journal article·2003-05

Scaling and dynamics of an interfacial crack front

Knut JØrgen MÅLØY, Jean SCHMITTBUHL, Alex HANSEN, G. George BATROUNI

International Journal of Fracture· Volume 121· Issue 1-2
Publisher page

Abstract

We report on in situ observations with a high speed CCD camera of an in-plane crack propagating through a transparent heterogeneous Plexiglas block. The toughness is controlled artificially and fluctuates spatially as a random noise. A stable crack in mode I was monitored by loading the system by an imposed displacement. We show that the movement of the fracture front is controlled by local instabilities triggered by the depinning of asperities even for very slow loading. Development of crack roughness is described in terms of a Family-Vicsek scaling with a roughness exponent ζ=0.60 and a dynamical exponent κ=1.2. We also study the system numerically using a Green function technique. We find ζ=0.6 and κ=1.5 in contrast to earlier numerical studies that reported a much smaller roughness exponent ζ≈1/3. We discuss this discrepancy.
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Research context

OpenAlex topics: Theoretical and Computational Physics · Random lasers and scattering media · Landslides and related hazards

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References (34)

Show source-provided references
1. Åström, J.A., Alava, M. and Timonen, J. (2000). Roughening of a propagating planar crack front. Phys. Rev. E62, 2878.
2. Batrouni, G.G. and Hansen, A. (1988). Fourier acceleration of iterative processes in disordered systems. J. Stat. Phys. 52, 747.10.1007/BF01019728 ↗
3. Batrouni, G.G., Hansen, A. and Schmittbuhl, J. (2002). Heterogeneous interfacial failure between two elastic blocks. Phys. Rev. E65, 036126.
4. Bouchaud, E. (1997). Scaling properties of cracks. J. Phys. Condens. Matter 9, 4319.10.1088/0953-8984/9/21/002 ↗
5. Bouchaud, J.P., Bouchaud, E., Lapaset, G. and Planés, J. (1993). Models of fractal cracks. Phys. Rev. Lett. 71, 2240.10.1103/PhysRevLett.71.2240 ↗
6. Bouchaud, E., Bouchaud, J.P., Fisher, D.S., Ramanathan, S. and Rice, J. (2002). Can crack waves explain the roughness of cracks? J. Mech. Phys. Solids 50, 1703.10.1016/S0022-5096(01)00137-5 ↗
7. Bouchaud, E., Lapasset, G. and Planés, J. (1990). Fractal dimension of fractured surfaces: A universal value? Europhys. Letters 13, 73.10.1209/0295-5075/13/1/013 ↗
8. Brown, S.R. and Scholz, C.H. (1985). Broad bandwidth study of the topography of natural rock surfaces. J. Geophys. Res. 90, 12575.10.1029/JB090iB14p12575 ↗
9. Chauve, P., Le Doussal, P. and Wiese, K.J. (2001). Renormalization of pinned elastic systems: How does it work beyond one loop?. Phys. Rev. Letters 86, 1785.10.1103/PhysRevLett.86.1785 ↗
10. Cox, B.L. and Wang, J.S.Y. (1993). Fractal surfaces: measurement and application in earth sciences. Fractals 1, 87.10.1142/S0218348X93000125 ↗
11. Delaplace, A., Schmittbuhl, J. and Måløy, K.J. (1999). High resolution description of a crack front in a heterogeneous Plexiglas block. Phys. Rev. E60, 1337.
12. Ertas, D. and Kardar, M. (1994). Critical dynamics of contact line depinning. Phys. Rev. E49, 2532.
13. Family, F. and Vicsek, T. (1985). Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model. J. Phys. A18, L75.
