Scaling of Static Fracture of Quasibrittle Structures: Strength, Lifetime and Fracture Kinetics
Zdenek Bazant, Jia-Liang Le
Report no. Journal of Applied Mechanics
The paper reviews a recently developed finite chain model for the weakest-link statistics of strength, lifetime and size effect of quasibrittle structures, which are structures in which the fracture process zone size is not negligible compared to the cross section size. The theory is based on the recognition that the failure probability is simple and clear only on the nano-scale since the probability and frequency of interatomic bond failures must be equal. The paper outlines how a small set of relatively plausible hypotheses about the nano-scale probability tail and its transition from nano- to macro-scale makes it possible to derive the distribution of structural strength with structural size and geometry effects, the static crack growth rate and the lifetime distribution, including the size and geometry effects on the lifetime (while an extension to fatigue crack growth rate and lifetime, published elsewhere, is left aside). A salient practical aspect of the theory is that, for quasibrittle materials, the chain model underlying the weakest-link statistics must be considered to have a finite number of links, which implies a major deviation from the Weibull distribution. Several new extensions of the theory are presented: 1) A derivation of the dependence of static crack growth rate on the structure size and geometry, 2) an approximate closed-form solution of the structure strength distribution, 3) an effective method to determine the cdf's of structure strength and lifetime based on the mean size effect curve. Finally, as an example, a probabilistic reassessment of the 1959 Malpasset Dam failure is demonstrated.
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