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Fracture Strength: Stress Concentration, Extreme Value Statistics, and the Fate of the Weibull Distribution

Zsolt Bertalan1, Ashivni Shekhawat2,3, James P. Sethna4, and Stefano Zapperi5,1,*

  • 1ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy
  • 2Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
  • 3Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 4LASSP, Physics Department, Cornell University, Ithaca, New York 14853-2501, USA
  • 5CNR, IENI, Via Roberto Cozzi 53, 20125 Milano, Italy

  • *stefano.zapperi@cnr.it
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Phys. Rev. Applied 2, 034008 – Published 17 September, 2014

DOI: https://doi.org/10.1103/PhysRevApplied.2.034008

Abstract

The statistical properties of fracture strength of brittle and quasibrittle materials are often described in terms of the Weibull distribution. However, the weakest-link hypothesis, commonly used to justify it, is expected to fail when fracture occurs after significant damage accumulation. Here we show that this implies that the Weibull distribution is unstable in a renormalization-group sense for a large class of quasibrittle materials. Our theoretical arguments are supported by numerical simulations of disordered fuse networks. We also find that for brittle materials such as ceramics, the common assumption that the strength distribution can be derived from the distribution of preexisting microcracks by using Griffith’s criteria is invalid. We attribute this discrepancy to crack bridging. Our findings raise questions about the applicability of Weibull statistics to most practical cases.

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Phys. Rev. Applied 2, 034008– Published 17 September, 2014
  • Received 17 April 2014
Article part of CHORUS

© 2014 American Physical Society

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