Embed Size (px)
Citation preview
FRACTURE MECHANICS OF METALS, COMPOSITES,
WELDS, AND BOLTED JOINTS Application ofLEFM, EPFM, And
FMDM Theory
FRACTURE MECHANICS OF METALS, COMPOSITES,
WELDS, AND BOLTED JOINTS Application ofLEFM, EPFM, And
FMDM Theory
by
Bahrain Farahmand, Ph.D. Boeing Technical Fellow
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Farahmand, Bahram. Fracture mechanics of metals, composites, welds, and bolted joints: application of LEFM, EPFM, and FMDM theory / by Bahram Farahmand.
p. cm. Includes bibliographical references and index. ISBN 978-1-4613-5627-1 ISBN 978-1-4615-1585-2 (eBook) DOI 10.1007/978-1-4615-1585-2
1. Fracture mechanics. 2. Metals—Fracture. 3. Welded joints—Cracking. 4. Composite materials—Fracture. 5. Bolted joints. I. Farahmand, Bahram. Ü. Title.
TA409 .F35 2000 620'.1126—dc21
00-048696
Copyright © 2001 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 1st edition 2001
A l l rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, L L C .
Printed on acid-free paper.
This book is lovingly dedicated to my beautiful wife, Vida, for her valuable advice throughout my long involvement with the book, to my mother, Gohartaj, who inspired me for higher education, and to my two beautiful children, Houman and Roxana, for their patience and understanding.
CONTENTS
CHAPTER 1 OVERVIEW OF FRACTURE MECHANICS AND FAILURE PREVENTION ...... ............................................. 1
1.0 Introduction ................................................................ 1
1.1 High Cycle Fatigue ...................................................... 6
1.2 Low Cycle Fatigue ...................................................... 12
1.3 Stress and Strain at Notch (Neuber Relationship) ............. 19
1.4 Linear Elastic Fracture Mechanics (LEFM) and
Applications .............................................................. 24
1.4.1 Application of LEFM ..... '" ........................................... 27
1.5 Elastic-Plastic Fracture Mechanics (EPFM) ..................... 31
1.5.1 Path Independent J-integral.. ........................................ 32
1.5.2 Crack Opening Displacement (COD) .............................. 33
1.6 Failure Prevention and Fracture Control Plan ................... 35
1.6.1 Material Selection, Testing, and Manufacturing ................ .40
1.6.2 Non Destructive Inspection (NDI) .................................. .41
1.6.2.1 Liquid Penetrant Inspection .......................................... 42
1.6.2.2 Magnetic Particle Inspection ......................................... 43
1.6.2.3 Eddy Current Inspection .............................................. 44
1.6.2.4 Ultrasonic Inspection .................................................. .45
1.6.2.5 Radiographic Inspection ............................................. .46
References ........................................................................... 47
CHAPTER 2 LINEAR ELASTIC FRACTURE MECHANICS (LEFM) AND APPLiCATIONS ...................................... .... 52
2.0 Introduction to Elastic Fracture ...................................... 52
2.1
2.2
2.2.1
2.2.2
2.2.3
2.2.3.1
2.2.4
2.3
2.4
2.5
2.6
2.6.1
2.6.2
2.6.3
2.6.4
2.7
2.7.1
2.7.2
2.8
2.8.1
2.8.2
2.8.3
2.8.4
2.9
2.9.1
2.9.2
Griffith Theory of Elastic Fracture .................................. 53
The Stress Intensity Factor Approach, K ......................... 56
GeneraL ................................................................... 56
Crack Tip Modes of Deformation ................................... 56
Derivation of Mode I Stress Intensity Factor ..................... 58
Stress Intensity Factor For Combined Loading ................. 63
Critical Stress Intensity Factor ....................................... 65
Fracture Toughness ................................................... 66
Material Anisotropy and its Effect on Fracture Toughness ... 69
Factors Affecting Fracture Toughness ............................ 71
Residual Strength Capability of a Cracked Structure ......... 74
Residual Strength Diagram for Material with Abrupt Failure.76
The Apparent Fracture Toughness ................................. 78
Development of the Resistance Curve (R-Curve) & KR ..... 79
Residual Strength Diagram for Structure with Built-Up
Feature .................................................................... 82
Plasticity at the Crack Tip within Small Scale yielding ........ 87
Plastic Zone Shape Based on the Von Mises Yield
Criterion .................................................................. 87
Plastic Zone Shape Based on Tresca Yield Criterion ......... 90
Surface or Part Through Cracks .................................... 91
Stress Intensity Factor Solution for a Part Through Crack ... 92
