Metal Fatigue Analysis Handbook

Metal FatigueAnalysis Handbook

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Metal FatigueAnalysis HandbookPractical Problem-Solving Techniques

for Computer-Aided Engineering

Yung-Li LeeMark E. BarkeyHong-Tae Kang

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Library of Congress Cataloging-in-Publication DataLee, Yung-Li.Metal fatigue analysis handbook : practical problem-solving techniques for

computer-aided engineering / Yung-Li Lee, Mark E. Barkey, Hong-Tae Kang.p. cm.

ISBN 978-0-12-385204-5 (hardback)1. Metals–Fatigue. 2. Computer-aided engineering. I. Barkey, Mark E.

II. Kang, Hong-Tae. III. Title.TA460.L416 2011620.1'66–dc23 2011020149

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.

For information on all Butterworth-Heinemann publicationsvisit our website: www.elsevierdirect.com

Printed in the United States11 12 13 14 15 10 9 8 7 6 5 4 3 2 1

Thank you to our families for their inspiration, encouragement,and patience!

To my friend, my love, my wife, Pai-Jen, and ourchildren, Timothy and Christine

Yung-Li Lee

To my wife, Tammy, and our daughters, Lauren,Anna, and Colleen

Mark E. Barkey

To my wife, Jung-Me, and our son, AnthonyHong-Tae Kang

Contents

Preface ................................................................................... xv

Acknowledgments ..................................................................... xix

About the Authors ................................................................... xxi

Nomenclature ........................................................................ xxiii

Chapter 1: Road Load Analysis Techniques in Automotive Engineering ..... 1Xiaobo Yang, Peijun Xu

Introduction ................................................................................. 1Fundamentals of Multibody Dynamics ............................................. 4

Conditions of Equilibrium .......................................................... 6D’Alembert’s Principle ............................................................... 7Multibody Dynamics Systems .................................................... 10

Generic Load Cases ..................................................................... 12Generic Load Events ................................................................ 13Analysis Procedure .................................................................. 19Results and Report ................................................................... 20

Semianalytical Analysis ............................................................... 22Powertrain Mount Load Analyses ............................................... 22Suspension Component Load Analysis ........................................ 30

Vehicle Load Analysis Using 3D Digitized Road Profiles ................. 39Vehicle Model Description ........................................................ 42Tire Model Description ............................................................. 43Model Validation Process ......................................................... 46

Summary ................................................................................... 56References ................................................................................. 57

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Chapter 2: Pseudo Stress Analysis Techniques ................................ 61Yung-Li Lee, Mingchao Guo

Introduction ................................................................................ 61Static Stress Analysis ................................................................... 62

Fixed Reactive Analysis ........................................................... 63Inertia Relief Analysis .............................................................. 66

Modal Transient Response Analysis ............................................... 71Natural Frequencies and Normal Modes ...................................... 72Orthonormalization of Normal Modes ......................................... 73Decoupled Modal Equations of Motion ....................................... 77Numerical Integration Method for Equations of Motion ................. 80

Summary ................................................................................... 85References ................................................................................. 86

Chapter 3: Rainflow Cycle Counting Techniques .............................. 89Yung-Li Lee, Tana Tjhung

Introduction ................................................................................ 89Uniaxial Rainflow Cycle Counting Techniques ................................ 90

Rainflow Counting Method by Matsuishi and Endo ...................... 90Three-Point Counting Technique ................................................ 94Four-Point Counting Technique ................................................ 102

Multiaxial Rainflow Reversal Counting Techniques ........................ 106Summary .................................................................................. 112References ................................................................................ 113

Chapter 4: Stress-Based Uniaxial Fatigue Analysis ......................... 115Yung-Li Lee, Mark E. Barkey

Introduction .............................................................................. 116Ultimate Tensile Strength of a Component .................................... 120

Reliability Correction Factor .................................................... 121Size Correction Factor ............................................................ 123Temperature Correction Factor for Ultimateand Yield Strengths ................................................................ 124Stress Correction Factor .......................................................... 126Load Correction Factor ........................................................... 126

Component Endurance Limit under Fully Reversed Loading ........... 128Temperature Correction Factor ................................................. 130Endurance Limit Factor ........................................................... 131

Contents

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Surface Treatment Factor ........................................................ 132Roughness Correction Factor ................................................... 132Fatigue Notch Factor .............................................................. 134

