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Metal Fatigue Analysis Handbook: Practical problem-solving techniques for computer-aided engineering

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Understand why fatigue happens and how to model, simulate, design and test for it with this practical, industry-focused reference

Written to bridge the technology gap between academia and industry, the Metal Fatigue Analysis Handbook presents state-of-the-art fatigue theories and technologies alongside more commonly used practices, with working examples included to provide an informative, practical, complete toolkit of fatigue analysis.

Prepared by an expert team with extensive industrial, research and professorial experience, the book will help you to understand:

  • Critical factors that cause and affect fatigue in the materials and structures relating to your work
  • Load and stress analysis in addition to fatigue damage-the latter being the sole focus of many books on the topic
  • How to design with fatigue in mind to meet durability requirements
  • How to model, simulate and test with different materials in different fatigue scenarios
  • The importance and limitations of different models for cost effective and efficient testing

Whilst the book focuses on theories commonly used in the automotive industry, it is also an ideal resource for engineers and analysts in other disciplines such as aerospace engineering, civil engineering, offshore engineering, and industrial engineering.

  • The only book on the market to address state-of-the-art technologies in load, stress and fatigue damage analyses and their application to engineering design for durability
  • Intended to bridge the technology gap between academia and industry-written by an expert team with extensive industrial, research and professorial experience in fatigue analysis and testing
  • An advanced mechanical engineering design handbook focused on the needs of professional engineers within automotive, aerospace and related industrial disciplines
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Editorial Reviews

From the Publisher

"The Metal Fatigue Analysis Handbook was written to bridge the technology gap between academia and industry. It presents state-of-the-art fatigue theories and technologies alongside more commonly used practices. Working examples are included to provide an informative, practical, complete tool kit of fatigue analysis. Prepared by an expert team with extensive industrial, research, and professorial experience, the book examines critical factors that cause and affect fatigue in the materials and structures, load and stress analysis, ways to design to meet durability requirements, and how to model, simulate, and test with different materials in different fatigue scenarios."--Mechanical Engineering Magazine, June 2012

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Product Details

  • ISBN-13: 9780123852045
  • Publisher: Elsevier Science
  • Publication date: 8/31/2011
  • Pages: 632
  • Product dimensions: 7.60 (w) x 9.30 (h) x 1.70 (d)

Meet the Author

Fatigue Expert and Technical Fellow at Chrysler Group LLC, Michigan, USA.
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Read an Excerpt

Metal Fatigue Analysis Handbook

Practical Problem-Solving Techniques for Computer-Aided Engineering
By Yung-Li Lee Mark E. Barkey Hong-Tae Kang


Copyright © 2012 Elsevier Inc.
All right reserved.

ISBN: 978-0-12-385205-2

Chapter One

Road Load Analysis Techniques in Automotive Engineering

Xiaobo Yang Oshkosh Corporation

Peijun Xu Ebco Inc.

Chapter Outline

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


The concept of design-by-analysis and validation-by-testing has been proven to be the most efficient and effective way to design a vehicle structure to meet its functional objectives, and universally adopted by most of the engineering communities.

The vehicle functional objectives include the federal regulations, such as emission and safety, and the mandatory requirements set up by each manufacturer, such as durability, reliability, vehicle dynamics, ride and comfort, noise, vibration and harshness (NVH), aerothermal and electromagnetic capability (EMC), among other things. The new concept can offer a chance to optimize a vehicle structure for these multifunctional objectives in a virtual engineering domain and to validate the structure by testing it in a physical world.

The validation-by-testing concept consists of development of accelerated test methods and reliability demonstration test planning strategies. Accelerated test method development is used to develop a pass or failure criterion for durability testing by using the damage equivalence theory. Examples could be vehicle proving grounds testing to represent the extreme customer usage profiles for the life of a design vehicle (so-called duty cycle data), real-time simulation testing on systems—that is, road test simulators (RTS) and multiaxial simulation table (MAST)—or simple life testing for components (e.g., constant amplitude loading or block cycle loading test).

