Probabilistic Mechanics of Quasibrittle Structures Strength, Lifetime, and Size Effect

Quasibrittle (or brittle heterogeneous) materials are becoming increasingly important for modern engineering. They include concretes, rocks, fiber composites, tough ceramics, sea ice, bone, wood, stiff soils, rigid foams, glass, dental and biomaterials, as well as all brittle materials on the micro or nano scale. Their salient feature is that the fracture process zone size is non-negligible compared to the structural dimensions. This causes intricate energetic and statistical size effects and leads to size-dependent probability distribution of strength, transitional between Gaussian and Weibullian. The ensuing difficult challenges for safe design are vanquished in this book, which features a rigorous theory with detailed derivations yet no superfluous mathematical sophistication; extensive experimental verifications; and realistic approximations for design. A wide range of subjects is covered, including probabilistic fracture kinetics at nanoscale, multiscale transition, statistics of structural strength and lifetime, size effect, reliability indices, safety factors, and ramification to gate dielectrics breakdown.

1. Introduction; 2. Review of classical statistical theory of structural strength and structural safety, and of classical fundamentals; 3. Review of fracture mechanics and deterministic size effect in quasibrittle structures; 4. Failure statistics of nanoscale structures; 5. Nano-macro scale bridging of probability distributions of static and fatigue strengths; 6. Multiscale modeling of fracture kinetics and size effect under static and cyclic fatigue; 7. Size effect on probability distributions of strength and lifetime of quasibrittle structures; 8. Computation of probability distributions of structural strength and lifetime; 9. Indirect determination of strength statistics of quasibrittle structures; 10. Statistical distribution and size effect on residual strength after sustained load; 11. Size effect on reliability indices and safety factors; 12. Crack length effect on scaling of structural strength and type 1 to 2 transition; 13. Effect of stress singularities on scaling of structural strength; 14. Lifetime of high-k gate dielectrics and its analogy with failure statistics of quasibrittle structures.

Zdenek P. Bazant received his PhD from the Czechoslovak Academy of Sciences in 1963.He joined Northwestern University, Illinois in 1969, where he has been W. P. Murphy Professor since 1990 and simultaneously McCormick Institute Professor since 2002, and Director of the Center for Geomaterials (1981–7). He is a member of the US National Academy of Sciences, the US National Academy of Engineering, the American Academy of Arts and Sciences, and the Royal Society of London, as well as the Austrian Academy of Sciences, the Engineering Academy of the Czech Republic, the Italian National Academy, the Spanish Royal Academy of Engineering, the Istituto Lombardo, Milan, the Academia Europaea, London, and the European Academy of Sciences and Arts. Bazant is an Honorary Member of the American Society of Civil Engineers (ASCE), the American Society of Mechanical Engineers (ASME), the American Concrete Institute, and RILEM (International Union of Laboratories and Experts in Construction Materials, Systems and Structures), Paris. He has received the Austrian Cross of Honor for Science and Art, First Class, 7 honorary doctorates, ASME Timoshenko, Nadai and Warner Medals, the ASCE von Karman, Newmark, Biot, Mindlin and Croes Medals and Lifetime Achievement Award, the Society of Engineering Science William Prager Medal, and the RILEM L'Hermite Medal, among others. He is the author of Scaling of Structural Strength (2002), Inelastic Analysis of Structures (with Milan Zirásek, 2001), Fracture and Size Effect in Concrete and Other Quasibrittle Materials (with Jaime Planas, 1997), Stability of Structures (with Luigi Cedolin, 2010) and Concrete at High Temperatures (with Maurice F. Kaplan, 1996). In 2015, ASCE established ZP Bažant Medal for Failure and Damage Prevention. He is one of the original top 100 ISI Highly Cited Scientists in Engineering (www.ISIhighlycited.com).
Jia-Liang Le is currently Associate Professor of Civil, Environmental, and Geo-Engineering at the University of M