TY - JOUR

T1 - Scaling of static fracture of quasi-brittle structures

T2 - Strength, lifetime, and fracture kinetics

AU - Le, Jia Liang

AU - Bažant, Zdeněk P.

PY - 2012

Y1 - 2012

N2 - The paper reviews a recently developed finite chain model for the weakest-link statistics of strength, lifetime, and size effect of quasi-brittle structures, which are the 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 nanoscale 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 failure probability tail at nanoscale and its transition from nano-to macroscale makes it possible to derive the distribution of structural strength, the static crack growth rate, and the lifetime distribution, including the size and geometry effects while an extension to fatigue crack growth rate and lifetime, published elsewhere (Le and Baant, 2011, Unified Nano-Mechanics Based Probabilistic Theory of Quasibrittle and Brittle Structures: II. Fatigue Crack Growth, Lifetime and Scaling, J. Mech. Phys. Solids, 1322-1337), is left aside. A salient practical aspect of the theory is that for quasi-brittle structures 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 structural strength distribution, and (3) an effective method to determine the cumulative distribution functions (cdf's) of structural 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.

AB - The paper reviews a recently developed finite chain model for the weakest-link statistics of strength, lifetime, and size effect of quasi-brittle structures, which are the 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 nanoscale 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 failure probability tail at nanoscale and its transition from nano-to macroscale makes it possible to derive the distribution of structural strength, the static crack growth rate, and the lifetime distribution, including the size and geometry effects while an extension to fatigue crack growth rate and lifetime, published elsewhere (Le and Baant, 2011, Unified Nano-Mechanics Based Probabilistic Theory of Quasibrittle and Brittle Structures: II. Fatigue Crack Growth, Lifetime and Scaling, J. Mech. Phys. Solids, 1322-1337), is left aside. A salient practical aspect of the theory is that for quasi-brittle structures 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 structural strength distribution, and (3) an effective method to determine the cumulative distribution functions (cdf's) of structural 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.

UR - http://www.scopus.com/inward/record.url?scp=84859919535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859919535&partnerID=8YFLogxK

U2 - 10.1115/1.4005881

DO - 10.1115/1.4005881

M3 - Review article

AN - SCOPUS:84859919535

VL - 79

JO - Journal of Applied Mechanics, Transactions ASME

JF - Journal of Applied Mechanics, Transactions ASME

SN - 0021-8936

IS - 3

M1 - 031006

ER -