CRC MECHANICAL ENGINEERING SERIES Series Editor Frank A. Kulacki, University of Minnesota Published Entropy Generation Minimization Adrian Bejan, Duke University The Finite Element Method Using MA TLAB Young W. Kwon, Naval Postgraduate School Hyochoong Bang, Korea Aerospace Research Institute Mechanics of Composite Materials Autar K. Kaw, University of South Florida Viscoelastic Solids Rode ric Lakes, University of Iowa Nonlinear Analysis of Structures M. Sathyamoorthy, Clarkson University Practical Inverse Analysis in Engineering David M. Trujillo, Trucomp Henry R. Busby, Ohio State University To be Published Fundamentals of Environmental Discharge Modeling Lorin R. Davis, Oregon State University Mechanics of Solids and Shells Gerald Wempner, Georgia Institute of Technology Demosthenes Talaslidis, Aristotle University of Thessalonika Mathematical and Physical Modeling of Materials Processing Operation Olusegun Johnson lleghusi, Northeastern University Manabu Iguchi, Osaka University Walter E. Wahnsiedler, Alcoa Technical Center Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business Library of Congress Cataloging-in-Publication Data Bolotin, V. V. (Vladimir Vasil 'evich) Mechanics of fatigue I Vladimir V. Bolotin. p. em. --(Mechanical engineering) Includes bibliographical references and index. ISBN 0-8493-9663-8 (alk. paper) 1. Materials--Fatigue--Testing. 2. Contact mechanics. I. Series: Mechanical engineering (CRC Press). TA418.38.B65 1998 620.1'126-dc21 98-29151 CIP This book contains information obtained from authentic and highly regarded sources. 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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are only used for identification and explanation, without intent to infringe. © 1999 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-9663-8 Library of Congress Card Number 98-29151 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper CONTENTS Preface .................................................................. IX 1. Introduction 1.1. Fatigue of Materials and Related Phenomena ......................... 1 1. 2. Fatigue Tests ......................................................... 6 1.3. Low-Cycle Fatigue ................................................... 9 1.4. Factors Influencing Fatigue Life ..................................... 11 1.5. Micro- and Macromechanics of Fracture ............................. 12 1.6. Linear Fracture Mechanics .......................................... 15 1.7. Nonlinear Fracture Mechanics ....................................... 19 1.8. Fatigue Crack Growth ............................................... 25 1.9. Traditional Engineering Design against Fatigue ...................... 28 1.10. Current State and Trends in Design against Fatigue ................. 32 1.11. Synthesis of Micro- and Macromechanics ............................ 35 1.12. Summary ........................................................... 36 2. Fatigue Crack Nucleation and Early Growth 2.1. Introductory Remarks ............................................... 37 2.2. Phenomenological Models of Fatigue Crack Nucleation ............... 39 2.3. Models of Continuum Damage Mechanics ............................ 44 2.4. Continuum Approach to Fatigue Crack Nucleation ................... 47 2.5. Micromechanical Models of Fatigue Crack Nucleation ................ 50 2.6. Formation and Early Growth of Fatigue Cracks ...................... 53 2.7. Summary ........................................................... 65 3. Mechanics of Fatigue Crack Growth 3.1. General Outlook .................................................... 67 3.2. Cracked Body as a Mechanical System .............................. 70 3.3. Application of Principle of Virtual Work ............................. 72 3.4. Generalized Forces in Analytical Fracture Mechanics ................. 76 3.5. Equations of Fatigue Crack Growth ................................. 81 3.6. Stability of Fatigue Cracks .......................................... 83 3.7. Patterns of Fatigue Crack Growth ................................... 86 3.8. Quasistationary Approximation in Mechanics of Fatigue ............. 92 3.9. Single-Parameter Fatigue Cracks .................................... 94 3.10. Summary ........................................................... 96 4. Fatigue Crack Growth in Linear Elastic Bodies 4 .1. Modeling of Material Properties ..................................... 97 4.2. Fatigue Crack in Griffith's Problem ................................ 100 4.3. Influence of Initial Conditions ...................................... 106 VI Mechanics of Fatigue 4.4. Influence of Loading Conditions .................................... 110 4.5. Influence of Damage Accumulation Process ......................... 