Constant Amplitude Stress-Life Curve for a NotchedComponent under Fully Reversed Loading .................................... 145

Constant Amplitude Nominal Stress-Life Curve .......................... 145Constant Amplitude Pseudo Stress-Life Curve ............................ 147

Stress-Life Curve for a Component under VariableAmplitude Loading .................................................................... 149Mean Stress Effect ..................................................................... 151Summary .................................................................................. 157References ................................................................................ 159

Chapter 5: Stress-Based Multiaxial Fatigue Analysis ....................... 161Yung-Li Lee, Mark E. Barkey

Introduction .............................................................................. 161Fatigue Damage Models ............................................................. 168

Empirical Formula Approach ................................................... 168Equivalent Stress Approach ..................................................... 170Critical Plane Approach .......................................................... 186Dang Van’s Multiscale Approach ............................................. 199

Summary .................................................................................. 210References ................................................................................ 211

Chapter 6: Strain-Based Uniaxial Fatigue Analysis ......................... 215Yung-Li Lee, Mark E. Barkey

Introduction .............................................................................. 215Steady State Cyclic Stress–Strain Relation .................................... 217Fully Reversed, Constant Amplitude Strain-Life Relation ................ 221Estimate of Cyclic Material and Fatigue Properties ......................... 223Strain-Life Equations with Mean Stress ........................................ 224

Morrow ................................................................................ 224Smith, Watson, and Topper ..................................................... 225

Notch Analysis ......................................................................... 231Neuber ................................................................................. 232Nominally Elastic Behavior ..................................................... 234Nominally Gross Yielding of a Net Section ............................... 235Modified Neuber Rule ............................................................ 236

Contents

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Molsky and Glinka ................................................................. 239Applications .......................................................................... 246


Chapter 7: Fundamentals of Cyclic Plasticity Theories ..................... 253Yung-Li Lee, Mark E. Barkey

Introduction .............................................................................. 254Tensor Notations ....................................................................... 254Theory of Elasticity ................................................................... 255Monotonic Plasticity Theories ..................................................... 257

Yield Surface Function ........................................................... 257Isotropic Hardening ................................................................ 259Flow Rules ........................................................................... 260Plastic Strains ........................................................................ 264

Cyclic Plasticity Theories ........................................................... 265Elastic and Plastic Processes .................................................... 270Associated Flow Rule ............................................................. 271Consistency Condition ............................................................ 272Kinematic Hardening Models ................................................... 272Determination of a Generalized Plastic Modulus ......................... 274Stresses and Strains ................................................................ 283

Applications: Notch Analyses Based on Pseudo Stresses ................. 284Hoffmann and Seeger ............................................................. 285Buczynski and Glinka ............................................................. 289Lee, Chiang, and Wong .......................................................... 292


Chapter 8: Strain-Based Multiaxial Fatigue Analysis ...................... 299Mark E. Barkey, Yung-Li Lee

Introduction .............................................................................. 299Fatigue Damage Models ............................................................. 300

Equivalent Strain Approaches .................................................. 300Energy Approaches ................................................................ 309Critical Plane Approaches ....................................................... 311

Strain Gage Rosette Analysis ...................................................... 316Strain Data Acquisitions .......................................................... 318Fatigue Analysis with Plasticity ................................................ 323

Contents

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Chapter 9: Vibration Fatigue Testing and Analysis ......................... 333Yung-Li Lee, Hong-Tae Kang

Introduction .............................................................................. 333Swept Sinusodial or Single-Frequency Sweep Test ......................... 336

Response to a Linear Single-Degree-of-Freedom SystemSubjected to Sinusoidal-Based Excitation ................................... 337Fatigue Damage Calculation .................................................... 341

Random Vibration Test .............................................................. 345Characteristics of Random Vibration ......................................... 345Responses to a Linear Single-Degree-of-Freedom SystemSubjected to Base Random Vibration ........................................ 356Fatigue Damage Models under Random Stress Process ................ 361


Chapter 10: Fatigue Life Prediction Methods of Seam-WeldedJoints .................................................................... 383

Hong-Tae Kang, Yung-Li Lee

Introduction .............................................................................. 383Parameters Affecting Fatigue Lives of Seam-Welded Joints ............. 384Fatigue Life Prediction Methods .................................................. 387

