The Practical Use of Fracture Mechanics

Transcription

1 The Practical Use of Fracture Mechanics

2 The Practical Use of Fracture Mechanics by DAVID BROEK FractuREsearch Inc., Galena, OR, USA Kluwer Academic Publishers Dordrecht / Boston / London

3 Library of Congress Cataloging in Publication Data Brock, David. The pract,ical use of fr'actuj'e mechanics. Bibliography: p. 1. Fract,ure mechanics. 1. TiUe. TA409.B ' ISBN-13: e-isbn-13: DOI: 10,1007/ Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press Sold and distributed in the U.S.A and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. first published in hardbound edition only in 1988 second printing with minor corrections in 1989 third printing 1991 reprinted 1994 reprinted 1996 reprinted 1997 hardback edition ISBN paperback edition ISBN printed Oil acid.ti ee paper All Rights Reserved 1989 by Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 1989 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

4 Preface This book is about the use of fracture mechanics for the solution of practical problems; academic rigor is not at issue and dealt with only in as far as it improves insight and understanding; it often concerns secondary errors in engineering. Knowledge of (ignorance of) such basic input as loads and stresses in practical cases may cause errors far overshadowing those introduced by shortcomings of fracture mechanics and necessary approximations; this is amply demonstrated in the text. I have presented more than three dozen 40-hour courses on fracture mechanics and damage tolerance analysis, so that I have probably more experience in teaching the subject than anyone else. I learned more than the students, and became cognizant of difficulties and of the real concerns in applications. In particular I found, how a subject should be explained to appeal to the practicing engineer to demonstrate that his practical problem can indeed be solved with engineering methods. This experience is reflected in the presentations in this book. Sufficient background is provided for an understanding of the issues, but pragamatism prevails. Mathematics cannot be avoided, but they are presented in a way that appeals to insight and intuition, in lieu of formal derivations which would show but the mathematical skill of the writer. A practicing engineer does care little about how a crack tip stress field is derived; he accepts that it can be done, as long as he can understand that the result must be of the form it is. His real concern is what it means for the solutions to practical problems. Mathematical background is of use to future scientists, but few engineering students taking fracture mechanics courses will become researchers in fracture mechanics. My advice is that indeed very few should. Fracture mechanics has matured to a useful engineering tool as has e.g. buckling analysis. Certainly, it is not perfect, but no engineering analysis is. Not much buckling research is practiced today; the present number of researchers in fracture mechanics is far out of proportion to the remaining engineering problems. Despite the acclaimed solid education of engineers, it is my experience in teaching fracture mechanics to literally hundreds of practicing engineers, that most have only a vague idea of such subjects as plastic deformation and design; to many Mohr's circle is an enigma; at most one in a class knows the stress concentration factor of a circular hole; fewer even remember yield criteria and their significance. For this reason Chapter 2 of the text discusses the effect of notches and local yielding and provides a simplified look at yield v

5 vi criteria. The treatment is necessarily compromising rigidity, but it serves the purpose of providing the insight without which fracture mechanics cannot be understood. My research work covered fundamental fracture and fatigue mechanisms, experimental evaluation of criteria for fatigue, fracture, and combined mode loading, the development of engineering procedures for arrest analysis in stiffened panels, collapse conditions, and damage tolerance analysis in general. My engineering background however, has always prevailed and forced me to consider the practicality of procedures. This book reflects a lifetime of experience in research and practical applications. No subject is discussed on the basis of hearsay. Instead the basis is "hands-on" experience with virtually every issue from the fundamental to the practical. I am aware of my shortcomings, prejudices and opinionations, but believe to be entitled to these on the basis of my engineering experience. This text reflects them, and I do not apologize. Too many "refinements" in engineering solutions pertain to secondary errors; they increase the complexity, but do not improve the solution. One does not improve the strength of a chain by improving the strong links. The weak links in the fracture mechanics analysis are the unknowns, not the procedures. This book is for engineering students and for engineers, who must solve urgent problems yesterday. Engineering solutions are always approximative, no matter what the subject is. Such is the nature of engineering. Necessary assumptions are far more influential than those due to limitations of fracture mechanics. The text is intended for the education of 'engineers'. At the same time it serves as a reference. For this reason there is some duplication and extensive crossreferences are provided. This may be objectionable to the reader going through the text from A to Z, but it will be of help to those who read sections here and there. It is not perfect as no human effort ever is, and I shall welcome constructive criticism with regard to the engineering applications. My haste in accomplishing things (enforced by the unfortunate situation that I have to make a living, while writing a book is an extraneous effort which is not very profitable) may be reflected in the text. Again, I am not apologizing, just explaining. I am grateful to my wife, Betty, for putting up with my preoccupations and moods while writing this text, and for submitting all writing to a word-processor. I am also thankful to my son Titus, who spent numerous hours in producing solutions to exercises and in drawing figures. I dedicate this book to the memory of my father, Harm Broek. Many sons see their father as the ultimate example. So do I. His unfailing support has always been a driver of my ambitions. Galena, Ohio, February 1988