Longitudinal Surface Crack in a Pressurized Pipe ............. 95
Part Through Fracture Toughness, Kle .......................... 96
The Leak-Before-Burst (LBB) Concept.. ......................... 99
A Brief Description of ASTM Fracture Toughness Testing.1 02
Plane Strain Fracture Toughness (KId Test.. ................. 103
Standard Klc Test and Specimen Preparation ................ 1 03
viii
2.9.3 Plane Stress Fracture Toughness (Kc) Test.. ................. 107
2.9.4 M{T) Specimen for Testing Kc .................................... 110
2.9.5 Grip Fixture Apparatus, Buckling Restraint, and Fatigue
Cracking ................................................................. 111
References ....................................... , .................................. 113
CHAPTER 3 FATIGUE CRACK GROWTH AND APPLiCATIONS ........................................................ ......... 118
3.1 Introduction ............................................................. 118
3.1.1 Stress Intensity Factor Range and Crack Growth Rate ..... 121
3.2 Crack Growth Rate Empirical Descriptions ..................... 122
3.2.1 Brief Review of Fatigue Crack Growth Testing ................ 127
3.3 Stress Ratio and Crack Closure Effect. ......................... 132
3.3.1 Elber Crack Closure Phenomenon ............................... 133
3.3.2 Threshold Stress Intensity Factor Range, ~Kth .............. 137
3.3.3 Newman Crack Closure Approach ............................... 141
3.4 Variable Amplitude Stress and the Retardation
Phenomenon ........................................................... 153
3.4.1 Wheeler Retardation ModeL ....................................... 156
3.4.2 Willenborg Retardation Model ..................................... 157
3.5 Cycle by Cycle Fatigue Crack Growth Analysis ............... 165
3.6 Environmental Assisted Corrosion Cracking ................... 167
3.6.1 Introduction ............................................................. 167
3.6.2 Threshold stress intensity factor { K1EAC and KEAC) .............. 170
3.6.3 ASTM Procedures for Obtaining K1EAC or KEAC •••••••••••••••• 173
References .......................................................................... 175
ix
CHAPTER 4 ELASTIC-PLASTIC FRACTURE MECHANICS (EPFM) AND APPLICATIONS ............................................ 180
4.0 Overview ................................................................ 180
4.1 Introduction ............................................................. 181
4.2 Introduction to Griffith Energy Balance Approach ............ 183
4.2.1 The Relationship Between Energy Release Rate, G, and
Complience ............................................................ 185
4.3 The Path Independent J- Integral and its Application ........ 189
4.3.1 Introduction ............................................................. 189
4.3.2 Derivation of Path Independent J- IntegraL .................... 191
4.4 Comments Concerning the Path Independent J-Integral
Concept. ................................................................ 200
4.5 J-Controlled Concept and Stable Crack Growth .............. 204
4.6 Experimental Evaluation of J-Integral and J1c Testing ....... 209
4.6.1 Multispecimen Laboratory Evaluation of the J-Integral
(Energy Rate Interpretation) ....................................... 210
4.6.2 Single Specimen Laboratory Evaluation of the J-lntegral. .. 215
4.6.3 Advanced Single Specimen Technique Using the C(T)
Specimen ............................................................... 220
4.7 Determination of Jlc Value Based on a Singie Specimen
Test. ..................................................................... 224
4.7.1 Validity Check for Fracture Toughness from the J-R
Curve .................................................................... 228
References ......................................................................... 233
CHAPTER 5 THE FRACTURE MECHANICS OF DUCTILE METALS THEORY ............................................................ 237
5.0 Introduction ............................................................. 237
x
5.1 The Extended Griffith Theory ...................................... 237
5.2 Fracture Mechanics Of Ductile Metals (FMDM) ............... 240
5.3 Determination of g, = aU/ac Term ................................. 241
5.4 Determination of the g2= aUjac Term ........................... 244
5.4.1 Octahedral Shear Stress Theory (Plane Stress
Conditions) ............................................................. 245
5.5 Octahedral Shear Stress Theory (Plane Strain
5.6
5.6.1
5.6.2
5.7
5.8
5.9
5.10
5.10.1
5.10.2
5.10.3
Conditions) ............................................................. 253
