Preface... xv Acknowledgments... xix About the Authors... xxi Nomenclature... xxiii Chapter 1: Road Load Analysis Techniques in Automotive Engineering... 1 Xiaobo Yang, Peijun Xu Introduction... 1 Fundamentals of Multibody Dynamics... 4 Conditions of Equilibrium... 6 D Alembert s Principle... 7 Multibody Dynamics Systems... 10 Generic Load Cases... 12 Generic Load Events... 13 Analysis Procedure... 19 Results and Report... 20 Semianalytical Analysis... 22 Powertrain Mount Load Analyses... 22 Suspension Component Load Analysis... 30 Vehicle Load Analysis Using 3D Digitized Road Profiles... 39 Vehicle Model Description... 42 Tire Model Description... 43 Model Validation Process... 46 Summary... 56 References... 57 vii
Chapter 2: Pseudo Stress Analysis Techniques... 61 Yung-Li Lee, Mingchao Guo Introduction... 61 Static Stress Analysis... 62 Fixed Reactive Analysis... 63 Inertia Relief Analysis... 66 Modal Transient Response Analysis... 71 Natural Frequencies and Normal Modes... 72 Orthonormalization of Normal Modes... 73 Decoupled Modal Equations of Motion... 77 Numerical Integration Method for Equations of Motion... 80 Summary... 85 References... 86 Chapter 3: Rainflow Cycle Counting Techniques... 89 Yung-Li Lee, Tana Tjhung Introduction... 89 Uniaxial Rainflow Cycle Counting Techniques... 90 Rainflow Counting Method by Matsuishi and Endo... 90 Three-Point Counting Technique... 94 Four-Point Counting Technique... 102 Multiaxial Rainflow Reversal Counting Techniques... 106 Summary... 112 References... 113 Chapter 4: Stress-Based Uniaxial Fatigue Analysis... 115 Yung-Li Lee, Mark E. Barkey Introduction... 116 Ultimate Tensile Strength of a Component... 120 Reliability Correction Factor... 121 Size Correction Factor... 123 Temperature Correction Factor for Ultimate and Yield Strengths... 124 Stress Correction Factor... 126 Load Correction Factor... 126 Component Endurance Limit under Fully Reversed Loading... 128 Temperature Correction Factor... 130 Endurance Limit Factor... 131 viii
Surface Treatment Factor... 132 Roughness Correction Factor... 132 Fatigue Notch Factor... 134 Constant Amplitude Stress-Life Curve for a Notched Component under Fully Reversed Loading... 145 Constant Amplitude Nominal Stress-Life Curve... 145 Constant Amplitude Pseudo Stress-Life Curve... 147 Stress-Life Curve for a Component under Variable Amplitude Loading... 149 Mean Stress Effect... 151 Summary... 157 References... 159 Chapter 5: Stress-Based Multiaxial Fatigue Analysis... 161 Yung-Li Lee, Mark E. Barkey Introduction... 161 Fatigue Damage Models... 168 Empirical Formula Approach... 168 Equivalent Stress Approach... 170 Critical Plane Approach... 186 Dang Van s Multiscale Approach... 199 Summary... 210 References... 211 Chapter 6: Strain-Based Uniaxial Fatigue Analysis... 215 Yung-Li Lee, Mark E. Barkey Introduction... 215 Steady State Cyclic Stress Strain Relation... 217 Fully Reversed, Constant Amplitude Strain-Life Relation... 221 Estimate of Cyclic Material and Fatigue Properties... 223 Strain-Life Equations with Mean Stress... 224 Morrow... 224 Smith, Watson, and Topper... 225 Notch Analysis... 231 Neuber... 232 Nominally Elastic Behavior... 234 Nominally Gross Yielding of a Net Section... 235 Modified Neuber Rule... 236 ix
