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28 March 2024
 
  » arxiv » cond-mat/0503724

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Scaling of Fracture Strength in Disordered Quasi-Brittle Materials
Phani Kumar V.V. Nukala ; Srdjan Simunovic ;
Date 31 Mar 2005
Journal Eur. Phys. J. B 37, 91-100 (2004)
Subject Materials Science; Statistical Mechanics | cond-mat.mtrl-sci cond-mat.stat-mech
AbstractThis paper presents two main results. The first result indicates that in materials with broadly distributed microscopic heterogeneities, the fracture strength distribution corresponding to the peak load of the material response does not follow the commonly used Weibull and (modified) Gumbel distributions. Instead, a {it lognormal} distribution describes more adequately the fracture strengths corresponding to the peak load of the response. Lognormal distribution arises naturally as a consequence of multiplicative nature of large number of random distributions representing the stress scale factors necessary to break the subsequent "primary" bond (by definition, an increase in applied stress is required to break a "primary" bond) leading up to the peak load. Numerical simulations based on two-dimensional triangular and diamond lattice topologies with increasing system sizes substantiate that a {it lognormal} distribution represents an excellent fit for the fracture strength distribution at the peak load. The second significant result of the present study is that, in materials with broadly distributed microscopic heterogeneities, the mean fracture strength of the lattice system behaves as $mu_f = frac{mu_f^star}{(Log L)^psi} + frac{c}{L}$, and scales as $mu_f approx frac{1}{(Log L)^psi}$ as the lattice system size, $L$, approaches infinity.
Source arXiv, cond-mat/0503724
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