Once the success criterion is established, numerous reliability demonstration test planning strategies have been proposed to demonstrate the reliability and confidence level of the designed products by testing them with a limited sample size. Depending on the failure criteria, the reliability demonstration test methods are recommended for components and the repairable systems, while the reliability growth model approaches are employed only for the repairable systems. Detailed discussion of these methods is beyond the scope of this chapter, and can be found elsewhere (Lee, Pan, Hathaway, & Barkey, 2005).

The design-by-analysis concept requires reliable virtual analytical tools for analyses. The quality of these tools relies on the accuracy of the mathematical model, material characterization, boundary conditions, and load determination. For durability analysis, the three important factors are:

• Loading

• Geometry

• Material

When external forces are applied to a multibody system, these forces are transferred through that system from one component to the next, where a component is defined as an element within that system. The fatigue life of a component is governed by the loading environment to which it is subject, the distribution of stresses and strains arising from that environment, and the response of the material from which it is manufactured. As a result, the major inputs to any fatigue analysis are loading, component geometry, and cyclic material properties.

A moving vehicle is a complex dynamic system primarily subjected to various static and dynamic external loads from tire/road interaction, aerodynamics, gravity, and payload, which yield overall vehicle motion in space and relative motions among various vehicle components. The relative motions of vehicle components are always constrained by joints and compliant elements (such as springs, shock absorbers, bushings/mounts, and jounce/rebound bumpers), and would induce internal forces and stresses that will possibly result in fatigue failures. Thus, it is crucial to predict these internal responses of vehicle components and systems for any failure prevention.

Loading information can be obtained using a number of different methods. Local or nominal strains can be measured by means of strain gages. Nominal loads can be measured through the use of load cells or, more recently, they can be derived externally by means of analysis. Since early methodologies relied on measurement from physical components, the application of fatigue analysis methods has been confined to the analysis of service failures or, at best, to the later stages of the design cycle where components and systems first become available.

The ability to predict component loads analytically means that physical components are no longer a prerequisite for durability analysis and so analysis can proceed much earlier in the design cycle. It is important to note that, in this context, loading environment is defined as the set of phase-related loading sequences (time histories) that uniquely map the cyclic loads to each external input location on the component.

Many virtual analysis tools for multibody dynamics (Gipser, Hofer, & Lugner, 1997; Tampi & Yang, 2005; Bäcker et al., 2007; Abd El-Gawwad, Crolla, Soliman, & El-Sayed, 1999a, 1999b; Stadterman, Connon, Choi, Freeman, & Peltz, 2003; Berzeri et al., 2004; Haga, 2006, 2007) have been developed to accurately calculate loads for components and systems. In addition to computer memory and speed, the efficiency of their engineering applications hinges on the availability of input data sources and modeling techniques. These tools have been widely adapted by the automotive engineering industry to predict vehicle road loads for fatigue damage assessments.

The objective of this chapter is to present the virtual analysis methods employed to characterize vehicle dynamic loads for one of the functional objectives—design for durability. More specifically, this chapter will cover the road load analysis techniques to predict vehicle component loads induced by irregular road surface profiles and driver's maneuvers (steering, braking/accelerating).

Fundamentals of Multibody Dynamics

A multibody system is used to model the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements. The vehicle suspension is a typical example of a multibody dynamic system. Multibody systems can be analyzed using the system dynamics method.

System dynamics (Randers, 1980) is an approach used to understand the behavior of complex systems over time. Generally, a dynamic system consists of three parts. The first part is the state of a system, which is a representation of all the information about the system at some particular moment in time. For example, the state of a simple two-degrees-of-freedom (DOF) quarter-car model for vehicle suspension ride analysis, as illustrated in Figure 1.1, can be summarized by the vertical displacement and velocity of sprung and unsprung masses. In general, the symbol X(t) = [x1(t), ..., xn(t)] will be used to denote the state of a system at time t.

