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Plasticity and avalanche behaviour in microfracturing phenomena

Nature volume 388, pages 658–660 (1997)Cite this article

Abstract

Inhomogeneous materials, such as plaster or concrete, subjected to an external elastic stress display sudden movements owing to the formation and propagation of microfractures. Studies of acoustic emission from these systems reveal power-law behaviour1. Similar behaviour in damage propagation has also been seen in acoustic emission resulting from volcanic activity2 and hydrogen precipitation in niobium3. It has been suggested that the underlying fracture dynamics in these systems might display self-organized criticality4, implying that long-ranged correlations between fracture events lead to a scale-free cascade of ‘avalanches’. A hierarchy of avalanche events is also observed in a wide range of other systems, such as the dynamics of random magnets5 and high-temperature superconductors6 in magnetic fields, lung inflation7 and seismic behaviour characterized by the Gutenberg–Richter law8. The applicability of self-organized criticality to microfracturing has been questioned9,10, however, as power laws alone are not unequivocal evidence for it. Here we present a scalar model of microfracturing which generates power-law behaviour in properties related to acoustic emission, and a scale-free hierarchy of avalanches characteristic of self-organized criticality. The geometric structure of the fracture surfaces agrees with that seen experimentally. We find that the critical steady state exhibits plastic macroscopic behaviour, which is commonly observed in real materials.

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Figure 1: The damage for a system of size L = 64.
Figure 2: The I–V characteristics of the present model for different values of the parameter a (see text).
Figure 3: a, The number of broken bonds s as a function of time.
Figure 4: The distribution of energy bursts, related to the experimentally observed acoustic emission.
Figure 5: The distribution of quiescent intervals Δt between two avalanches in the plastic state.

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Acknowledgements

We thank G. Caldarelli, R. Cuerno, J. Kertész, H. J. Herrmann, K. B. Lauritsen, A. Petri, C. Rebbi and P. Stroeven for suggestions and discussions. The Center for Polymer Studies is supported by NSF.

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Authors and Affiliations

  1. Center for Polymer Studies and Department of Physics, Boston University, Boston, 02215, Massachusetts, USA

    Stefano Zapperi & H. Eugene Stanley

  2. Instituut-Lorentz, University of Leiden, PO Box 9506, 2300 RA, Leiden, The Netherlands

    Alessandro Vespignani

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  1. Stefano Zapperi
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Correspondence to Stefano Zapperi.

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Zapperi, S., Vespignani, A. & Stanley, H. Plasticity and avalanche behaviour in microfracturing phenomena. Nature 388, 658–660 (1997). https://doi.org/10.1038/41737

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