Nominal Stress Approaches ..................................................... 388Structural Stress Approaches .................................................... 389Notch Pseudo Stress or RXMS Approach .................................. 407


Chapter 11: Fatigue Life Prediction Methods of ResistanceSpot-Welded Joints ................................................ 429

Hong-Tae Kang, Yung-Li Lee

Introduction .............................................................................. 429Parameters Affecting Spot-Welded Joints ...................................... 430

Nugget Diameter .................................................................... 430Sheet Metal Thickness ............................................................ 431

Contents

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Specimen Width .................................................................... 431Base Metal Strength ............................................................... 432Specimen Type ...................................................................... 432Multiaxial Loading ................................................................. 433

Fatigue Life Prediction Methods .................................................. 435Load Life Approach ............................................................... 435Linear Elastic Fracture Mechanics Approach .............................. 436Structural Stress Approach ...................................................... 442Applications .......................................................................... 448


Chapter 12: Design and Analysis of Metric Bolted Joints—VDIGuideline and Finite Element Analysis ........................ 461

Yung-Li Lee, Hsin-Chung Ho

Introduction .............................................................................. 462Overview of Bolted Joints and Mechanical Properties ..................... 462Estimate of a Bolt Diameter ........................................................ 471Estimate of Joint Elastic Compliance (Resilience) .......................... 472

Elastic Compliance of a Bolt ................................................... 473Elastic Compliance of Clamped Plates for ConcentricallyBolted Joints ......................................................................... 475External Loads—Load Plan Factor (n) and Load Factor (Φ) ......... 479

Assembly Loads on Bolted Joints ................................................ 482Embedding Effect .................................................................. 483Tightening Torque .................................................................. 484Assembly Preload .................................................................. 485Clamped Plate Pressure ........................................................... 491Minimum Thread Engagement Length ....................................... 491

Service Loads on Bolted Joints .................................................... 495Bolt Yielding Due to Overstressing .......................................... 495Clamp Load Loss Due to Gapping ........................................... 496Thread Stripping .................................................................... 496Clamped Plates Crushing Due to Excessive Pressure ................... 496Slipping Due to Transverse Loads ............................................ 497Fatigue Failure ...................................................................... 497

Application ............................................................................... 498Solution ................................................................................ 499

Contents

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Finite Element-Based Fatigue Analysis of Thread Bolts .................. 507Solid Bolt Model ................................................................... 508Spider Bolt Model .................................................................. 510


Index ................................................................................... 515

Contents

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Preface

Fatigue analysis of metals has been developing for more than 150 years from asimple approach involving elementary stress calculation based on the theory ofelasticity, to a sophisticated treatment demanding a thorough knowledge of com-plex multiaxial loading and material behavior. Present engineering practice forcomprehensive fatigue analysis requires computer-aided engineering (CAE) toolsthat use knowledge of material properties for cyclic stress–strain and fatiguebehavior, structural kinematics for load simulations, finite element analysis forstress–strain calculations, and fatigue damage assessment for crack initiation andpropagation life predictions.

Since the state-of-the-art technologies’ load, stress, and fatigue analyses and theirapplications to engineering design for durability have been commonly adopted innumerous commercial analysis products, this publication strives to present, in alogical manner, the theoretical background needed for explaining and interpretingthe analysis requirement and outputs. Ultimately, this book is intended to serve thereader as a theoretical manual or an analysis handbook. Beginning with coverageof background material, including references to pertinent research, the developmentof the formulas or theories applied in these CAE tools is followed by a number ofexamples to illustrate the process of designing structures to prevent fatigue failuresin detail.

Considerable emphasis has been placed on including for the advanced student, aswell as the practicing engineer, the present techniques used in CAE for road loadsimulations, pseudo stress calculations, estimates of material properties, incremen-tal plasticity theories, and multiaxial fatigue life predictions. The understandingof these is essential to properly applying mechanical designs for durability. Thespecific illustrative examples are generally treated in separate sections within thechapters so that the reader can easily grasp the concepts.

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The following list details the information provided in each chapter.

• Chapter One covers the three road-load analysis techniques to predict vehiclecomponent loads for mechanical design for durability. They are the genericload case analysis for extreme loads; the semianalytical load analysis with theinput of the acquired spindle forces, displacements, and accelerations; and thevehicle dynamics analysis with a tire model and the input of three-dimensionaldigitized terrain profiles. Commonly used commercial tire models are alsointroduced in this chapter.