The second part is the state space of a system. This is a set that contains all the possible states to which a system can be assigned. The state space of the two-DOF quarter-car model is the 2n ensemble containing all the possible configurations for the n-element sprung and unsprung mass vertical motions within a given timeframe. The symbol Ω is commonly used to denote the state space of a dynamic system, and X(t) [member of] Ω.

The third part is the state-transition function that is used to update and change the state from one moment to another. For example, the state-transition function of the two-DOF quarter-car model is defined by the governing state equation that changes the sprung and unsprung motion state at one step X(t) to the next step X(t + 1).

The objective of dynamic systems analysis is thus to understand or predict all possible state transitions due to the state-transition function. In other words, the dynamic system analysis for the two-DOF quarter-car model is to predict the motions (displacements and velocities) of sprung and unsprung masses with given road displacement input within a given time frame. It can be seen that during the displacements and velocities are solved, the loads associated with tire stiffness, spring stiffness, and damper also can be resolved.

Depending on the differences of the state space, the state-transition function, and the excitation of a dynamic system, the dynamic response of the system may demonstrate different behaviors such as nonlinearity and hysteresis. For example, when the excitation of the road input is small, the spring stiffness, damper force-velocity characteristics, and tire stiffness may be of linear characteristics, thus the state-transition function may be expressed by a linear state equation. Then the state response of the two-DOF quarter car model may demonstrate linear behavior.

On the other hand, if the road excitation is significant enough, the nonlinear characteristics of the tire, spring stiffness, and damper force-velocity function may not be negligible. In this case, a nonlinear state-transition function is required to present the dynamic behavior of this system, thus the nonlinearity and hysteresis of the state responses may be yielded.

For a simple linear mechanical dynamics system, the state-transition function or governing state equation can be easily established based on a certain rule of the system, such as D'Alembert's principle or Newton's second law. The iterative solution for the state-transition function in a time domain is also not very difficult, as compared to a full multibody vehicle model that has large degree of complexity.

For a nonlinear multibody dynamic system, different numerical integration techniques may be required to solve for the ordinary differential equation (ODE). The linear explicit numerical integration methods with a constant time step are well applicable to most of the ODEs, but perform poorly for a class of "stiff" systems where the rates of change of the various solution components differ significantly. Consider, for example, the motion solution of a stiff suspension system when the system is being driven at a low oscillation frequency and then run into a deep pothole.

In principle, the stability region of a stiff system must include the eigenvalues of the system to be stable. Consequently, the linear explicit methods have a penalty of requiring an extremely small time step to be stable, causing unacceptable increases in the number of integration steps, integration times, and accumulated errors. On the other hand, the implicit methods with variable time steps are often recommended for stiff systems because of the better stability properties in the numerical integration process. Thus, depending on the nature of a system, stiff or nonstiff integrators may be applied to solve the dynamics equations (Newmark, 1959; Hilber, Hughes, & Taylor, 1977).

The dynamic behavior results from the equilibrium of applied forces and the rate of change in the momentum. Nowadays, the term multibody system is related to a large number of engineering fields of research, especially in vehicle dynamics. As an important feature, multibody system formalisms usually offer an algorithmic, computer-aided way to model, analyze, simulate, and optimize the arbitrary motion of possibly thousands of interconnected bodies.


Excerpted from Metal Fatigue Analysis Handbook by Yung-Li Lee Mark E. Barkey Hong-Tae Kang Copyright © 2012 by Elsevier Inc.. Excerpted by permission of Butterworth-Heinemann. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