14. Gao, H. and Rice, J.R. (1989). A first order perturbation analysis of trap cracking by arrays of obstacles. ASME J. Appl. Mech. 56, 828.10.1115/1.3176178 ↗
15. Johnson, K.L. (1985). Contact Mechanics, Cambridge University Press, Cambridge.10.1017/CBO9781139171731 ↗
16. Landau, L. and Lifshitz, E.M. (1958). Theory of Elasticity. Clarendon Press, Oxford.
17. Måløy, K.J. and Schmittbuhl, J. (2001). Dynamical events during slow crack propagation. Phys. Rev. Lett. 87, 105502.10.1103/PhysRevLett.87.105502 ↗
18. Måløy, K.J., Hansen, A., Hinrichsen, E.L., and Roux, S. (1992). Experimental measurements of the roughness of brittle cracks. Phys. Rev. Lett. 68, 213.10.1103/PhysRevLett.68.213 ↗
19. Mandelbrot, B.B, Passoja, D.E. and Paullay, A.J. (1984). Fractal character of fracture surfaces of metals. Nature 308, 721.10.1038/308721a0 ↗
20. Morrissey, J.W. and Rice, J.R. (1998). Crack front waves. J. Mech. Phys. Solids 46, 467.10.1016/S0022-5096(97)00072-0 ↗
21. Morrissey, J.W. and Rice, J.R. (2000). Perturbative simulations of crack front waves. J. Mech. Phys. Solids 48, 1229.10.1016/S0022-5096(99)00069-1 ↗
22. Perrin, G. and Rice, J.R. (1994). Disordering of dynamic planar crack front in a model elastic medium of random variable toughness. J. Mech. Phys. Solids 42, 1047.10.1016/0022-5096(94)90083-3 ↗
23. Press, H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992). Numerical Recipes in Fortran 77: the Art of Scientific Computing. Cambridge University Press, Cambridge.
24. Prevost, A., Rolley, E. and Guthmann, C. (2002). Dynamics of helium-4 meniscus on a strongly disordered cesium substrate. Phys. Rev. B65, 064517.10.1103/PhysRevB.65.064517 ↗
25. Ramanathan, S. and Fisher, D.S. (1997). Dynamics and instability of planar cracks in heterogeneous media. Phys. Rev. Lett. 79, 877.10.1103/PhysRevLett.79.877 ↗
26. Ramanathan, S. and Fisher, D.S. (1998). Onset and propagation of planar cracks in heterogeneous media. Phys. Rev. B58, 6026.10.1103/PhysRevB.58.6026 ↗
27. Rosso, A. and Krauth, W. (2002). Roughness at the depinning threshold for a long-range elastic string. Phys. Rev. E65, 025101.
28. Roux, S. and Hansen, A. (1994). Interfacial roughening and pinning. J. Phys. I4, 515.
29. Schmittbuhl, J. and Måløy, K.J. (1997). Direct observation of a self-affine crack propagation. Phys. Rev. Lett. 78, 3888.10.1103/PhysRevLett.78.3888 ↗
30. Schmittbuhl, J., Delaplace, A. and Måløy, K.J. (2000). Propagation of an interfacial crack front in an heterogeneous medium: experimental observations. Physical Aspects of Fracture (Edited by E. Bouchaud, D. Jeulin and C. Prioul), Kluwer Academic Publishers, Dordrecht, Holland.
31. Schmittbuhl, J., Gentier, S. and Roux, S. (1993). Field measurements of the roughness of falt surfaces. Geophys. Res. Lett. 20, 639.10.1029/93GL00170 ↗
32. Schmittbuhl, J., Hansen, A. and Batrouni, G.G. (2003). Roughness of interfacial crack fronts: Stress-weighted percolation in the damage zone. Phys. Rev. Lett. 90, 045505.10.1103/PhysRevLett.90.045505 ↗
33. Schmittbuhl, J., Schmitt, F. and Scholz, C.H. (1995). Scaling invariance of crack surfaces. J. Geophys. Res. 100, 5953.10.1029/94JB02885 ↗
34. Schmittbuhl, J., Roux, S., Vilotte, J.P. and Måløy, K.J. (1995). Interfacial crack pinning: Effect of nonlocal interactions. Phys. Rev. Letters 74, 1787.10.1103/PhysRevLett.74.1787 ↗