Applied Stress, 0', and Half Crack Length, c, Relationship.255
Determination of Wand h Terms Separately ................ 255 u u
Applied Stress and Crack Length Relationship ............... 256
Mixed Mode Fracture and Thickness Parameters ............ 257
The Stress-Strain Curve ............................................ 259
Verification of FMDM Results with the Experimental Data.259
Fracture Toughness Computation by the FMDM Theory ... 262
Introduction ............................................................. 262
Fracture Toughness Evaluation for 2219-T87 Aluminum
Alloy ...................................................................... 263
Fracture Toughness Evaluation for 7075-T73 Aluminum
Alloy ...................................................................... 267
References .................................................................... 272
CHAPTER 6 WELDED JOINTS AND APPLICATIONS ......... 274
6.0 Introduction ............................................................. 274
6.1 Welding of Aluminum Alloys ....................................... 275
6.2 Variable Polarity Plasma Arc (VPPA) ............................ 277
6.2.1 Static and Fracture properties of VPPA weld .................. 281
xi
6.3
6.3.1
6.3.2
6.3.2.1
6.4
Friction Stir Welding (FSW) ........................................ 287
Static and Fracture Properties of FSW .......................... 290
Application of FSW to Space Structures ........................ 292
Metallurigical Examination of Fracture Surfaces .............. 298
Summary ................................................................ 299
References .......................................................................... 302
CHAPTER 7 BOLTED JOINTS AND APPLICATIONS ........ . 304
7.1 Introduction ............................................................. 304
7.2 Bolted Joint Subjected to Cyclic Loading ....................... 305
7.3 Bolt Preload ............................................................ 307
7.3.1 Bolt Analysis ............................................................ 310
7.4 Fatigue Crack Growth Analysis of Pads in a Bolted Joint...317
7.5 Riveted Joints .......................................................... 328
7.6 Material Anisotropy and its Application in Bolt Analysis ..... 330
References ........................................................................... 332
CHAPTER 8 DURABILITY AND DAMAGE TOLERANCE OF COMPOSiTES ................................................................. .. 334
8.1 Overview of Composite .............................................. 334
8.2 Overview of Textiles Composites ................................. 337
8.2.1 Categorizations ........................................................ 339
8.3 Progressive Fracture Methodology ............................... 342
8.3.1 Characterization of Composite Degradation ................... 343
8.3.2 Composite Simulation Software ................................... 343
8.3.3 Progressive Fracture Analysis (PFA) ............................ 346
8.3.3.1 Computational Simulation Strategy .............................. 349
xii
8.3.3.2 Damage Tracking Process ......................................... 351
8.3.3.3 Failure Evaluation Approach ....................................... 353
8.3.3.4 Damage Evolution Metrics .......................................... 354
8.3.3.4.1 Total Damage Energy Release Rate (TDERR} ............... 355
8.3.3.4.2 Damage Energy Release Rate (DERR} ........................ 357
8.3.3.4.3 Strain Energy Damage Rate (SEDR} ............................ 358
8.3.3.4.4 Equivalent far field stress O'e ....................................... 358
8.3.3.4.5 The length of crack opening (a} ................................... 359
8.3.3.4.6 Equivalent fracture toughness from DERR or SEDR ........ 359
8.3.3.5 Evaluation of Elastic Constants ................................... 359
8.3.3.5.1 Stitched Simulation Capability ..................................... 360
8.3.3.5.2 Woven Patterns ....................................................... 361
8.3.3.5.3 Fiber Arrangement. ................................................... 361
8.3.3.6 Finite Element Analysis in PFA ................................... 363
8.3.3.7 Simulation of Damage Progression ............................. 364
8.3.4 Methodology of Mesh Refinement in Progressive Failure
8.3.5
8.3.6
8.3.6.1
8.4
8.4.1
8.4.2
8.4.3
8.4.4
8.4.5
Analysis ................................................................. 365
Simulation of Reshaping Braided Fiber Preforms to Assist
Manufacturing ......................................................... 365
Probabilistic Failure Analysis ...................................... 367
