FRACTURE MECHANICS F o u rt h E d i t i o n Fundamentals and Applications PDF

Preview

Summary

Fourth Edition FRACTURE MECHANICS Fundamentals and Applications Fourth Edition FRACTURE MECHANICS Fundamentals and Applications T.L. Anderson Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken So...

Description

Fourth Edition

FRACTURE MECHANICS Fundamentals and Applications

Fourth Edition

FRACTURE MECHANICS Fundamentals and Applications

T.L. Anderson

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2017 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20161102 International Standard Book Number-13: 978-1-4987-2813-3 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

To Vanessa, Molly, Aleah, and Tom

Contents Preface .............................................................................................................................................xv

Section I

Introduction

1. History and Overview ...........................................................................................................3 1.1 Why Structures Fail ......................................................................................................3 1.2 Historical Perspective ...................................................................................................6 1.2.1 Early Fracture Research ..................................................................................8 1.2.2 The Liberty Ships .............................................................................................8 1.2.3 Postwar Fracture Mechanics Research .........................................................9 1.2.4 Fracture Mechanics from 1960 through 1980 ............................................. 10 1.2.5 Fracture Mechanics from 1980 to the Present ............................................ 12 1.3 The Fracture Mechanics Approach to Design ........................................................ 12 1.3.1 The Energy Criterion ..................................................................................... 13 1.3.2 The Stress Intensity Approach ..................................................................... 14 1.3.3 Time-Dependent Crack Growth and Damage Tolerance ......................... 15 1.4 Effect of Material Properties on Fracture ................................................................ 16 1.5 A Brief Review of Dimensional Analysis ................................................................ 17 1.5.1 The Buckingham Π-Theorem ....................................................................... 18 1.5.2 Dimensional Analysis in Fracture Mechanics........................................... 19 References ............................................................................................................................... 21

Section II

Fundamental Concepts

2. Linear Elastic Fracture Mechanics .................................................................................... 25 2.1 An Atomic View of Fracture...................................................................................... 25 2.2 Stress Concentration Effect of Flaws ........................................................................ 27 2.3 The Griffith Energy Balance ......................................................................................30 2.3.1 Comparison with the Critical Stress Criterion .......................................... 32 2.3.2 Modified Griffith Equation ........................................................................... 33 2.4 Energy Release Rate.................................................................................................... 35 2.5 Instability and the R Curve ....................................................................................... 39 2.5.1 Reasons for the R Curve Shape .................................................................... 40 2.5.2 Load Control versus Displacement Control............................................... 41 2.5.3 Structures with Finite Compliance .............................................................42 2.6 Stress Analysis of Cracks ...........................................................................................44 2.6.1 The Stress Intensity Factor............................................................................44 2.6.2 Relationship between K and Global Behavior ........................................... 47 2.6.3 Effect of Finite Size ........................................................................................ 51 2.6.4 Principle of Superposition ............................................................................ 55 2.6.5 Weight Functions ........................................................................................... 57 vii

viii

Contents

Relationship between K and G .................................................................................. 60 Crack Tip Plasticity ..................................................................................................... 62 2.8.1 The Irwin Approach ......................................................................................63 2.8.2 The Strip Yield Model ................................................................................... 66 2.8.3 Comparison of Plastic Zone Corrections.................................................... 68 2.8.4 Plastic Zone Shape ......................................................................................... 69 2.9 K-Controlled Fracture ................................................................................................. 71 2.10 Plane Strain Fracture: Fact versus Fiction ............................................................... 75 2.10.1 Crack Tip Triaxiality ...................................................................................... 76 2.10.2 Effect of Thickness on Apparent Fracture Toughness ............................. 78 2.10.3 Plastic Zone Effects ........................................................................................ 81 2.10.4 Implications for Cracks in Structures .........................................................83 2.11 Mixed-Mode Fracture .................................................................................................84 2.11.1 Propagation of an Angled Crack .................................................................85 2.11.2 Equivalent Mode I Crack .............................................................................. 87 2.11.3 Biaxial Loading .............................................................................................. 88 2.12 Interaction of Multiple Cracks...................................................................................90 2.12.1 Coplanar Cracks .............................................................................................90 2.12.2 Parallel Cracks ................................................................................................90 Appendix 2A: Mathematical Foundations of Linear Elastic Fracture Mechanics: Selected Results ...................................................................................... 92 References ............................................................................................................................. 107 2.7 2.8

3. Elastic–Plastic Fracture Mechanics ................................................................................. 109 3.1 Crack Tip Opening Displacement .......................................................................... 109 3.2 The J Contour Integral .............................................................................................. 114 3.2.1 Nonlinear Energy Release Rate ................................................................. 115 3.2.2 J as a Path-Independent Line Integral....................................................... 117 3.2.3 J as a Stress Intensity Parameter ................................................................ 118 3.2.4 The Large-Strain Zone ................................................................................ 119 3.2.5 Laboratory Measurement of J..................................................................... 121 3.3 Relationships between J and CTOD ....................................................................... 127 3.4 Crack Growth Resistance Curves ........................................................................... 129 3.4.1 Stable and Unstable Crack Growth ........................................................... 131 3.4.2 Computing J for a Growing Crack ............................................................ 133 3.5 J-Controlled Fracture ................................................................................................ 135 3.5.1 Stationary Cracks ......................................................................................... 136 3.5.2 J-Controlled Crack Growth ........................................................................ 138 3.6 Crack Tip Constraint under Large-Scale Yielding ............................................... 141 3.6.1 The Elastic T Stress ...................................................................................... 145 3.6.2 J–Q Theory .................................................................................................... 147 3.6.2.1 The J–Q Toughness Locus .......................................................... 149 3.6.2.2 Effect of Failure Mechanism on the J–Q Locus ....................... 150 3.6.3 Scaling Model for Cleavage Fracture ........................................................ 152 3.6.3.1 Failure Criterion ........................................................................... 152 3.6.3.2 The Jo Parameter ........................................................................... 153 3.6.3.3 Three-Dimensional Effects ......................................................... 154 3.6.3.4 Application of the Model ............................................................ 155 3.6.4 Limitations of Two-Parameter Fracture Mechanics ............................... 157

