The Ohio State University

Abstract:
For ductile structures, the strength distribution is known to be Gaussian (normal), and for brittle structures Weibullian. However, from Maxwell-Boltzmann type statistics of thermal fluctuations and stress dependence of the activation energy barrier of the free energy potential of an atomic system of a rupturing nano-scale connection it may be inferred that, for quasibrittle structures failing at macro-crack initiation from one representative volume element (RVE) of material, the distribution type changes with structure size (as well as geometry) from essentially Gaussian for one RVE size to perfectly Weibullian for infinite size of structures following the weakest-link model. Noting that, relative to the standard deviation of strength, the distance from the mean to the point of failure probability 10-6 is roughly doubled when passing from Gaussian to Weibull distribution, one finds that the safety factors for strength (or ‘understrength' factors) of large concrete structures, as well as the strength and lifetime of large fiber-composite parts of modern aircraft and ships, must be considered as size (and shape) dependent. So must be the mean and the coefficient of variation of strength. For structural lifetime, the size effect is shown to be more pronounced than it is for strength. The transitional probability distribution of strength does not allow a closed-form analytical expression, but can be calculated numerically and approximated by asymptotic matching. From the stress-dependence of nano-scale activation energy, it is further deduced that the threshold of Weibull distribution of strength must be zero. This requires major corrections of reliability predictions of advanced tough ceramics, for which the use of non-zero threshold has recently become widespread. Experimental verifications are presented and computational modeling is discussed.

Bio:
Born and educated in Prague (Ph.D. 1963), Bazant joined Northwestern in 1969, where he has been W.P. Murphy Professor since 1990 and simultaneously McCormick Institute Professor since 2002. He was inducted to NAS and NAE, as well as Italian National Academy (dei Lincei), Austrian Academy of Sciences, Czech Academy of Engrg. and Lombard Academy. An ASCE Hon. Member, he received six honorary doctorates (Prague, Karlsruhe, Colorado, Milan, Lyon, Vienna), ASCE von Krmán, Newmark and Croes Medals, SES Prager Medal, ASME Warner Medal, RILEM L'Hermite Medal, Torroja Medal, etc. He authored six books: Scaling of Structural Strength, Inelastic Analysis, Fracture and Size Effect, Stability of Structures, Concrete at High Temperatures, and Concrete Creep. His H-index is 42 (www.ISIhighlycited.com); www.civil.northwestern.edu/people/bazant.html.