114 4.6. Threshold and Related Effects ...................................... 118 4.7. Crack Closure Effect ............................................... 128 4.8. Differential Equations of Fatigue Crack Growth ..................... 137 4.9. Comparison with Semi-Empirical Equations ........................ 140 4.10. Interaction between Microdamage and Material Properties .......... 144 4.11. Discussion of Numerical Results .................................... 149 4.12. Assessment of Parameters for Microscale Models .................... 154 4.13. Summary .......................................................... 158 5. Fatigue Crack Growth in Linear Elastic Bodies ( cont'd) 5.1. Stress Distribution near the Crack Tips ............................ 159 5.2. Some Generalizations of Griffith's Problem in Fatigue ............... 162 5.3. Circular Planar Crack in Tension ................................... 167 5.4. Elliptical Planar Cracks. Driving Forces ............................ 169 5.5. Elliptical Planar Cracks. Resistance Forces ......................... 174 5.6. Elliptical Crack Growth in Fatigue ................................. 175 5.7. Planar Cracks of Arbitrary Shape .................................. 181 5.8. Mixed-Mode Fatigue Cracks ........................................ 183 5.9. Nonplanar Crack Propagation ...................................... 186 5.10. First Kinking of Fatigue Cracks .................................... 189 5.11. Prediction of Fatigue Crack Trajectories ............................ 195 5.12. Fatigue Crack Propagation in Random Media ...................... 203 5.13. Randomization of Material Resistance to Fatigue Crack Growth .... 206 5.14. Monte Carlo Simulation ............................................ 210 5.15. Meandering of Fatigue Cracks ...................................... 214 5.16. Summary .......................................................... 221 6. Fatigue Cracks in Elasto-Plastic Bodies 6.1. Effects of Plastic Straining on Fatigue Crack Propagation ........... 223 6.2. Stress and Displacement Distribution for Cracks with Loaded Faces. 228 6.3. Generalized Driving Forces ......................................... 232 6.4. Models of Damage Accumulation ................................... 235 6.5. Generalized Resistance Forces ...................................... 239 6.6. Constitutive Relationships and Computational Procedure ........... 241 6.7. Discussion of Numerical Results .................................... 243 6.8. Penny-Shape Fatigue Crack ........................................ 251 6.9. Crack Propagation under Nonsteady Loading ....................... 257 6.10. Influence of Cyclic Softening on Fatigue Crack Growth ............. 263 6.11. Summary .......................................................... 271 7. Crack Growth in Hereditary Media 7 .1. Introductory Remarks .............................................. 273 7.2. Linear Visco-Elastic Media ......................................... 277 7.3. Generalized Driving Forces for Linear Visco-Elasticity .............. 281 7.4. Crack Growth under Sustained Loading ............................ 287 7.5. Combination of Sustained and Cyclic Loading ...................... 291 7.6. Fatigue Crack Growth in Polymer Materials ........................ 296 7.7. Creep Deformation and Damage Accumulation in Metals ........... 301 Contents VII 7 .8. Generalized Driving Forces in Creep ................................ 304 7 .9. Crack Growth Associated with Creep ............................... 308 7.10. Creep Crack Growth in Turbine Disks .............................. 311 7.11. Summary .......................................................... 315 8. Environmentally Affected Fatigue and Related Phenomena 8 .1. Interaction of Mechanical and Environmental Factors in Fatigue .... 317 8.2. Transport of Environmental Agents within Cracks .................. 319 8.3. Corrosion Damage Accumulation ................................... 322 8.4. Stress Corrosion Cracking .......................................... 324 8.5. Numerical Simulation .............................................. 326 8.6. Threshold Problem in Stress Corrosion Cracking .................... 330 8.7. Corrosion Fatigue .................................................. 332 8.8. Frequency Effects in Corrosion Fatigue ............................. 336 8.9. Quasistationary Approximation .................................... 339 8.10. Application of the Thin Plastic Zone Model ........................ 341 8.11. Hydrogen Embrittlement and Related Phenomena .................. 343 8.12. Combination of Cyclic Fatigue and Hydrogen Degradation .......... 349 8.13. Summary .......................................................... 350 9. Fracture and Fatigue of Fiber Composites 9.1. Composite Materials and Composite Structures ..................... 