Crack Propagation as a Free Boundary Problem


Article Preview

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a sharp interface method and a phase field approach to investigate the model. The simulations confirm analytical predictions for fast crack propagation.



Key Engineering Materials (Volumes 345-346)

Edited by:

S.W. Nam, Y.W. Chang, S.B. Lee and N.J. Kim




R. Spatschek et al., "Crack Propagation as a Free Boundary Problem", Key Engineering Materials, Vols. 345-346, pp. 429-432, 2007

Online since:

August 2007




[1] A. A. Griffith, Philos. Trans. R. Soc. A 21, 163 (1921).

[2] L. B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, (1998).

[3] J. Hauch et al., Phys. Rev. Lett. 82, 3823 (1999).

[4] A. Karma, D. Kessler, and H. Levine, Phys. Rev. Lett. 87, 045501 (2001); A. Karma and A. Lobkovsky, Phys. Rev. Lett. 92, 245510 (2004).

[5] H. Henry and H. Levine, Phys. Rev. Lett. 93, 105504 (2004).

[6] I. S. Aranson, V. A. Kalatsky, and V. M. Vinokur, Phys. Rev. Lett. 85, 118 (2000); L. Eastgate et al., Phys. Rev. E 65, 036117 (2002).

[7] K. Kassner et al., Phys. Rev E 63, 036117 (2001).

[8] J. Fineberg and M. Marder, Phys. Rep. 313, 1 (1999).

[9] E. A. Brener and R. Spatschek, Phys. Rev. E 67, 016112 (2003).

[10] R. Spatschek, M. Hartmann, E. Brener, H. Müller-Krumbhaar, and K. Kassner, Phys. Rev. Lett. 96, 015502 (2006).

[11] R. J. Asaro and W. A. Tiller, Metall. Tran. 3, 1789 (1972); M. A. Grinfeld, Sov. Phys. Dokl. 31, 831 (1986).

[12] P. Nozières, J. Phys. I France 3, 681 (1993).

[13] D. Pilipenko, R. Spatschek, E. Brener, and H. Müller-Krumbhaar, submitted for publication.

Fetching data from Crossref.
This may take some time to load.