Zusammenfassung
The sample-size dependence of the strength of materials is an old problem that
is best treated with statistical mechanics. We have recently analyzed its
basics using the Random Fuse Model (1) and scaling arguments 2. These allow to
connect the classical results using extremal statistics for disordered but
statistically homogeneous systems 3 to ones with defects. This can also
be interpreted as a crossover between a disorder-induced statistical regime
and a regime controlled by the stress-concentration of the defect. The long-range elastic field enhancement of such defects is revealed by the
simulations to be partially screened by dynamically created disorder or damage.
The numerical results follow a scaling law, which contains the screening
effect in a statistical sense, as a statistical fracture process zone in the fracture mechanics language. The results are compared to experimental data from paper samples.
1) M.J. Alava, P.K.K.V. Nukala, and S. Zapperi, Adv. Phys. 55, 349 (2006).\\
2) M.J. Alava, P.K.K.V. Nukala, and S. Zapperi, submitted for publication.\\
3) P.M. Duxbury et al., Phys. Rev. Lett. 57, 1052 (1986).
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