353 9.2. Micromechanics of Dispersed Damage .............................. 356 9.3. Microdamage Accumulation in Cyclic Loading ...................... 365 9.4. Fracture Due to the Loss of Integrity ............................... 367 9.5. Macrocrack Initiation .............................................. 373 9.6. Types of Cracks in Unidirectional Fiber Composites ................ 375 9.7. Evaluation of the Fracture Work ................................... 379 9.8. Stability with Respect to Brush-Like Fracture ...................... 383 9.9. Fatigue Brush-Like Crack Propagation ............................. 386 9.10. Growth Rate Diagrams for Brush-Like Cracks ...................... 391 9.11. Summary .......................................................... 396 10. Fracture and Fatigue in Laminate Composite Sructures 10.1. lnterlaminar Defects in Composite Materials ...................... 397 10.2. lnterlaminar Fracture Work ....................................... 401 10.3. Generalized Resistance Forces ..................................... 407 10.4. Internal Fatigue Cracks in Composites ............................ 411 10.5. Buckling and Stability of Near-Surface Delaminations ............. 415 10.6. Elliptical Delamination ........................................... 420 10.7. Interlaminar Damage in Cyclic Loading ........................... 423 10.8. Application of Mechanics of Multilayered Structures ............... 427 10.9. Growth of Delamination in Cyclic Compression ................... .431 10.10. Growth of Delaminations in Cyclic Bending ....................... 437 10.11. Summary ......................................................... 440 References ............................................................. 443 Subject Index ......................................................... 453 Author Index .......................................................... 461 Preface IX PREFACE This book is dedicated to the fatigue of materials and structural components of en- gineering systems. The term fatigue is understood in a broad sense, including crack nucleation and growth up to the final failure under cyclic and/or sustained loads and actions. In addition to the classic high-cycle and low-cycle fatigue, such phenomena as fatigue associated with creep, corrosion fatigue, stress corrosion cracking, etc., are also discussed. Fatigue and related phenomena are the most frequent causes of failures in en- gineering systems, beginning from minor failures that result in the interruption of operation and the accompanying economic loss up to major accidents with disas- trous consequences. Fatigue is a subject of extensive study by engineers in various branches of in- dustry as well as by researchers in the mechanics of solids and material science. As a complement to already published works, this book discusses the subject in a more theoretical way. Fatigue and all kinds of delayed fracture are considered here from the unified viewpoint of the mechanics of solids and structures. As with other cen- tered positions, this approach cannot be comprehensive. However, it allows deeper insight into fatigue phenomena using the terms and concepts more appropriate for mechanical, civil, naval, and aeronautical engineers. Such an approach develops more detailed planning of fatigue tests, their statistical treatment and interpreta- tion, as well as more efficient use of the known experimental data. In addition, this approach presents new analytical and numerical tools for the analysis of structural safety and reliability, as well as for life-time prediction and other important aspects of an engineer's activities. The core of this book is built upon the synthesis of micro- and macromechanics of fracture. By micromechanics, the author means both the modeling of mechani- cal phenomena on the level of material structure (i.e., on the level of grains, fibers, microinclusions, microcracks and micropores) and the continuous approach based on the use of certain internal field parameters characterizing the dispersed micro- damage. This is so-called continuum damage mechanics. As for macromechanics of fracture, the version used here is that developed by the author and called ana- lytical fracture mechanics. This term means that the system cracked body-loading or loading device is considered as a mechanical system, and the tools of analytical (rational) mechanics are applied thoroughly to describe the crack propagation until the final failure. The book consists of ten chapters. Chapter 1 is of an introductory character. It contains preliminary information on fatigue and engineering methods for the design of machines and structures against failures caused by fatigue. Fatigue crack nucleation is the subject of Chapter 2. As this early stage of