Molsky and Glinka... 239 Applications... 246 Summary... 249 References... 250 Chapter 7: Fundamentals of Cyclic Plasticity Theories... 253 Yung-Li Lee, Mark E. Barkey Introduction... 254 Tensor Notations... 254 Theory of Elasticity... 255 Monotonic Plasticity Theories... 257 Yield Surface Function... 257 Isotropic Hardening... 259 Flow Rules... 260 Plastic Strains... 264 Cyclic Plasticity Theories... 265 Elastic and Plastic Processes... 270 Associated Flow Rule... 271 Consistency Condition... 272 Kinematic Hardening Models... 272 Determination of a Generalized Plastic Modulus... 274 Stresses and Strains... 283 Applications: Notch Analyses Based on Pseudo Stresses... 284 Hoffmann and Seeger... 285 Buczynski and Glinka... 289 Lee, Chiang, and Wong... 292 Summary... 293 References... 294 Chapter 8: Strain-Based Multiaxial Fatigue Analysis... 299 Mark E. Barkey, Yung-Li Lee Introduction... 299 Fatigue Damage Models... 300 Equivalent Strain Approaches... 300 Energy Approaches... 309 Critical Plane Approaches... 311 Strain Gage Rosette Analysis... 316 Strain Data Acquisitions... 318 Fatigue Analysis with Plasticity... 323 x
Summary... 329 References... 330 Chapter 9: Vibration Fatigue Testing and Analysis... 333 Yung-Li Lee, Hong-Tae Kang Introduction... 333 Swept Sinusodial or Single-Frequency Sweep Test... 336 Response to a Linear Single-Degree-of-Freedom System Subjected to Sinusoidal-Based Excitation... 337 Fatigue Damage Calculation... 341 Random Vibration Test... 345 Characteristics of Random Vibration... 345 Responses to a Linear Single-Degree-of-Freedom System Subjected to Base Random Vibration... 356 Fatigue Damage Models under Random Stress Process... 361 Summary... 381 References... 381 Chapter 10: Fatigue Life Prediction Methods of Seam-Welded Joints... 383 Hong-Tae Kang, Yung-Li Lee Introduction... 383 Parameters Affecting Fatigue Lives of Seam-Welded Joints... 384 Fatigue Life Prediction Methods... 387 Nominal Stress Approaches... 388 Structural Stress Approaches... 389 Notch Pseudo Stress or RXMS Approach... 407 Summary... 421 References... 423 Chapter 11: Fatigue Life Prediction Methods of Resistance Spot-Welded Joints... 429 Hong-Tae Kang, Yung-Li Lee Introduction... 429 Parameters Affecting Spot-Welded Joints... 430 Nugget Diameter... 430 Sheet Metal Thickness... 431 xi
Specimen Width... 431 Base Metal Strength... 432 Specimen Type... 432 Multiaxial Loading... 433 Fatigue Life Prediction Methods... 435 Load Life Approach... 435 Linear Elastic Fracture Mechanics Approach... 436 Structural Stress Approach... 442 Applications... 448 Summary... 455 References... 456 Chapter 12: Design and Analysis of Metric Bolted Joints VDI Guideline and Finite Element Analysis... 461 Yung-Li Lee, Hsin-Chung Ho Introduction... 462 Overview of Bolted Joints and Mechanical Properties... 462 Estimate of a Bolt Diameter... 471 Estimate of Joint Elastic Compliance (Resilience)... 472 Elastic Compliance of a Bolt... 473 Elastic Compliance of Clamped Plates for Concentrically Bolted Joints... 475 External Loads Load Plan Factor (n) and Load Factor (Φ)... 479 Assembly Loads on Bolted Joints... 482 Embedding Effect... 483 Tightening Torque... 484 Assembly Preload... 485 Clamped Plate Pressure... 491 Minimum Thread Engagement Length... 491 Service Loads on Bolted Joints... 495 Bolt Yielding Due to Overstressing... 495 Clamp Load Loss Due to Gapping... 496 Thread Stripping... 496 Clamped Plates Crushing Due to Excessive Pressure... 496 Slipping Due to Transverse Loads... 497 Fatigue Failure... 497 Application... 498 Solution... 499 xii
Finite Element-Based Fatigue Analysis of Thread Bolts... 507 Solid Bolt Model... 508 Spider Bolt Model... 510 Summary... 512 References... 513 Index... 515 xiii