Quasibrittle fracture mechanics and size effect : a first course / Zdenek P. Bažant, Jia-Liang Le, Marco Salviato.

Format:

Book

Author/Creator:

Bažant, Z. P., author.

Le, Jia-Liang, author.

Salviato, Marco, author.

Series:

Oxford scholarship online.

Oxford scholarship online

Language:

English

Subjects (All):

Fracture mechanics.

Brittleness.

Elastic analysis (Engineering).

Physical Description:

1 online resource (332 pages)

Edition:

First edition.

Place of Publication:

Oxford, United Kingdom : Oxford University Press, 2022.

Summary:

Designed for graduate and upper-level undergraduate university courses, this book provides a comprehensive treatment of quasibrittle fracture mechanics, including its practical applications across a range of materials and engineering structures, and features exercises and problems to test understanding.

Contents:

Cover

Quasibrittle Fracture Mechanics and Size Effect: A First Course

Copyright

Dedication

Foreword

Preface

Contents

1 Introduction

1.1 Why Fracture Mechanics?

1.2 Three Kinds of Fracture Mechanics

1.3 Crack-Parallel Stresses and Tensorial Damage as Quasibrittle Fracture Basis

1.4 Size Effect Type and Role of Material Randomness

1.5 Applications of Size Effect in Structural Analysis and Design

Exercises

2 Fundamentals of Linear Elastic Fracture Mechanics

2.1 Energy Release Rate and Fracture Energy

2.1.1 Energy Balance Analysis

2.1.2 Elastic Potential and Energy Release Rate

2.2 General Form of Near-Tip and Far Fields of a Notch

2.3 Stress Singularities and Energy Flux at a Sharp Crack Tip

2.4 Westergaard's Solution for Crack in Infinite Body

2.5 Stress Intensity Factor, Near-Tip Field, and Remote Field

2.6 Fracture Modes I, II, and III

2.7 Irwin's Relationship between Stress Intensity Factors and Energy Release Rate

2.8 Rice's J-Integral

2.9 Numerical Calculation of Stress Intensity Factors

2.9.1 Incremental sti ness method

2.9.2 Near-tip field fitting

J-Integral Evaluation

2.10 Stress Intensity Factors for Typical Simple Geometries

2.11 Calculation of Elastic Compliance and Deection from Stress Intensity Factors

2.12 Bimaterial Interfacial Cracks

2.13 Comments on Anisotropic Materials and Three-Dimensional Singularities

3 Nonlinear Fracture Mechanics-Line Crack Idealization

3.1 Types of Fracture Behavior and Nonlinear Zone

3.1.1 Three Types of Fracture Behaviors

3.1.2 E ect of Crack-Parallel Stresses

3.2 Irwin's Estimate of the Size of the Inelastic Zone

3.3 Estimation of FPZ Size for Quasibrittle Materials

3.3.1 Uniform cohesive stress profile

3.3.2 Linear cohesive stress profile.

3.3.3 Quadratic cohesive stress profile

3.4 Equivalent Linear Elastic Crack Model

3.5 R-Curves

3.5.1 Definition of an R-Curve

3.5.2 Stability of Fracture and Critical States

3.5.3 Stability under Load-Control Condition

3.5.4 Stability under Displacement-Control Condition

3.5.5 Experimental Characterization of R-Curve

3.6 Cohesive Crack Model

3.6.1 Cohesive Law and Its Relation with Fracture Energy

3.6.2 Relationship between Cohesive Law and Strain Softening Behavior

3.6.3 Softening Curve, Fracture Energy, and Other Properties

3.7 Integral Equations of Mode I Cohesive Crack Model

3.8 Eigenvalue Analysis of Peak Load and Size Effect

4 Nonlinear Fracture Mechanics-Diffuse Crack Model

4.1 Why Crack Band?-Crack-Parallel Stress and Other Evidence

4.2 Strain Localization, Mesh Sensitivity, and Localization Limiters

4.2.1 Bifurcation of Equilibrium Path

4.2.2 Stability of Bifurcated Path and Implied Necessity of Localization Limiter

4.3 Crack Band Model

4.3.1 Basic Concepts

4.3.2 Rescaling of Softening Law for Increased Finite Element Mesh

4.3.3 Compatibility of Energy Density, Softening Law and Element Size

4.3.4 Calibration of Crack Band Width or Element Size

4.3.5 Implementation in General FE Analysis

4.3.6 Recent Development for Stochastic Computations

4.4 Nonlocal Integral and Gradient Models

4.5 Discrete Computational Models

5 Energetic Size Effect in Quasibrittle Fracture

5.1 Nominal Structural Strength and Size Effect

5.2 Power-Law Scaling in Absence of Characteristic Length

5.3 Dimensional Analysis of Size Effect

5.4 Second-Order Asymptotic Scaling Behavior at Small Size Limit

5.5 Derivation of Size Effect Equations Using Equivalent LEFM

5.5.1 Type 2 size effect

Type 2 size effect via asymptotic matching.

