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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

vii

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

ix

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

Summary .................................................................................. 249References ................................................................................ 250

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

Summary .................................................................................. 293References ................................................................................ 294

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

x

Summary .................................................................................. 329References ................................................................................ 330

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

Summary .................................................................................. 381References ................................................................................ 381

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

Summary .................................................................................. 421References ................................................................................ 423

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

xi

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

Summary .................................................................................. 455References ................................................................................ 456

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

xii

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

Summary .................................................................................. 512References ................................................................................ 513

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

Contents

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