation increases with decreasing velocity. This is confirmed by numerical calculations. The latent heat released at the solidification front is taken into account in the thermomechanical linear-elastic model of propagating shrinkage. Our calculations show that the solidification front is positioned not far ahead of the crack tips, which influences the result considerably. The results agree reasonably well with new measured data of basalt columns. By use of the analogy between contraction due to cooling and that due to drying the model is applied for columns in dried cornstarch, too, showing good agreement with recent experimental data.