5.5.2 Type 1 size effect

5.5.3 Simple Derivation of Size E ect Law from Dimensional Analysis

5.6 Determination of R-Curve from Size Effect Analysis

5.7 Size Effect Testing of Cohesive Law Parameters

6 Probabilistic Theory of Quasibrittle Fracture

6.1 Weibull Statistics of Structural Strength

6.1.1 Infinite Weakest-Link Model

6.1.2 Size Effect Derived From the Weibull Theory

6.1.3 Equivalent number of elements

6.1.4 Extreme Value Statistics and Stability Postulate

6.2 Finite Weakest-Link Model of Strength Distribution of Quasibrittle Structures

6.2.1 Failure Statistics at Nanoscale as the Basis of Power-Law Probability Tail

6.2.2 Multiscale Transition of Failure Statistics

6.2.3 Macroscopic Strength Distribution and Experimental Validation

6.3 Mean Size Effect on Structural Strength

6.4 Problem with Applying Three-Parameter Weibull Distribution

6.4.1 Theoretical argument against three-parameter Weibull distribution

6.4.2 Mean size effect analysis

6.5 Aperçu of Fishnet Statistics for Biomimetic, Architectured, Octet-Lattice and Some Particulate Materials

6.5.1 Brittle Fishnet Statistics

6.5.2 Softening Fishnet, Order Statistics and Quantile Statistics

6.5.3 Octet Lattice and Other Quasibrittle Materials

6.6 Remark on Failure Probability of Concrete Specimens of Random Mean Strength in Large Database

7 Quasibrittle Size Effect Analysis in Practical Problems

7.1 Tensile Fracture Problems

7.1.1 Anchor Failure in Concrete

7.1.2 Modulus of Rupture or Flexural Strength

7.1.3 Plates under Biaxial Bending

7.1.4 Case Study of Type 1 Structural Failure-Malpasset Dam

7.1.5 Is No-Tension Material a Safe Alternative to Fracture Mechanics?

7.2 Tensile Fracture of Sea Ice

7.2.1 Thermal bending fracture

7.2.2 Vertical penetration failure.

7.2.3 Breakup of ice plate pushing against an obstacle

7.3 Compression Fracture with Shear and Size Effects

7.3.1 Diagonal Shear Failure of Reinforced Concrete Beams

7.3.2 Punching Shear Failure in Reinforced Concrete Flat Slabs

7.3.3 Size Effect in Borehole Breakout

7.3.4 Kink Band Compression Failures in Fiber Composites

7.4 Tensile Fracture and Size Effect in Fiber Composites

7.4.1 Measurement of Post-Peak Softening in Fiber Composites

7.4.2 Characterization of Fracture Energy and Size Effect in Textile Composites

7.4.3 Size Effect in Transverse and Sideways Fracture of Unidirectional Composites

7.4.4 Size Effect in Mode I and II Inter-laminar Fracture of Composites

7.4.5 Size Effect in Fracture of Sandwich Structures

7.5 Bone Fracture and Size Effect

7.6 Size Effect in Polymer Nanocomposites

7.7 Interfacial Fracture of Metal-Composite Hybrid Joints

7.8 Reliability of Polycrystalline Silicon MEMS Devices

7.9 Analogy with Scaling of Small-Scale Yielding Fracture of Metals

8 Overview of History

8.1 Classical Theories of Fracture Mechanics and Scaling

8.2 Development of Cohesive Crack Model

8.3 Rice's J-Integral

8.4 Quasibrittlenes, Scaling, and Fictitious Crack Model

8.5 Crack Band Model

8.6 Nonlocal Continuum Modeling of Softening Damage

8.7 Size Effect in Shear Failure of RC Beams

Appendix A Mathematical Proof of Path Independence of J-Integral

Appendix B Derivation of Size Effect Equations by Dimensional Analysis and Asymptotic Matching

B.1 Type 2 size effect

B.2 Type 1 size effect

Appendix C Universal Size Effect Law and Crack Length Effect

Bibliography

Author index

Subject index.

Notes:

This edition also issued in print: 2022.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-19-193857-2

0-19-266138-8