Scaling of fracture strength in disordered quasi-brittle materials*
Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6359, USA
Corresponding author: a firstname.lastname@example.org
Published online: 19 February 2004
This 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 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 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 , and scales as as the lattice system size, L, approaches infinity.
PACS: 62.20.Mk – Fatigue, brittleness, fracture, and cracks / 46.50.+a – Fracture mechanics, fatigue and cracks
The submitted manuscript has been authored by a contractor of the US Government under Contract No. DE-AC05-00OR22725. Accordingly, the US Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004