Probabilistic Mechanics of Quasibrittle Structures

Strength, Lifetime, and Size Effect

Zdenek P. Bazant, Jia-Liang Le

• Publisher: Cambridge University Press
• Year: 2017
• Print ISBN:
  9781107151703
• eBook ISBN:
  9781108133739
• Topic: Scienze fisiche
• Subtopic: Meccanica

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.

Table of contents

• Cover
• Half title
• Title
• Copyright
• Dedication
• Contents
• Foreword
• Preface
• 1 Introduction
• 2 Review of Classical Statistical Theory of Structural Strength and Structural Safety, and of Statistics Fundamentals
• 3 Review of Fracture Mechanics and Deterministic Size Effect in Quasibrittle Structures
• 4 Failure Statistics of Nanoscale Structures
• 5 Nano–Macroscale 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 Statistics 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 Analogy with Failure Statistics of Quasibrittle Structures
• Appendix A: Power-Law Scaling of Boundary Value Problems
• Appendix B: Proof of Transitional Size Effects of Types 1 and 2 by Dimensional Analysis and Asymptotic Matching up to Second Order
• Appendix C: Proof of Small-Size Asymptotics of Cohesive Crack Model up to Second Order
• References
• Author Index
• Subject Index