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Probabilistic mechanics of quasibrittle structures : strength, lifetime, and size effect / Zdenek P. Bazant, Northwestern University, Jia-Liang Le, University of Minnesota

Author
Bažant, Z. P.
Additional Titles
Probabilistic mechanics of quasi brittle structures
Published
Cambridge : Cambridge University Press, 2017.
Physical Description
1 online resource
Additional Creators
Le, Jia-Liang, 1980-
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Contents
Machine generated contents note: 1.Introduction -- 1.1.The Problem of Tail of Probability Distribution -- 1.2.History in Brief -- 1.2.1.Classical History -- 1.2.2.Recent Developments -- 1.3.Safety Specifications in Concrete Design Codes and Embedded Obstacles to Probabilistic Analysis -- 1.4.Importance of Size Effect for Strength Statistics -- 1.5.Power-Law Scaling in the Absence of Characteristic Length -- 1.5.1.Nominal Strength of Structure and Size Effect -- 1.6.Statistical and Deterministic Size Effects -- 1.7.Simple Models for Deterministic Size Effects -- 1.7.1.Type 1 Size Effect for Failures at Crack Initiation -- 1.7.2.Type 2 Size Effect for Structures with Deep Cracks or Notches -- 1.8.Probability Distributions of Strength of Ductile and Brittle Structures -- 2.Review of Classical Statistical Theory of Structural Strength and Structural Safety, and of Statistics Fundamentals -- 2.1.Weakest-Link Model -- 2.2.Weibull Theory -- 2.3.Scaling of Weibull Theory and Pure Statistical Size Effect -- 2.4.Equivalent Number of Elements -- 2.5.Stability Postulate of Extreme Value Statistics -- 2.6.Distributions Ensuing from Stability Postulate -- 2.7.Central Limit Theorem and Strength Distribution of Ductile Structures -- 2.8.Failure Probability When Both the Strength and Load Are Random, and Freudenthal Integral -- 3.Review of Fracture Mechanics and Deterministic Size Effect in Quasibrittle Structures -- 3.1.Linear Elastic Fracture Mechanics -- 3.2.Cohesive Crack Model -- 3.3.Crack Band Model -- 3.4.Nonlocal Damage Models and Lattice-Particle Model -- 3.5.Overcoming Instability of Tests of Post-Peak Softening of Fiber-Polymer Composites -- 3.6.Dimensional Analysis of Asymptotic Size Effects -- 3.7.Second-Order Asymptotic Properties of Cohesive Crack or Crack Band Models -- 3.8.Types of Size Effect Distinguished by Asymptotic Properties -- 3.9.Derivation of Quasibrittle Deterministic Size Effect from Equivalent LEFM -- 3.9.1.Type 2 Size Effect -- 3.9.2.Type 1 Size Effect -- 3.10.Nonlocal Weibull Theory for Mean Response -- 3.11.Combined Energetic-Statistical Size Effect Law and Bridging of Type 1 and 2 Size Effects -- 4.Failure Statistics of Nanoscale Structures -- 4.1.Background of Modeling of Nanoscale Fracture -- 4.2.Stress-Driven Fracture of Nanoscale Structures -- 4.3.Probability Distribution of Fatigue Strength at Nanoscale -- 4.4.Random Walk Aspect of Failure of Nanoscale Structures -- 5.Nano--Macroscale Bridging of Probability Distributions of Static and Fatigue Strengths -- 5.1.Chain Model -- 5.2.Fiber-Bundle Model for Static Strength -- 5.2.1.Brittle Bundle -- 5.2.2.Plastic Bundle -- 5.2.3.Softening Bundle with Linear Softening Behavior -- 5.2.4.Bundle with General Softening Behavior and Nonlocal Interaction -- 5.3.Fiber-Bundle Model for Fatigue Strength -- 5.4.Hierarchical Model for Static Strength -- 5.5.Hierarchical Model for Fatigue Strength -- 6.Multiscale Modeling of Fracture Kinetics and Size Effect under Static and Cyclic Fatigue -- 6.1.Previous Studies of Fracture Kinetics -- 6.2.Fracture Kinetics at Nanoscale -- 6.3.Multiscale Transition of Fracture Kinetics for Static Fatigue -- 6.4.Size Effect on Fracture Kinetics under Static Fatigue -- 6.5.Multiscale Transition of Fracture Kinetics under Cyclic Fatigue -- 6.6.Size Effect on Fatigue Crack Growth Rate and Experimental Evidence -- 6.7.Microplane Model for Size Effect on Fatigue Kinetics under General Loading -- 7.Size Effect on Probability Distributions of Strength and Lifetime of Quasibrittle Structures -- 7.1.Probability Distribution of Structural Strength -- 7.2.Probability Distribution of Structural Lifetime -- 7.2.1.Creep Lifetime -- 7.2.2.Fatigue Lifetime -- 7.3.Size Effect on Mean Structural Strength -- 7.4.Size Effects on Mean Structural Lifetimes and Stress-Life Curves -- 7.5.Effect of Temperature on Strength and Lifetime Distributions -- 8.Computation of Probability Distributions of Structural Strength and Lifetime -- 8.1.Nonlocal Boundary Layer Model for Strength and Lifetime Distributions -- 8.2.Computation by Pseudo-random Placing of RVEs -- 8.3.Approximate Closed-Form Expression for Strength and Lifetime