Crack propagation under thermal loads
In collaboration with J.-J. Marigo (Université Pierre et Marie Curie, France)Wavy crack pattern are observed while filling up heated flasks with cold liquid, quenching glass strips, or tearing elastic films.
![Flask (credit [Bah91])](ThermalCracks_files/Flask.png)
![Oscillating crack (credit [YS93])](ThermalCracks_files/Oscillating-3.png)
![Erratic cracks (credit [YS93])](ThermalCracks_files/Erratic.png){kind=small}
images from [Bah91] (left) and [YS93]
This numerical experiment replicates the experimental
setting in [YS93] [RHP95] [RP95] [RP97] [YS97] [YR00]: 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
experiments seem to reveal a fourth regime, periodic but
non-oscillatory which has not been observed in
experiments.
clicking on each image will start an animation in a new
window
The wide variety of qualitative results and their lack
of symmetry suggest that this problem admit many local
minimizers, a challenging issue in numerical experiments.
The generalization of this experiment to more complicated
settings also raises several questions. If one quenches a
block of glass, does one obtain planar cracks that start
oscillating? Do they form patterns similar to that observed
in drying soils? Is the 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?
Support for this work was provided in part by the National
Science Foundation under grant DMS-0605320. The
computations presented in these pages have been performed
on the teragrid supercomputers, under NSF Cyber-Infrastructure Partnership
Development Allocation TG-DMS060010N.
References
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[DCP03] R.D. Deegan, S. Chheda, L. Patel, M. Marder, H.L. Swinney, J. Kim, and A. de Lozanne, Wavy and rough cracks in silicon, Phys. Rev. E 67 (2003). [DOI: 10.1103/PhysRevE.67.066209]
[RHP95] O. Ronsin, F. Heslot, and B. Perrin, Experimental study of quasistatic brittle crack propagation, Phys. Rev. Lett. 75 (1995), no. 12, 2352–2355. [DOI: 10.1103/PhysRevLett.75.2352]
[RP97] O. Ronsin and B. Perrin, Multi-fracture propagation in a directional crack growth experiment, Europhys. Lett. 38 (1997), no. 6, 435–440. [DOI: 10.1209/epl/i1997-00264-2]
[RP98] O. Ronsin and B. Perrin, Dynamics of quasistatic directional crack growth, Phys. Rev. E 58 (1998), no. 6, 7878–7886. [DOI: 10.1103/PhysRevE.58.7878]
[YR00] B. Yang and K. Ravi-Chandar, Crack path instabilities in a quenched glass plate, J. Mech. Solids. Phys. 49 (2000), 91-130. [DOI: 10.1016/S0022-5096(00)00022-3]
[YS93] A. Yuse and A.M. Sano, Transition between crack patterns in quenched glass plates, Nature 362 (1993), 329-330.
[YS97] A. Yuse and M. Sano, Instability of quasi-static crack patterns in quenched glass plates, Physica D 108 (1997), 365-378. [DOI: 10.1016/S0167-2789(97)00011-0]