Recent Progress in Energetic Probablistic Scaling Laws for Quasi-Brittle Fracture
Rational determination of safety factors necessitates establishing the probability density function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf’s of the nominal strength of structure are known to be Gaussian and Weibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. The recent results are reviewed, and then mathematically extended in two ways: (1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and (2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Finally, recent experimental data are analyzed and applicability of the present theory is verified.
KeywordsProbabilistic mechanics extreme value statistics structural strength cohesive fracture scaling size effect
Unable to display preview. Download preview PDF.
- 1.Bažant, Z.P. “Scaling theory for quasibrittle structural failure.” Proceedings of the National Academy of Sciences 101 (37), 2004, 14000–14007.Google Scholar
- 4.Bažant, Z.P., and Pang, S.D. “Revision of reliability concepts for quasibrittle structures and size effect on probability distribution of structural strength.” Proceedings of the 9th International Conference on Structural Safety and Reliability (ICOSSAR), Rome, G. Augusti, G.I. Schuëller and M. Ciampoli, eds., Milpress, Rotterdam, 2005, pp. 377–386.Google Scholar
- 5.Bažant, Z.P., Vořechovský, M., and Novák, D. “Asymptotic prediction of energetic-statistical size effect from deterministic finite element solutions.” Journal of Engineering Mechanics ASCE 128, 2007, 153–162.Google Scholar
- 6.Bažant, Z.P., Vořechovský, M., and Novák, D. “Energetic-Statistical Size Effect Simulated by SFEM with Stratified Sampling and Crack Band Model.” International Journal of Numerical Methods in Engineering, 71 (11), 2007, 1297–1320.Google Scholar