Distributions -- 8.4.Analysis of Strength Statistics of Beams under Flexural Loading -- 8.5.Optimum Fits of Strength and Lifetime Histograms -- 8.5.1.Optimum Fits of Strength Histograms -- 8.5.2.Optimum Fits of Histograms of Creep Lifetime -- 8.5.3.Optimum Fits of Histograms of Fatigue Lifetime -- 9.Indirect Determination of Strength Statistics of Quasibrittle Structures -- 9.1.Relation between Mean Size Effect Curve and Probability Distribution of RVE Strength -- 9.2.Experimental Verification -- 9.2.1.Description of Experiments -- 9.2.2.Analysis of Test Results -- 9.3.Determination of Large-Size Asymptotic Properties of the Size Effect Curve -- 9.4.Comparison with the Histogram Testing Method -- 9.5.Problems with the Three-Parameter Weibull Distribution of Strength -- 9.5.1.Theoretical Argument -- 9.5.2.Evidence from Histogram Testing -- 9.5.3.Mean Size Effect Analysis -- 9.6.Alternative Proof of Strength Distribution of an RVE Based on Stability Postulate and Atomistic Analysis -- 10.Statistical Distribution and Size Effect on Residual Strength after Sustained Load -- 10.1.Nanomechanics Based Relation between Monotonic Strength and Residual Strength of One RVE -- 10.2.Analysis of Residual Strength Degradation for One RVE -- 10.3.Probability Distribution of Residual Strength -- 10.3.1.Formulation of Statistics of Residual Strength for One RVE -- 10.3.2.Formulation of Residual Strength cdf of Geometrically Similar Structures of Different Sizes -- 10.4.Comparison among Strength, Residual Strength, and Lifetime Distributions -- 10.5.Experimental Validation -- 10.5.1.Optimum Fits of Strength and Residual Strength Histograms of Borosilicate Glass -- 10.5.2.Optimum Fits of Strength Histograms and Prediction of Lifetime and Mean Residual Strength for Unidirectional Glass/Epoxy Composites -- 10.5.3.Prediction of Strength Degradation Curve for Soda-Lime Silicate Glasses -- 10.6.Comparison of Size Effects on Mean Strength, Residual Strength, and Lifetime -- 11.Size Effect on Reliability Indices and Safety Factors -- 11.1.Size Effect on the Cornell Reliability Index -- 11.2.Size Effect on the Hasofer-Lind Reliability Index -- 11.3.Approximate Equation for Scaling of Safety Factors -- 11.4.Analysis of Failure Statistics of the Malpasset Arch Dam -- 11.4.1.Model Description -- 11.4.2.Discussion of Cornell and Hasofer-Lind Indices -- 11.4.3.Discussion of Central and Nominal Safety Factors -- 12.Crack Length Effect on Scaling of Structural Strength and Type 1 to 2 Transition -- 12.1.Type 1 Size Effect in Terms of Boundary Strain Gradient -- 12.2.Universal Size Effect Law -- 12.3.Verification of the Universal Size Effect Law by Comprehensive Fracture Tests -- 13.Effect of Stress Singularities on Scaling of Structural Strength -- 13.1.Strength Scaling of Structures with a V-Notch under Mode 1 Loading -- 13.1.1.Energetic Scaling of Strength of Structures with Strong Stress Singularities -- 13.1.2.Generalized Finite Weakest-Link Model -- 13.2.Numerical Simulation of Mode I Fracture of Beams with a V-Notch -- 13.2.1.Model Description -- 13.2.2.Results and Discussion -- 13.3.Scaling of Fracture of Bimaterial Hybrid Structures -- 13.3.1.Energetic Scaling with Superposed Multiple Stress Singularities -- 13.3.2.Finite Weakest-Link Model for Failure of Bimaterial Interface -- 13.4.Numerical Analysis of Bimaterial Fracture -- 13.4.1.Description of Analysis -- 13.4.2.Results and Discussion -- 14.Lifetime of High-k Gate Dielectrics and Analogy with Failure Statistics of Quasibrittle Structures -- 14.1.Deviation of Lifetime Histograms of High-k Dielectrics from the Weibull Distribution -- 14.2.Breakdown Probability -- 14.2.1.Analogy with Strength of Quasibrittle Structures -- 14.2.2.Application to Dielectric Breakdown -- 14.2.3.Microscopic Statistical Models -- 14.2.4.Breakdown Voltage Distribution -- 14.3.Breakdown Lifetime under Constant Voltage -- 14.3.1.Relation between Lifetime and Breakdown Voltage -- 14.3.2.Microscopic Physics -- 14.3.3.Probability Distribution of Breakdown Lifetime -- 14.4.Breakdown Lifetime under Unipolar AC Voltage -- 14.5.Experimental Validation -- 14.5.1.Breakdown under Constant Gate Voltage Stress -- 14.5.2.Breakdown under Unipolar AC Voltage Stress -- 14.6.Size Effect on Mean Breakdown Lifetime.
Summary
This book presents an experimentally validated probabilistic strength theory of structures made of concrete, composites, ceramics and other quasibrittle materials.
Subject(s)
ISBN
9781108135184 (electronic bk.)
1108135188 (electronic bk.)
9781316585146
131658514X
Bibliography Note
Includes bibliographical references and author index.
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