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Transition between crack patterns in quenched glass plates

Abstract

THE study of fracture is an old topic1, but only recently has an understanding begun to emerge of crack formation, propagation and morphology (which is often fractal) 2–8. When a brittle material such as glass is broken under tensile stress9, the cracks have a complicated morphology10. Fineberg et al.11 showed that this process may be caused by a dynamic instability, whereby the speed of crack propagation increases until it approaches the speed of sound: at this point, complex structures appear. But crack morphology in quasistatic fracture, where the speed of the crack tip is much smaller than the speed of sound, can also exhibit marked changes12. Here we present studies of crack propagation in glass plates caused by sudden but carefully controlled cooling. We observe a transition from straight to regular, wavy cracks as the tip speed increases. The scaling behaviour of an appropriately defined relaxation time suggests that this transition is a Hopf bifurcation13, like those seen in a variety of other nonlinear systems. At still higher speeds, the oscillatory cracks split into first two and then four or more branches.

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References

  1. Griffith, A. A. Phil. Trans. R. Soc. A221, 163–198 (1920).

    ADS  Google Scholar 

  2. Herrmann, H. J. & Roux, S. (eds) Statistical Models for the Fracture of Disordering Media (North-Holland, Amsterdam, 1990).

  3. Charmet, J. C., Roux, S. & Guyon, E. (eds) Disorder and Fracture (Plenum, New York, 1990).

    Google Scholar 

  4. Mandelbrot, B. B. & Paullay, D. E. Nature 308, 721–722 (1984).

    Article  ADS  CAS  Google Scholar 

  5. Takayasu, H. Prog. theor. Phys. 74, 1343–1345 (1985).

    Article  ADS  Google Scholar 

  6. Skjeltop, A. T. & Meakin, P. Nature 335, 424–426 (1988).

    Article  ADS  Google Scholar 

  7. Herrmann, H. J., Kertesz, J. & de Arcangelis, L. Europhys. Lett. 10, 147–152 (1989).

    Article  ADS  Google Scholar 

  8. Mori, Y., Kaneko, K. & Wadachi, M., J. phys. Soc. Japan, 60, 1591–1599 (1991).

    Article  ADS  CAS  Google Scholar 

  9. Yoffe, E. H. Phil. Mag. 42, 739–750 (1951).

    Article  MathSciNet  Google Scholar 

  10. Ravi-Chandar, K. & Knauss, W. G. Int. J. Fracture 25, 247–252 (1984); 26, 65–80 (1984); 26, 141–154 (1984); 26, 189–200 (1984).

    Article  Google Scholar 

  11. Fineberg, J., Gross, S. P., Marder, M. & Swinney, H. L. Phys. Rev. Lett. 67, 457–460 (1991).

    Article  ADS  CAS  Google Scholar 

  12. Hirata, M. Scient. Pap. Inst. phys. chem. Res. (Japan) 16, 172–195 (1931).

    Google Scholar 

  13. Guckenheimer, J. & Holmes, P. Nonlinear Oscillations and Bifurcation of Vector Fields (Springer. Berlin. 1983).

    Book  Google Scholar 

  14. Stevels, J. M. in Handbuch der Physik Vol. 13 (ed. Flugge, S.) (Springer, Berlin, 1962).

    Google Scholar 

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Yuse, A., Sano, M. Transition between crack patterns in quenched glass plates. Nature 362, 329–331 (1993). https://doi.org/10.1038/362329a0

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