Size effect on strength and lifetime distributions of quasibrittle structures

Zdeněk P. Bažant, Jia Liang Le

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


Engineering structures such as aircraft, bridges, dams, nuclear containments and ships, as well as computer circuits, chips and MEMS, should be designed for failure probability < 10-6-10-7 per lifetime. The safety factors required to ensure it are still determined empirically, even though they represent much larger and much more uncertain corrections to deterministic calculations than do the typical errors of modern computer analysis of structures. The empirical approach is sufficient for perfectly brittle and perfectly ductile structures since the cumulative distribution junction (cdf) of random strength is known, making it possible to extrapolate to the tail from the mean and variance. However, the empirical approach does not apply to structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared to structure size. This paper presents a refined theory on the strength distribution of quasibrittle structures, which is based on the fracture mechanics of nanocracks propagating by activation energy controlled small jumps through the atomic lattice and an analytical model for the multi-scale transition of strength statistics. Based on the power law for creep crack growth rate and the cdf of material strength, the lifetime distribution of quasibrittle structures under constant loads is derived. Both the strength and lifetime cdf's are shown to be size- and geometry- dependent. The theory predicts intricate size effects on both the mean structural strength and lifetime, the latter being much stronger. The theory is shown to match the experimentally observed systematic deviations of strength and lifetime histograms of industrial ceramics from the Weibull distribution.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages9
ISBN (Print)9780791843840
StatePublished - 2010
EventASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009 - Lake Buena Vista, FL, United States
Duration: Nov 13 2009Nov 19 2009

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings


OtherASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009
Country/TerritoryUnited States
CityLake Buena Vista, FL


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