Probabilistic Evaluation of Composite Damage
Propagation ........................................................... 368
Composite Structural Analysis and Input and Output...... 369
Composite Analysis under Static Loading .................... 370
Composite Analysis under Low-Cycle Fatigue Loading ... 371
Composite Analysis under High-Cycle Fatigue Loading.. 372
Random Power Spectral Density Fatigue Loading ......... 375
Composite Analysis under Impact Loading .................. 376
xiii
8.4.6 Composite Analysis under Creep Loading................... 377
8.5 Conclusions.................................................. .. ...... 379
References............................. .......................................... 379
APPENDIX A ..................................................................... 384
INDEX ............................................................................... 402
xiv
Preface
In the preliminary stage of designing new structural hardware to perform a given mission in a fluctuating load environment, there are several factors that the designer should consider. Trade studies for different design configurations should be performed and, based on strength and weight considerations, among others, an optimum configuration selected. The selected design must withstand the environment in question without failure. Therefore, a comprehensive structural analysis that consists of static, dynamic, fatigue, and fracture is necessary to ensure the integrity of the structure. Engineers must also consider the feasibility of fabricating the structural hardware in the material selection process. During the past few decades, fracture mechanics has become a necessary discipline for the solution of many structural problems in which the survivability of structure containing pre-existing flaws is of great interest. These problems include structural failures resulting from cracks that are inherent in the material, or defects that are introduced in the part due to improper handling or rough machining, that must be assessed through fracture mechanics concepts.
The importance of fatigue and fracture in nuclear, pressure vessel, aircraft, and aerospace structural hardware cannot be overemphasized whenever safety is of utmost concern. This book is written for the designer and strength analyst, as well as for the material and process engineer, who is concerned with the integrity of the structural hardware under load-varying environments in which fatigue and fracture must be given special attention. The book is a result of years of both academic and industrial experiences that the author has accumulated during his work with nuclear, aircraft, and aerospace structures. However, the material contained in this book is sufficient to be applied to other industries, where fracture and fatigue are equally important. Moreover, the scope and contents of the book are adequate for use as a textbook for both graduate and undergraduate level courses in the mechanical, material, and aerospace engineering departments with emphasis given to the application of theory rather than the detail mathematical derivation of fracture parameters. Each chapter has several example problems that have been hand-picked from industrial experiences which the authors
have accumulated throughout the years in the field of fracture mechanics.
This book addresses the traditional fatigue approach to life evaluation of structural parts where it is assumed that the structure is initially free from cracks and, after N number of load cycles, the crack will initiate in some highly localized stressed areas. .In contrast to the traditional fatigue approach, Linear Elastic Fracture Mechanics (LEFM) assumes the existence of a crack in the structural part in the most unfavorable location perpendicular to the applied load. Chapter 1 covers both traditional fatigue (stress to life, S-N, and strain to life, eN) and an overview of the field of fracture mechanics, which includes, the Griffith energy balance, the LEFM concept, Elastic-Plastic Fracture Mechanics (EPFM), Fracture Mechanics of Ductile Metals (FMDM), and the failure prevention concept. The content of Chapter 1 is informative enough for the reader to become knowledgeable with the development of fracture mechanics and its application to structural parts. In Chapters 2 and 3, the application of fracture mechanics in determining the life of a structure is fully discussed through the use of the stress intensity factor parameter, K. The critical value of K is called fracture toughness and is discussed in Chapter 2. The development of the fatigue crack growth curve (da/dn versus L\K) is presented in Chapter 3.