ix

Contents

Appendix 3A: Mathematical Foundations of Elastic–Plastic Fracture Mechanics: Selected Results .................................................................................... 160 References ............................................................................................................................. 178 4. Dynamic and Time-Dependent Fracture ....................................................................... 181 4.1 Dynamic Fracture and Crack Arrest ...................................................................... 181 4.1.1 Rapid Loading of a Stationary Crack ........................................................ 182 4.1.2 Rapid Crack Propagation and Arrest ........................................................ 187 4.1.2.1 Crack Speed................................................................................... 189 4.1.2.2 Elastodynamic Crack Tip Parameters ....................................... 190 4.1.2.3 Dynamic Toughness .................................................................... 193 4.1.2.4 Crack Arrest .................................................................................. 194 4.1.3 Dynamic Contour Integrals ....................................................................... 197 4.2 Creep Crack Growth ................................................................................................. 198 4.2.1 The C* Integral ............................................................................................. 199 4.2.2 Short-Time versus Long-Time Behavior ................................................... 202 4.2.2.1 The Ct Parameter .......................................................................... 203 4.2.2.2 Primary Creep .............................................................................. 205 4.3 Viscoelastic Fracture Mechanics ............................................................................. 206 4.3.1 Linear Viscoelasticity .................................................................................. 206 4.3.2 The Viscoelastic J Integral .......................................................................... 209 4.3.2.1 Constitutive Equations ................................................................ 209 4.3.2.2 Correspondence Principle ........................................................... 210 4.3.2.3 Generalized J Integral .................................................................. 210 4.3.2.4 Crack Initiation and Growth ...................................................... 212 4.3.3 Transition from Linear to Nonlinear Behavior ....................................... 213 Appendix 4A: Dynamic Fracture Analysis: Selected Results ........................................ 216 References .............................................................................................................................223

Section III

Material Behavior

5. Fracture Mechanisms in Metals ...................................................................................... 229 5.1 Ductile Fracture......................................................................................................... 229 5.1.1 Void Nucleation ............................................................................................ 231 5.1.2 Void Growth and Coalescence ................................................................... 232 5.1.3 Ductile Crack Growth ................................................................................. 241 5.2 Cleavage...................................................................................................................... 244 5.2.1 Fractography ................................................................................................. 244 5.2.2 Mechanisms of Cleavage Initiation ........................................................... 244 5.2.3 Mathematical Models of Cleavage Fracture Toughness ........................ 249 5.3 The Ductile–Brittle Transition ................................................................................. 256 5.4 Intergranular Fracture .............................................................................................. 258 Appendix 5A: Statistical Modeling of Cleavage Fracture.............................................. 259 References ............................................................................................................................. 264 6. Fracture Mechanisms in Nonmetals............................................................................... 267 6.1 Engineering Plastics ................................................................................................. 267

x

Contents

6.1.1

Structure and Properties of Polymers....................................................... 268 6.1.1.1 Molecular Weight ......................................................................... 268 6.1.1.2 Molecular Structure ..................................................................... 269 6.1.1.3 Crystalline and Amorphous Polymers ..................................... 269 6.1.1.4 Viscoelastic Behavior ................................................................... 271 6.1.1.5 Mechanical Analogs .................................................................... 273 6.1.2 Yielding and Fracture in Polymers............................................................ 274 6.1.2.1 Chain Scission and Disentanglement ....................................... 275 6.1.2.2 Shear Yielding and Crazing ........................................................ 276 6.1.2.3 Crack Tip Behavior ....................................................................... 277 6.1.2.4 Rubber Toughening ..................................................................... 279 6.1.2.5 Fatigue............................................................................................ 279 6.1.3 Fiber-Reinforced Plastics ............................................................................ 280 6.1.3.1 An Overview of the Failure Mechanisms ................................ 281 6.1.3.2 Delamination ................................................................................ 282 6.1.3.3 Compressive Failure .................................................................... 286 6.1.3.4 Notch Strength.............................................................................. 288 6.1.3.5 Fatigue Damage ............................................................................ 291 6.2 Ceramics and Ceramic Composites........................................................................ 291 6.2.1 Microcrack Toughening .............................................................................. 295 6.2.2 Transformation Toughening ...................................................................... 297 6.2.3 Ductile Phase Toughening ......................................................................... 298 6.2.4 Fiber and Whisker Toughening ................................................................. 299 6.3 Concrete and Rock .................................................................................................... 301 References .............................................................................................................................304

Section IV

Applications

7. Fracture Toughness Testing of Metals ...........................................................................309 7.1 General Considerations ............................................................................................309 7.1.1 Specimen Configurations ........................................................................... 310 7.1.2 Specimen Orientation.................................................................................. 310 7.1.3 Fatigue Precracking ..................................................................................... 314 7.1.4 Instrumentation ........................................................................................... 315 7.1.5 Side Grooving ............................................................................................... 316 7.2 K Ic Testing ......................................................