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

Format:

Book

Author/Creator:

Bažant, Z. P., author.

Le, Jia-Liang, 1980- author.

Contributor:

Cambridge University Press.

Language:

English

Subjects (All):

Fracture mechanics.

Brittleness.

Elastic analysis (Engineering).

Structural analysis (Engineering).

Physical Description:

1 online resource (xvi, 302 pages) : illustrations

Other Title:

Probabilistic mechanics of quasi brittle structures

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2017.

[Place of publication not identified] : [publisher not identified], [2017]

System Details:

text file

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.

Notes:

Includes bibliographical references (pages 269-289) and indexes.

Electronic reproduction. Cambridge Available via World Wide Web.

Description based on print version record.

ISBN:

9781316585146

131658514X

Publisher Number:

99988720142

Access Restriction:

Restricted for use by site license.