Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Zdeněk P. Bažant, Jia Liang Le, Martin Z. Bazant

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


The failure probability of engineering structures such as aircraft, bridges, dams, nuclear structures, and ships, as well as microelectronic components and medical implants, must be kept extremely low, typically <10-6. The safety factors needed to ensure it have so far been assessed empirically. For perfectly ductile and perfectly brittle structures, the empirical approach is sufficient because the cumulative distribution function (cdf) of random material strength is known and fixed. However, such an approach is insufficient for structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared with the structure size. The reason is that the strength cdf of quasibrittle structure varies from Gaussian to Weibullian as the structure size increases. In this article, a recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activation-energy-controlled, random jumps through the atomic lattice. This refinement also provides a plausible physical justification of the power law for subcritical creep crack growth, hitherto considered empirical. The theory is further extended to predict the cdf of structural lifetime at constant load, which is shown to be size- and geometry-dependent. The size effects on structure strength and lifetime are shown to be related and the latter to be much stronger. The theory fits previously unexplained deviations of experimental strength and lifetime histograms from the Weibull distribution. Finally, a boundary layer method for numerical calculation of the cdf of structural strength and lifetime is outlined.

Original languageEnglish (US)
Pages (from-to)11484-11489
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number28
StatePublished - Jul 14 2009


  • Cohesive fracture
  • Crack growth rate
  • Extreme value statistics
  • Multiscale transition
  • Size effect

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