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.

Global bifurcation criterion for oscillatory crack path instability.

A bifurcation criterion for the transition from straight to oscillatory quasistatic crack propagation in an isotropic material is derived from the requirement of pure mode I stress fields at the crack tip (K_{II}=0) on the entire crack path, henceforth called global bifurcation criterion. For a small-amplitude sine-shaped crack path which is observed in experiments at the transition, it is shown to be sufficient to postulate K_{II}=0 only for two phases of the crack path instead, which simplifies calculations. By using the measured temperature fields to solve the thermoelastic problem of dipping a hot thin glass slab into cold water, critical wavelengths of the oscillating crack growth obtained with the derived global bifurcation criterion agree remarkably well with those observed in experiments by Ronsin and Perrin. It is also shown that local bifurcation criteria, which do not take into account K_{II}=0 on the entire crack path, lead to incorrect results for the oscillatory crack path instability.