In manufacturing space or aircraft structures, it is common practice for pieces of structure that are mated together in a mar-mer strong enough to withstand the load environment while allowing the transfer of load from one segment of the structure to another. Chapter 7 fully discusses the stress concentration sites in a bolted jOint that are the prime location for fatigue failure, where cracks can initiate from the threaded region or the periphery of the bolted joint. Welding is another commonly used technique join structural parts in space, aircraft and nuclear structure. A good quality weld can yield almost the same fatigue properties as the parent material. On the other hand, a poorly welded joint with an unacceptable amount of porosity, shrinkage, cavities, or incomplete fusion can be the source of crack initiation and premature failure of the structure. Chapter 6 discusses the Variable Polarity Plasma Arc (VPPA) and a new state-of-the-art technique called Friction Stir Welding (FSW) that are classified as fusion and non-fusion welding techniques, respectively.
In using the LEFM approach to evaluate the life of a part, crack tip yielding must be small and localized and no net section yielding is allowed in the part. Two fracture mechanics approaches are discussed in this book for analysis of tough metals where fracture behavior often extends beyond the elastic dominant regime. The first is called the EPFM theory and uses the J-integral concept first proposed by Rice
xvi
as a path independent integral based on the deformation theory of plasticity (Chapter 4). The second approach is called the FMDM theory. The crack tip plastic deformation defined by the FMDM theory is composed of two distinct regions: 1) the local strainability at the crack tip (the region of highly plastic deformation) and 2) the uniform strainability near the crack tip. The energy absorption rate for these two regions was calculated (see chapter 6) and used to extend the Griffith theory of fracture that originally was developed for brittle materials. In contrast to LEFM, the FMDM theory was shown to accurately correlate with test data for commonly used structural metals over a wide range of crack sizes at stresses above, as well as below the yield stress. The FMDM computer program is capable of generating the variation of fracture toughness as a function of the material thickness for ductile metals and requires only the stress-strain curve as an input.
In structural applications, the use of composites is sometimes advantageous over metallic material because of their light weight and higher stiffness. Damage tolerance and durability of composite material is not yet fully understood. Fracture initiation in composites is associated with defects such as voids, machining irregularities, stress concentrating, damage from impacts with tools or other objects resulting in discrete source damage, delamination, and non-uniform material properties stemming, for example, from improper heat treatment. After a crack initiates, it can grow and progressively lower the residual strength of a structure to the point where it can no longer support design loads, making global failure imminent. Chapter 8 discusses various modes of failure in composite materials and emphasis is given to the GENOA-PFA computer code that enables the engineer to analyze durability and damage tolerance in 20 and 3D woven braided stitched composite materials and structures.
The contents of this book represent a complete overview of the field of fatigue and fracture mechanics, a field that is continuously being advanced by many investigators. This book is divided into 8 chapters:
• Chapter 1. Overview of Fracture Mechanics and Failure Prevention
• Chapter 2. Linear Elastic Fracture Mechanics (LEFM) and Applications
• Chapter 3. Fatigue Crack Growth and Applications
• Chapter 4. Elastic-Plastic Fracture Mechanics (EPFM) and Applications
xvii
• Chapter 5. Fracture Mechanics of Ductile Metals (FMDM) Theory
• Chapter 6. Welded Joints and Applications
• Chapter 7. Bolted Joints and Applications
• Chapter 8. Durability and Damage Tolerance of Composites
Fracture properties for conducting fatigue crack growth and structural life analysis are included in Appendix A. which was extracted from the NASAIFLAGRO material library.
The author wishes to express his appreciation to Mr. David Ollodort (The Boeing Co.) for his editorial assistance with the entire manuscript. Dr. V. L. Chen (The Boeing Co.) for his comments to Chapter 8. Dr. Ares Rosakis (from California Institute of Technology) for his valuable comments to the EPFM concepts. and Mr. Bruce Young (McDermott Technology) for his comments to Chapter 4. He would also like to thank Mr. Doug Waldron (The Boeing Co.) for contributing a portion of Chapter 6. and Dr. Frank Abdi (Alpha STAR Corporation). Dr. Levon Minnetyan (Clarkson University). and Dr. Chris Cham is (NASAlGlenn Research Center) for their contributions to Chapter 8. Finally. the support of his family. especially his loving and devoted wife. children. and dear mother. is gratefully acknowledged. Their sacrifices made it possible to complete this book.
xviii