• Chapter Two details the three pseudo stress analysis techniques: fixed reactivemethod, inertia relief method, and modal transient response analysis method.The pseudo stresses are the stresses calculated from a linear elastic finiteelement analysis. These stresses are named because they are different fromthe true stresses as plasticity occurs. The pseudo stresses can be directlyemployed for stress-based fatigue assessment in the high cycle fatigue (HCF)regime or for strain-based fatigue damage analysis in the low cycle fatigue(LCF) regime in conjunction with the multiaxial notch analysis to estimatethe local true stresses and strains.

• Chapter Three overviews the historical rainflow cycle counting techniquesfor uniaxial load time history and the latest rainflow reversal extractiontechniques for multiaxial load time histories. For multiaxial fatigue analyses,the uniaxial rainflow cycle counting method and the multiaxial rainflowreversal extraction method have been widely employed in the critical planesearch approach and the equivalent stress–strain approach, respectively.

• Chapter Four provides an in-depth presentation on the stress-based uniaxialfatigue analysis, which focuses on the techniques provided by FKM-Guideline(Analytical Strength Assessment of Components in Mechanical Engineering)that are used to generate the synthetic nominal stress life and the local pseudostress-life curves of a component, based on a given material’s ultimate tensilestrength, and to account for the mean stress effect with the mean stresssensitivity factor for various materials.

• Chapter Five introduces the concept of proportional and nonproportionalloading, or stressing in the state of multiaxial stresses, and the nonproportionalloading effect on fatigue strength; it also presents the popular stress-basedtheories (empirical formulas, equivalent stresses, critical plane approach, and

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Preface

Dang Van multiscale method) for assessing fatigue damage under the state ofmultiaxial stresses.

• Chapter Six reviews the strain-based fatigue analysis techniques for amaterial under the state of uniaxial stress, which demands the familiarRamberg–Osgood and the Masing equations for hysteresis loop simulations,the modified Neuber method or Molsky–Glinka’s energy density methodfor the notch analysis, and finally the modified Morrow or Smith–Watson–Topper (SWT) mean stress corrected strain-life equation for fatigue behavior.The incorporation of residual stress and surface finish factor in the notch stressanalysis is presented.

• Chapter Seven details the presentations of theories of plasticity, includingthe introduction of associated flow rule, consistency condition, and kinematichardening rules, for simulating the material hysteresis behaviors under thestate of multiaxial stresses, and of the multiaxial notch analysis techniquesfor estimating local material responses based on the input of pseudostresses.

• Chapter Eight extends the discussion of multiaxial stress–strain relationand multiaxial notch analysis methods of Chapter Seven, and focuses onthe presentation of strain-based fatigue damage assessment techniques fora material under multiaxial stress state. Particularly, the critical planeapproach with the damage parameter such as the Fatemi–Socie, SWT,or Brown–Miller method has been introduced and discussed for thepros and cons.

• Chapter Nine presents an analytical solution to assess fatigue damageseverity for various vibration test specifications. This chapter also reviewsthe fundamentals of sinusoidal and random vibration test methods andintroduces the fatigue damage spectrum (FDS) calculation technique foreach test method.

• Chapter Ten introduces some fatigue analysis techniques for seam-weldedjoints using linear elastic finite element analysis results. Especially, structuralstress approaches developed by Dong and Femer were described in detailwith examples.

• Chapter Eleven presents a summary of the primary factors affecting fatiguelife and strength of resistance spot-welded joints and then focuses on some

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Preface

particular fatigue analysis techniques (the linear elastic fracture mechanicsapproach and the structural stress approach) and the relation of basicmaterial specimens test to design.

• Chapter Twelve introduces the basics of the VDI 2230 guideline for ISOmetric bolted joints to prevent potential failure modes such as embedding,clamp load loss, clamped plates crushing and slipping, bolt yielding, threadstripping, and bolt fatigue failure. The assumptions and the calculationprocedure to estimate the elastic compliances of the bolt and the clampedplates are also described. In addition, the last portion of this chapter presentsthe commonly used finite element (FE) bolt-modeling techniques for forcesand stress analysis, and recommends the appropriate fatigue damageassessment method for two different threaded bolts (e.g., rolled before andafter heat treatment).

