A class of brittle materials, including iron, ceramics, glass and rocks, are often referred to as being defect-sensitive. The failure in these materials, which is common attributable to the presence of ubiquitous preexisting micro defects, occurs abruptly and without warning. The determination of the rupture strength of the considered class of the brittle materials with heterogeneous microstructure depends almost entirely on the extreme value statistics of the largest defects. In the heterogeneous materials with uncorrelated random microsructure (which is likely to fracture in a brittle cleavage mode), if the rupture stress is the stress at crack tip with scaling provided by the expression for stress intensity factor and if the applied stress is known, the probability of failure is of the Gumbel (double exponential) type. The Gumbel distribution belongs to a particular class of extreme-value statistics which concernes the minimum of continuous variables which are unbounded but have a distribution decaying faster than any power at -ƒ. A very intriguing thing is that in the Parisi's 'replica symmetry breaking' (RSB) scheme, the class of system with a first-order RSB,'one-step RSB', is identical to the Gumbel class. A very interesting question is: can we use the 'one-step RSB' scheme to study the fracture probability in this particular class of brittle materials?

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