6 Notice Extensive computer software for fracture mechanics analysis was developed by the author of this book. This software is capable of - performing residual strength analysis in accordance with Chapters 3, 4 and lo both for LEFM and EPFM. - performing fatigue crack growth analysis for constant amplitude, random loading and semi random loading in accordance with Chapters 5 and lo, with or without retardation. There are options for various retardation models, rate equations and tabular rate data (Chapter 7). - automatically generating semi-random stress histories on the basis of exceedance diagrams (Chapter 6) and performing clipping and truncation upon command. - determining inspection intervals and cumulative probability of detection in accordance with the procedure discussed in Chapter 11, using the calculated crack growth curves, and accounting for specificity and accessibility. - providing professional plots. An extensive library of materials data is included, as well as an extensive library of geometry factors. Besides a pre-processor can generate geometry factors, using most of the procedures discussed in Chapter 8. The above software is available for personal computers. Because of the large size of the software, it is split up in seven modules, each of which fits in a personal computer. The modules communicate through disket files that are generated automatically. The software can be obtained from FractuREsearch Inc, 9049 Cupstone Drive, Galena, OH 43021, USA. A much simplified version of the same software (also by the author) is available from the American Society of Metals (ASM), Metals Park, OH 44073, USA. This simplified version has no data library, no preprocessor for geometry factor, cannot do retardation, and does not generate semi-random stress histories. Vll

7 Contents Preface Notice v VB Chapter 1. INTRODUCTION 1.1. Fracture control The two objectives of damage tolerance analysis Crack growth and fracture Damage tolerance and fracture mechanics The need for analysis: purpose of this book Exercises 20 Chapter 2. EFFECTS OF CRACKS AND NOTCHES: COLLAPSE Scope An interrupted load path Stress concentration factor State of stress at a stress concentration Yielding at a notch Plastic collapse at a notch Fracture at notches: brittle behavior Measurement of collapse strength Exercises 46 Chapter 3. LINEAR ELASTIC FRACTURE MECHANICS Scope Stress at a crack tip General form of the stress intensity factor Toughness Plastic zone and stresses in plane stress and plane strain Thickness dependence of toughness Measurement of toughness Competition with plastic collapse The energy criterion The energy release rate The meaning of the energy criterion The rise in fracture resistance: redefinition of toughness Exercises 86 ix

8 x Chapter 4. ELASTIC-PLASTIC FRACTURE MECHANICS 4.1. Scope 4.2. The energy criterion for plastic fracture 4.3. The fracture criterion 4.4. The rising fracture energy 4.5. The residual strength diagram in EPFM: collapse 4.6. The measurement of the toughness in EPFM 4.7. The parameters of the stress-strain curve 4.8. The h-functions 4.9. Accuracy Historical development of J Limitations of EPFM CTOD measurements Exercises Chapter 5. CRACK GROWTH ANALYSIS CONCEPTS 5.1. Scope 5.2. The concept underlying fatigue crack growth 5.3. Measurement of the rate function 5.4. Rate equations 5.5. Constant amplitude crack growth in a structure 5.6. Load interaction: Retardation 5.7. Retardation models 5.8. Crack growth analysis for variable amplitude loading 5.9. Parameters affecting fatigue crack growth rates Stress corrosion cracking Exercises Chapter 6. LOAD SPECTRA AND STRESS HISTORIES 6.1. Scope 6.2. Types of stress histories 6.3. Obtaining load spectra 6.4. Exceedance diagram 6.5. Stress history generation 6.6. Clipping 6.7. Truncation 6.8. Manipulation of stress history 6.9. Environmental effects Standard spectra Exercises

9 Chapter 7. DATA INTERPRETATION AND USE Scope Plane strain fracture toughness Plane stress and transitional toughness, R-curve Toughness in terms of J and J R Estimates of toughness General remarks on fatigue rate data Fitting the da/dn data Dealing with scatter in rate data 232' 7.9. Accounting for the environmental effect Obtaining retardation parameters 238 7:11. Exercises 241 Chapter 8. GEOMETRY FACTORS Scope The reference stress Compounding Superposition A simple method for asymmetric loading cases Some easy guesses Simple solutions for holes and stress concentrations Simple solutions for irregular stress distributions Finite element analysis Simple solutions for crack arresters and multiple elements Geometry factors for elastic-plastic fracture mechanics Exercises 279 Chapter 9. SPECIAL SUBJECTS Scope Behavior of surface flaws and corner cracks Break through: leak-before-break Fracture arrest Multiple elements, multiple cracks, changing geometry Stop holes, cold worked holes and interference fasteners Residual stresses in general Other loading modes: mixed mode loading Composites Exercises 329 Chapter 10. ANALYSIS PROCEDURES Scope Ingredients and critical locations 332 xi

10 Xll Critical locations and flaw assumptions LEFM versus EPFM Residual strength analysis Use of R-curve and JR-curve Crack growth analysis Exercises Chapter II. FRACTURE CONTROL ILl. Scope Fracture control options The probability of missing the crack The physics and statistics of crack detection Determining the inspection interval Fracture control plans Repairs Statistical aspects The cost of fracture and fracture control 11.1 O. Exercises Chapter 12. DAMAGE TOLERANCE SUBSTANTIATION Scope Objectives Analysis and damage tolerance substantiation Options to improve damage tolerance Aircraft damage tolerance requirements Other requirements Flaw assumptions Sources of error and safety factors Misconceptions Outlook Exercises Chapter 13. AFTER THE FACT: FRACTURE MECHANICS AND FAILURE ANALYSIS Scope The cause of service fractures Fractography Features of use in fracture mechanics analysis Use of fracture mechanics Possible actions based on failure analysis Exercises 440

11 xiii Chapter 14. APPLICATIONS Scope Storage tank (fictitious example) Fracture arrest in ships Piping in chemical plant (fictitious example) Fatigue cracks in railroad rails Underwater pipeline Closure Chapter 15. SOLUTIONS TO EXERCISES SUBJECT INDEX