This book does not cover present nonlinear damage rules, but instead it emphasizesthe application of the linear damage rule (LDR). The LDR has been universallyadopted due to its simplicity and can account for load sequence and hardeningeffect, if used with the appropriate damage parameter. This book does not addressdetailed analytical models for crack growth behavior such as crack growth direction,growth rates, closures, R ratio effect, small crack effects, and threshold. However,the book does present the crack initiation life prediction models for metalliccomponents subjected to the state of uniaxial and multiaxial stresses, and thecrack growth approaches for life predictions of welded joints.

The plasticity theories introduced here do not apply to rate-dependent yielding,elevated temperature effect, and anisotropic materials. This book is not intendedto be a comprehensive review of all published research in each respective sub-ject area, but instead it presents the theories and problem-solving techniquescommonly employed in automotive engineering.

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Preface

Acknowledgments

Special thanks are due to Dr. Xiaobo Yang of Oshkosh Corporation, Dr. PeijunXu of Ebco Inc., Dr. Mingchao (Mike) Guo of Chrysler Group LLC, Dr. TanaTjhung of Chrysler Group LLC, and Mr. Hsin-Chung (Simon) Ho of ChryslerGroup LLC for contributing to some chapters. Also, the authors are greatlyindebted to Professor Jwo Pan of The University of Michigan–Ann Arbor,Professor Norman Dowling of Virginia Polytechnic Institute and State University,Professor Steve Tipton of the University of Tulsa, and Dr. Peter Heyes of HBM-nCode International for their valuable suggestions and encouragement.

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About the Authors

Yung-Li Lee is a Technical Fellow in Science Labs & Proving Grounds atChrysler Group LLC where he started his career as a product developmentengineer in 1988. He was elected as a Fellow of the Society of AutomotiveEngineers (SAE) and received the SAE Forest R. McFarland Award in 2006.His expertise includes durability/reliability testing and simulation.

Since 1997, he has been an Adjunct Professor of Mechanical Engineering atOakland University in Rochester, Michigan, where he teaches graduate schoolcourses on fundamentals of metal fatigue, accelerated test method development,reliability demonstration test planning, vibration test method development,frequency-based fatigue analysis, multiaxial fatigue, and fatigue of bolted andwelded joints.

He received his B.S. in Civil Engineering from the National Central University inTaiwan in 1979, and M.S. and Ph.D. in Structural Engineering from the Universityof Wisconsin–Madison in 1984 and 1988, respectively. He is the primary authorof the book, Fatigue Testing and Analysis: Theory and Practice, published byElsevier in 2005.

Mark E. Barkey is a Professor in the Aerospace Engineering and MechanicsDepartment at the University of Alabama, where he joined the faculty in 1995.During this time, he has directed student theses and research in the area of fati-gue testing and analysis of materials and structures. He has received support forhis research from Ford, General Motors, Chrysler, Sandia National Laboratories,and NASA. He received a B.S. in Engineering Mechanics with a Minor inMathematics from the University of Missouri-Rolla in 1989, and an M.S. andPh.D. from the University of Illinois in Theoretical and Applied Mechanics in1991 and 1993, respectively. He served as a Visiting Assistant Professor in theMechanical and Industrial Engineering Department at the University of Illinoisin 1994.

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Dr. Barkey is a member of the Society of Automotive Engineering (SAE),the American Society of Mechanical Engineers (ASME), and the Society forExperimental Mechanics (SEM). He has made several presentations to theSAE Fatigue Design and Evaluation Committee, and was selected to receivethe SAE Arch T. Colwell Merit Award for an SAE technical paper in 2005.

Hong-Tae Kang is an Associate Professor in the Mechanical EngineeringDepartment at the University of Michigan-Dearborn where he joined the facultyin 2003. He has been conducting researches on fatigue life prediction methodsusing finite element analysis results for spot-welded joints and seam-weldedjoints. He received his B.S. in Earth Science Education from the Seoul NationalUniversity in Korea in 1992, and M.S. and Ph.D. in Engineering Mechanicsfrom the University of Alabama in 1997 and 1999, respectively.

Since graduation, he has worked for automotive companies in Detriot, Michigan,as a CAE analyst and project engineer for almost three years. He is a memberof the Society of Automotive Engineering (SAE) and the American Society ofMechanical Engineers (ASME).

About the Authors

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Metal Fatigue Analysis Handbook

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