  1. Road Load Analysis Techniques in Automotive Engineering - Xiaobo Yang & Peijun Xu

  2. Pseudo Stress Analysis Techniques - Yung-Li Lee & Mingchao Guo

  3. Rainflow Cycle Counting Techniques - Yung-Li Lee & Tana Tjhung

  4. Stress-Based Uniaxial Fatigue Analysis - Yung-Li Lee & Mark E. Barkey

  5. Stress-Based Multiaxial Fatigue Analysis - Yung-Li Lee & Mark E. Barkey

  6. Strain-Based Uniaxial Fatigue Analysis - Yung-Li Lee & Mark E. Barkey

  7. Fundamentals of Cyclic Plasticity Theories - Yung-Li Lee & Mark E. Barkey

  8. Strain-Based Multiaxial Fatigue Analysis -Mark E. Barkey & Yung-Li Lee

  9. Vibration Fatigue Testing and Analysis - Yung-Li Lee & Hong-Tae Kang

  10. Fatigue of Seam Welded Joints - Hong-Tae Kang & Yung-Li Lee

  11. Fatigue Life Prediction Methods of Resistance Spot Welded Joints - Hong-Tae Kang & Yung-Li Lee

  12. Design and Analysis of Metric Bolted Joints (VDI Guideline and Finite Element Analysis) - Yung-Li Lee & Hsin-Chung Ho
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  • Anonymous

    Posted June 20, 2012

    The new book from Lee, Barkey and Kang, Metal Fatigue Analysis H

    The new book from Lee, Barkey and Kang, Metal Fatigue Analysis Handbook, calls itself a handbook, it goes far beyond the scope of most handbooks by including in-depth explanations of nearly all of the analysis techniques that are likely to be employed by engineers and scientists concerned with durability and fatigue issues in any ground-based vehicle and machinery industries. The book is replete with example problems that are explained in much greater detail than is typically seen in books on this topic. It is also richly illustrated and thoroughly referenced.
    The book covers all of the issues and topics that most ground vehicle engineers will address, from the basics of stress-based uniaxial fatigue analysis, to multiaxial strain-based analysis, and the very specialized and often overlooked topics of vibration fatigue, weld fatigue life-prediction and the finite element analysis (FEA) of bolted joints. Chapter 1, Road Load Analysis Techniques in Automotive Engineering, covers the types of loads and load histories that automobiles are subjected to, and how those loads are captured and converted into component stresses and strains for further analysis. It describes the standard testing and analysis procedures that are employed, the instruments that record data, and the commercial FEA models that are used to analyze the data. Chapter 2, Psuedo Stress Analysis Techniques, delves into the basics of the linear-elastic (LE-) FEA methods that are the most commonly used techniques for static stress and modal transient stress response analyses. Chapter 3, Rainflow Cycle Counting Techniques, is a very thorough and complete description of rainflow techniques. Chapters 4 and 5 cover stress-based fatigue analysis, for both uniaxial stresses, and the complex multi-axial stress environments. Strain-based uniaxial fatigue analysis is covered in chapter 6, followed by cyclic plasticity theories in chapter 7, and multi-axial strain-based fatigue analysis in chapter 8.
    Chapters 9-12 cover topics that are not normally covered in general fatigue books, but are discussed in detail in this work. Chapter 9 details Vibration Fatigue Testing and Analysis and discusses the standard fatigue damage spectrum procedure, and methods for calculating fatigue damage were explained for both sinusoidal and random fatigue tests. Chapter 10 contained a treatment of a variety of techniques for conducting life-prediction analyses for seam–welded joints. These methods generally use elementary structural mechanics, which were obtained from LE-FEA. Spot weld life prediction is the subject of chapter 11, where the load-life, linear elastic fracture mechanics (LEFM), and the stress life approach are explained as the primary methods of spot weld life prediction. In the final chapter 12, the authors discuss the design and analysis of bolted joints, and the basics of VDI 2230, the European standard for the design and analysis of bolted joints. In this chapter, two different FEA models are described: The solid bolt model and the spider bolt method.
    This book is an excellent reference for both students at the graduate school level, and practicing engineers. It covers in detail the fundamentals theories and the applications of modern computer aided engineering software in the field of durability and fatigue analysis. It also contains well documented examples, which are invaluable tools for applying the concepts that are laid out in this book.

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