Crack pattern in ceramics subject to thermal shock

Oscillating cracks in glass.

Wavy crack patterns are observed while filling up heated flasks with cold liquid, quenching glass strips, or tearing elastic films.

Oscillating cracks in glass.
Oscillating cracks in a flask (Bahat, 1991) and a microscope slide (Yuse & Sano, 1993) subject to rapid cooling.

This numerical simulation replicates the experimental setting in (Yuse & Sano, 1993), (Ronsin, Heslot, & Perrin, 1995), (Ronsin & Perrin, 1997), (Ronsin & Perrin, 1998), (Yang & Ravi-Chandar, 2000): a microscope slide is heated then dipped in a cold liquid. Depending on the quenching speed, cracks tend to propagate along a straight line, to oscillate or to become unstable and split, leading each branch to repeat the same type of behavior. These behaviors can be captured numerically. For a very narrow set of parameters, numerical simulations seem to reveal a fourth regime, periodic but non-oscillatory which has not been observed in experiments.

Numerical simulation of Yuse and Sano’s quenching experiments, for different values of the quenching velocity and temperature contrast.

The wide variety of qualitative results and their lack of symmetry suggest that this problem admit many local minimizers, a challenging issue in numerical simulations. Is this periodic but non oscillatory regime a local minimizer with little physical relevance, or is it a new behavior that has yet to be observed in experiments?


  1. Bahat, D. (1991). Tectonofractography. Berlin: Springer Verlag.
  2. Yuse, A., & Sano, A. M. (1993). Transition between crack patterns in quenched glass plates. Nature, 362, 329–330. DOI:10.1038/362329a0
  3. Ronsin, O., Heslot, F., & Perrin, B. (1995). Experimental Study of Quasistatic Brittle Crack Propagation. Phys. Rev. Lett., 75(12), 2352–2355. DOI:10.1209/epl/i1997-00264-2
  4. Ronsin, O., & Perrin, B. (1997). Multi-fracture propagation in a directional crack growth experiment. Europhys. Lett., 38(6), 435–440.
  5. Ronsin, O., & Perrin, B. (1998). Dynamics of quasistatic directional crack growth. Phys. Rev. E, 58(6), 7878–7886. DOI:10.1103/PhysRevE.58.7878
  6. Yang, B., & Ravi-Chandar, K. (2000). Crack path instabilities in a quenched glass plate. J. Mech. Phys. Solids, 49, 91–130. DOI:10.1016/S0022-5096(00)00022-3