Scaling of Structural Strength

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ISBN: 9780750668491 | 0750668490
Cover: Paperback
Copyright: 9/29/2005

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Summary

Supplemental Materials

An understanding of the effect of structure size on structural strength and failure behavior is an important element in the study of the mechanics of materials and structures.

Foreword

Author's Preface

About the Author

xiii

1 Introduction

(20)

1.1. Nature of Problem and Approach

(2)

1.2. Classical History

(3)

1.3. Recent Developments in Quasibrittle Materials

(4)

1.4. Basic Theories of Size Effect

(1)

1.5. Power Scaling in Absence of Characteristic Length

(2)

1.6. Transitional Size Effect Bridging Power Laws for Different Scales

(4)

1.7. Deductions from Dimensional Analysis

(2)

1.8. Stability of Structures and Size Effect

(2)

2 Asymptotic Analysis of Size Effect

(32)

2.1. Asymptotic Analysis of Size Effect in Structures with Notches or Large Cracks

(4)

2.2. Energetic Size Effect Law and Its Asymptotic Matching Character

(2)

2.3. Size Effect Law in Terms of LEFM Energy Release Function

(1)

2.4. Use of J-Integral for Asymptotic Scaling Analysis

(2)

2.5. Identification of Fracture Parameters from Size Effect Tests

(4)

2.6. Validation by Fracture Test Data and Numerical Simulation

(5)

2.7. Size Effect for Crack Initiation via Energy Release

(4)

2.8. Stress Redistribution Caused by Boundary Layer of Cracking

(3)

2.9. Strain Gradient Effect on Failures at Crack Initiation

(1)

2.10. Universal Size Effect Law

(2)

2.11. Asymptotic Scaling and Interaction Diagram for the Case of Several Loads

(2)

2.12. Size Effect on Approach to Zero Size

(3)

3 Randomness and Disorder

(24)

3.1. Is Weibull Statistical Theory Applicable to Quasibrittle Structures?

(4)

3.2. Nonlocal Probabilistic Theory of Size Effect

(5)

3.3. Energetic-Statistical Formula for Size Effect for Failures at Crack Initiation

(5)

3.4. Size Effect Ensuing from J-Integral for Randomly Located Cracks

(2)

3.5. Could Fracture Fractality Be the Cause of Size Effect?

(3)

3.6. Could Lacunar Fractality of Microcracks Be the Cause of Size Effect?

(5)

4 Energetic Scaling for Sea Ice and Concrete Structures

(44)

4.1. Scaling of Fracture of Floating Sea Ice Plates

(12)

4.2. Size Effect on Softening Inelastic Hinges in Beams and Plates

(4)

4.3. Size Effect in Beams and Frames Failing by Softening Hinges

(6)

4.4. Size Effect in Floating Ice Subjected to Line Load

(2)

4.5. Steel-Concrete Composite Beams and Compound Size Effect

101

(9)

4.6. Size Effect Formulae for Concrete Design Codes

110

(4)

4.7. Size Effect Hidden in Excessive Dead Load Factor in Codes

114

(3)

4.8. No-Tension Design of Concrete or Rock from the Size Efffect Viewpoint

117

(4)

5 Energetic Scaling of Compression Fracture and Further Applications to Concrete, Rock and Composites

121

(16)

5.1. Propagation of Damage Band Under Compression

121

(3)

5.2. Size Effect in Reinforced Concrete Columns

124

(6)

5.3. Fracturing Truss (Strut-and-Tie) Model for Shear Failure of Reinforced Concrete

130

(2)

5.4. Breakout of Boreholes in Rock

132

(1)

5.5. Asymptotic Equivalent LEFM Analysis for Cracks with Residual Bridging Stress

133

(1)

5.6. Application to Compression Kink Bands in Fiber Composites

134

(1)

5.7. Effect of Material Orthotropy

135

(2)

6 Scaling via J-Integral, with Application to Kink Bands in Fiber Composites

137

(14)

6.1. J-Integral Analysis of Size Effect on Kink Band Failures

137

(3)

6.2. J-integral Calculations

140

(4)

6.3. Case of Long Kink Band

144

(1)

6.4. Failure at the Start of Kink Band from a Notch or Stress-Free Crack

145

(2)

6.5. Comparison with Size Effect Tests of Kink Band Failures

147

(4)

