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Criterion for crack formation in disordered materials Peter F. Arndt and Thomas Nattermann
 

Summary: Criterion for crack formation in disordered materials
Peter F. Arndt and Thomas Nattermann
Institut fu¨r Theoretische Physik, Universita¨t zu Ko¨ln, Zu¨lpicher Straße 77, D-50937 Ko¨ln, Germany
Received 1 September 2000; published 7 March 2001
Crack formation is conventionally described as a nucleation phenomenon despite the fact that the tempera-
tures necessary to overcome the nucleation barrier are far too high. In this paper we consider the possibility that
cracks are created due to the presence of frozen disorder e.g., heterogeneities or frozen dislocations . In
particular we calculate the probability for the occurrence of a critical crack in a quasi-two-dimensional disor-
dered elastic system. It turns out that this probability takes the form of an Arrhenius law as for thermal
nucleation but with the temperature T replaced by an effective disorder temperature Teff which depends on the
strength of the disorder. The extension of these results to d 3 dimensions is briefly discussed.
DOI: 10.1103/PhysRevB.63.134204 PACS number s : 62.20.Mk, 61.43. j
I. INTRODUCTION
Cracks are one of the most important sources for the fail-
ure of solids.1
Despite continuous efforts for more than a
century a full understanding of fracture has not yet been
reached.2­4
A simple but very appealing picture for the oc-
currence of cracks goes back to Griffith.5

  

Source: Arndt, Peter - Max-Planck-Institut für molekulare Genetik
Spang, Rainer - Computational Molecular Biology Group, Max-Planck-Institut für molekulare Genetik

 

Collections: Biology and Medicine; Biotechnology; Computer Technologies and Information Sciences; Physics