Fatigue Design

Life Expectancy of Machine Parts

Eliahu Zahavi

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781351448819
• Edition: 1
• Topic: Technologie et ingénierie
• Subtopic: Ingénierie

Modern analytical theories of fatigue coupled with a knowledge of processing effects on metals make up the sound basis for designing machine parts that are free from unexpected failure. Fatigue Design: Life Expectancy of Machine Parts provides the information and the tools needed for optimal design. It highlights practical approaches for effectively solving fatigue problems, including minimizing the risk of hidden perils that may arise during production processes or from exposure to the environment.The material is presented with a dual approach: the excellent coverage of the theoretical aspects is accented by practical illustrations of the behavior of machine parts. The theoretical approach combines the fundamentals of solid mechanics, fatigue analysis, and crack propagation. The chapters covering fatigue theories are given special emphasis, starting with the basics and progressing to complicated multiaxial nonlinear problems.The practical approach concentrates on the effects of surface processing on fatigue life and it illustrates many faceted fatigue problems taken from case studies. The solutions demonstrate the authors' detailed analyses of failure and are intended to be used as preventive guidelines. The cases are a unique feature of the book. The numerical method used is the finite element method, and is presented with clear explanations and illustrations.Fatigue Design: Life Expectancy of Machine Parts is an extremely valuable tool for both practicing design engineers and engineering students.

CHAPTER

1

INTRODUCTION

If it were feasible to endow an individual who sets out to design machinery with all the knowledge that engineering design directly or indirectly relies on, there is no doubt that such an individual would need no assistance other than from his creative mind. The body of knowledge that machine design relies on includes a great number of disciplines. A few of these are: solid mechanics, including the elasticity and plasticity theories; metallurgy with its many faceted applications; manufacturing processes and surface effects; and numerical applications, especially the finite element method. To compromise with reality, the design engineer relies on the experience and fruits of research of other specialists.

A machine design process is comprised of many different aspects. The objective of this book is to delve into that phase of the process which is concerned with fatigue. Namely, creating machine parts, operating under fluctuating loading, with no risk of an unexpected failure. The challenge in creating a part with a predictable life expectancy is great because it is a known fact that a large number of machine parts fail due to fatigue. Some specialists claim fatigue failure reaches up to 80 percent, others claim the percentage at one hundred.

The history of fatigue design goes back to the middle of the nineteenth century, marked by the beginning of industrial revolution and, in particular, the advent of rail-roads in central Europe. The first known investigators concerned with fatigue phenomena were designers of axles for locomotives and wagons. Wohler’s experiments (1858)¹ with axles were the first known laboratory tests with the objective to derive and quantitatively describe the limits of fatigue. This was followed by more elaborate analyses of stresses and their effect on fatigue by Gerber,² Goodman³ and others. Continuous efforts of researchers in the twentieth century have given a new impetus to the development of theories, such as the effects of plastic deformation on fatigue—resulting in the strain method discovered by Manson⁴ and Coffin.⁵ In parallel, the theory of crack propagation started by Griffith (1921)⁶ was continued by Paris⁷ and others. Research accomplishments of Morrow,⁸ Socie⁹ and their followers brought the state of fatigue analysis to the present day level. Of special importance are works published by SAE Fatigue Design and Evaluation Committee.¹⁰ The challenges of ever growing modern technology demand a continuation of research efforts toward the more exact prediction of fatigue lives.

SCOPE OF THE BOOK

The topics in the book are grouped into four distinctive parts as follows: fundamentals of solid mechanics, Chapter 2; methods of fatigue analysis, Chapters 3, 4 and 5; impact of production processes upon the fatigue, Chapters 6 and 7; and design cases, Chapter 8.

An analysis of fatigue phenomena requires a thorough understanding of the interaction of stresses and strains within the body under loading. We address this topic in Chapter 2, presenting the necessary fundamentals of the theories of elasticity and plasticity. The advent of digital computers has made possible the application of these theories by means of numerical methods. A description follows of the most practical method as applied to the stress and strain analysis—the finite element method. Solutions to nonlinear problems encountered in fatigue design are reached by a special adaptation of this method. Equipped with this knowledge, the reader can proceed to the topic of fatigue analysis.

The organization of the second section follows the chronological development of the methods of fatigue analysis, comprising three known approaches—the stress method, the strain method and crack propagation theory, respectively. Chapter 3 is devoted to the description of the basic approach, the stress method. The method stems from the assumption that a machine part under fluctuating loading undergoes elastic deformation only. The method was developed for designing of parts with an infinite life introducing a safety factor as a measure. With time it was extended to include the design of parts with a limited life, a given life expectancy. The strain method, Chapter 4, is based on a more profound approach, taking into consideration the occurrence of plastic deformation, as well. As a result of an extended theoretical base and better accuracy, the method has found wide application in the automotive and aviation industries. The theory that deals with the final stage of fatigue, the crack propagation, is described in Chapter 5. The theory considers the fatigue life of the machine part—the period from an initiation of a crack to its causing a fracture and final failure of the machine part. The period following the initial crack which continues to grow to a final fracture of a machine part, is called the destruction period.

