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The fracture strength distribution of materials is often described in termsof the Weibull law which can be derived by using extreme value statistics ifelastic interactions are ignored. Here, we consider explicitly the interplaybetween elasticity and disorder and test the asymptotic validity of the Weibulldistribution through numerical simulations of the two-dimensional random fusemodel. Even when the local fracture strength follows the Weibull distribution,the global failure distribution is dictated by stress enhancement at the tip ofthe cracks and sometimes deviates from the Weibull law. Only in the case of apre-existing power law distribution of crack widths do we find that the failurestrength is Weibull distributed. Contrary to conventional assumptions, even inthis case, the Weibull exponent can not be simply inferred from the exponent ofthe initial crack width distribution. Our results thus raise some concerns onthe applicability of the Weibull distribution in most practical cases.

Fracture strength: Stress concentration, extreme value statistics and the fate of the Weibull distribution