7 Time Dependence, Repeated Loads and Energy Absorption Capacity

151

(14)

7.1. Influence of Loading Rate on Size Effect

151

(3)

7.2. Size Effect on Fatigue Crack Growth

154

(2)

7.3. Wave Propagation and Effect of Viscosity

156

(1)

7.4. Ductility and Energy Absorption Capacity of Structures

157

(8)

8 Computational Approaches to Quasibrittle Fracture and Its Scaling

165

(12)

8.1. Eigenvalue Analysis of Size Effect via Cohesive (Fictitious) Crack Model

165

(2)

8.2. Microplane Model

167

(2)

8.3. Spectrum of Distributed Damage Models Capable of Reproducing Size Effect

169

(1)

8.4. Simple, Practical Approaches

170

(1)

8.5. Nonlocal Concept and Its Physical Justification

171

(1)

8.6. Prevention of Spurious Localization of Damage

172

(2)

8.7. Discrete Elements, Lattice and Random Particle Models

174

(3)

9 New Asymptotic Scaling Analysis of Cohesive Crack Model and Smeared-Tip Method

177

(42)

9.1. Limitations of Cohesive Crack Model

179

(3)

9.2. K-Version of Smeared-Tip Method for Cohesive Fracture

182

(3)

9.3. Nonstandard Cohesive Crack Model Defined by a Fixed K-Profile

185

(4)

9.4. Asymptotic Scaling Analysis

189

(15)

9.4.1. Case 1. Positive Geometry with Notch or Stress-Free Initial Crack, for Fixed K-Density (go > 0, go > 0)

189

(6)

9.4.2. Case 2. Fracture Initiation from Smooth Surface, for Fixed K-Density (g0 = 0, g'0 > 0)

195

(3)

9.4.3. Cases 1 and 2 for Standard Cohesive Crack Model or First Three Terms of Asymptotic Expansion

198

(1)

9.4.4. Case 3. Negative-Positive Geometry Transition (g0 > 0, g'0 = 0, g''0 > 0)

199

(5)

9.5. Small-Size Asymptotics of Cohesive Crack Model

204

(2)

9.6. Nonlocal LEFM—A Simple Approach to Cohesive Fracture and Its Scaling

206

(2)

9.7. Broad-Range Size Effect Law and Its Dirichlet Series Expansion

208

(5)

9.8 Size Effect Law Anchored in Both Small and Large Size Asymptotics

213

(2)

9.9 Recapitulation

215

(4)

10 Size Effect at Continuum Limit on Approach to Atomic Lattice Scale

219

(20)

10.1. Scaling of Dislocation Based Strain-Gradient Plasticity

219

(9)

10.2. Scaling of Original Phenomenological Theory of Strain-Gradient Plasticity

228

(8)

10.3. Scaling of Strain-Gradient Generalization of Incremental Plasticity

236

(1)

10.4. Closing Observations

237

(2)

11 Future Perspectives

239

(30)

Addendum

241

(1)

A1. Size Effect Derivation by a New Method for Asymptotic Matching

241

(8)

A2. Size Effect of Finite-Angle Notches

249

(3)

A3. Size Effect on Flexural Strength of Fiber-Composite Laminates

252

(2)

A4. Size Effect in Fracture of Closed-Cell Polymeric Foam

254

(1)

A5. Variation of Cohesive Softening Law Tail in Boundary Layer of Concrete

255

(3)

A6. Can Fracture Energy Be Measured on One-Size Specimens with Different Notch Lengths?

258

(2)

A7. Notched–Unnotched Size Effect Method and Standardization of Fracture Testing

260

(2)

A8. Designing Reinforced Concrete Beams against Size Effect

262

(2)

A9. Scaling of Probability Density Distribution (pdf) of Failure Load

264

(1)

A10. Recent Debates on Fractal Theory of Size Effect and Their Impact on Design Codes

264

(1)

A11. Boundary Layer Size Effect in Thin Metallic Films at Micrometer Scale

265

(2)

A12. Size Effect on Triggering of Dry Snow Slab Avalanches

267

(2)

Bibliography

269

(44)

Subject Index

313

(8)

Reference Citation Index

321

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Scaling of Structural Strength

Summary

Table of Contents

Supplemental Materials