An overview is needed to understand the relation of the first two methods (the stress method and the strain method) to the third one, the crack propagation method. The first two differ fundamentally in defining the limits of fatigue life. The stress method includes the destruction period, while the strain method limits the life up to the presence of a visible crack up to 3–6 mm in length. Accordingly, in computation, the former method uses parameters taken from tests which include the destruction period, while the latter uses test data that limit the fatigue life to the onset of the crack.

Having created an optimal design of a machine part with the help of the appropriate fatigue design theories, presented above, the manufactured part may still meet with hidden perils of failure that must be foreseen during the design. To minimize such risks that stem from manufacture and later from the adverse conditions in operation, the discussion here relates to certain aspects of the production processes. One of the critical influences on the fatigue life is the condition of the machined surface. A fatigue failure begins in most cases at the surface because the surface layer bears the greatest load and is exposed to environmental effects. Part three of the book is concerned with the surface layer quality, Chapter 6, and fatigue life improvement, Chapter 7.

The surface is conditioned by the production process. The finish operation creates surface roughness and, due to plastic deformation and heating, structural changes and residual stresses arise. An unsuitable or faulty surface roughness can cause crack initiation and propagation, while unfavorable residual stresses impair the fatigue life. It is imperative therefore to consider the available preventive measures at the design stage. A number of methods to improve the fatigue strength of a machine part are presented.

The last section of the book (Chapter 8) illustrates three design cases all experiencing fatigue problems. The diversified cases were chosen from real experiences concerning aircraft, military equipment and oil refineries. As is shown by the analysis, in all three cases no fault could be attributed to a negligent design of the corresponding parts. This fact highlights the presence of perilous factors that can not be predicted at the design stage.

The illustrated solutions in this part include the application of the theories of fatigue analysis discussed elsewhere in the book and demonstrate the use of the finite element method. The data fed into the solution are mostly based on the available professional literature and assumptions, without direct involvement in the cases. The solutions used two computer programs, ANSYS and MSC/NASTRAN, as per printouts. These solutions are to be considered as illustrative examples only, based on our limited understanding of the conditions leading to failure.

NOMENCLATURE

The careful reader will note different nomenclature throughout the book, as used in conjunction with different analytical methods. This applies especially to the designation of stresses: letter S is used in the stress method while elsewhere the stress is designated by σ. The reason for this discrepancy is due to a tradition of the stress method throughout its long history. This nomenclature continues to be the one in use by design engineers in application of this method. (It is still covered by SAE¹¹ and ASTM¹² standards.)

REFERENCES

1.  Wohler, A. 1858. “Uber die Festigkeitsversuche mit Eisen und Stahl,” Z. Bauwesen. 8, 641.

2.  Gerber, W. 1874 “Bestimmung der zulassigen Spannungen in Eisenkonstruktionen,” Z. Bayer, Arch, Ing. Ver, 101.

3.  Goodman, J. 1899. Mechanics Applied to Engineering. London: Longmans.

4.  Manson, S.S. 1954. “Behavior of Materials under Conditions of Thermal Stress,” NACA Tech. Note 2933.

5.  Coffin, L.F. 1954. “A Study of Cyclic-Thermal Stresses in a Ductile Material,” Trans. ASME. 76, 931–950.

6.  Griffith, A.A. 1921. “The Phenomena of Rupture and Fracture in Solids,” Phil. Trans. Roy. Soc. A 221, 163–197.

7.  Paris, P.G. 1963. “The Fracture Mechanics Approach to Fatigue,” Proc. 10th Sagamore Conference. Syracuse University Press.

8.  Morrow, J. 1965. “Cyclic Plastic Strain Energy and Fatigue of Metals,” Internal Friction, Damping and Cyclic Plasticity, ASTM STP 378, 45–87.

9.  Socie, D.F. 1977. “Fatigue Life Prediction Using Local Stress-Strain Concepts,” Experimental Mechanics. 17, No, 2.

10.  “Fatigue Under Complex Loading.” 1977. Wetzel, R.M. ed., Warrendale, PA: Society of Automotive Engineers. P.G.

11.  “SAE Handbook.” 1989. Warrendale, PA: Society of Automotive Engineers.

12.  “Annual Book of ASTM Standards. 1980.” Part 10, Philadelphia, PA: ASTM.

CHAPTER

2

SOLID MECHANICS

The fatigue failure of a machine part under loading is contingent first and for...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Chapter 1 Introduction
• Chapter 2 Solid Mechanics
• Chapter 3 Stress Method
• Chapter 4 Strain Method
• Chapter 5 Crack Propagation
• Chapter 6 Surface Integrity and Fatigue
• Chapter 7 Fatigue Life Improvement
• Chapter 8 Diagnosis of Fatigue Cases
• Appendix
• Nomenclature
• Index