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Mechanics and Mechanisms of Fracture: An Introduction

Mechanics and Mechanisms of Fracture: An Introduction

© 2005 ASM

© 2005 ASM International. All Rights Reserved. Mechanics and Mechanisms of Fracture: An Introduction (#06954G) Preface Failure of a machine part (or structural part) could be attributed to many known or unknown factors. The most fundamental one is due to static overload of a structural member. The term overload might mean the structural member is subjected to a load that exceeds the ultimate strength of the material. Overload might also mean the applied load is higher than the anticipated design load of the structure, the value of which is normally set to lower than the material’s ultimate strength. Incidentally, structural parts often fail at load levels much lower than the design load. An initial defect (or damage) in the part, cyclic load-induced cracking, or time-dependent/environmentally-assistedcracking all can cause a machine part to fail prematurely. The studies of the problems and the remedies for handling the failure modes in the first two types of failures mentioned are called fracture mechanics and fatigue; high-temperature creep, stress-corrosion, corrosion-fatigue, or hydrogenembrittlement are the sources for the rest. Fracture mechanics is the study of the influence of loading, crack size, and structural geometry on the fracture resistance of materials containing natural flaws and cracks. When applied to design, the objective of the fracture mechanics analysis is to limit the operating stress level so that a preexisting crack would not grow to a critical size during the service life of the structure. Fatigue is the study of the effects of repeated loading on a machine part that was initially defect free, and how those loads (in combination with other factors) may shorten its anticipated life. Understanding the mechanisms of creep and stress-corrosion/hydrogen-embrittlement is important when a machine part is intended for use in an extreme environment. Both the metallurgical and mechanical elements in each type of these failure modes will be discussed. In the metallurgical field, the model that offers explanations to a phenomenon is often case specific. Experience gained may or may not be applicable to another case, however similar it may seem. Revised or updated concepts or solutions appear in the literature from time to time. It is impossible to discuss all the concepts and methods in a single book. Only those relevant to the intended specific themes are included here. In contrast, the mechanical causes of failure can be analyzed by means of solid mechanics. Nevertheless, the solution to a problem is valid only for the set-up and assumptions as intended; thus it is also somewhat case specific. The main focus of this book is to explicate how materials respond to applied forces, and relate them to design analysis, material evaluation, and failure prevention. Metals occupy the main part of the book; also included are non-metallic materials such as ceramics, plastics, and fiber-reinforced polymer-matrix composites. Both the fundamental and practical concepts of fracture are described in terms of stress analysis and the mechanical behavior of materials. The metallurgical aspects of deformation and fracture in metals also are discussed. The first two chapters of this book can be regarded as the fundamentals of stress analysis and mechanical behavior of materials. These chapters provide necessary knowledge for the understanding and appreciation of the contents in chapters that follow. With regard to structural design and analysis, a strong emphasis is placed on showing how fracture mode is influenced by the state of stress in the part. The stress analysis section in Chapter 1 serves as a crash course (or a refresher course) in the strength of materials and prepares the reader with the basic analytical tools for the remainder of the book. A progressive approach is taken to show the effect of structural geometry and loading conditions to the resulting stresses—first to show the stresses in undamaged structural members; next to show the stresses in structures that contain a geometric v www.asminternational.org

© 2005 ASM International. All Rights Reserved. Mechanics and Mechanisms of Fracture: An Introduction (#06954G) discontinuity; then finally, to show the stress field in the vicinity of a crack. Stress analysis of cracks requires the use of a new analytical tool called fracture mechanics. This is discussed in Chapter 1 for primary elastic with small scale yielding at the crack tip, and in Chapter 6 for large scale yielding at the crack tip. Application of fracture mechanics to design/analysis and the related tasks is presented in Chapters 4 through 6. Numerous examples are given throughout this book to illustrate the elastic and plastic behavior of materials at a stress raiser, and how the static, fatigue, and residual strengths of a machine part might be affected by it. Finally, the structural analysis methods, as well as the damage tolerant aspects of fiber-reinforced composites, are discussed in Chapter 8. Strangely, in the last couple years, “101” has become a household term. It penetrates into our homes by way of television, radio, and newspaper. Politicians, entertainers, the media, and talk show hosts and their guests, would freely use “ ‘Whatever’ 101” to link to the topic or event that is being discussed. Therefore this book could, in that sense, qualify to be titled “Mechanics and Mechanical Behavior of Materials 101.” To reiterate: This book is about how machine (or structural) parts fail, why one piece fails in a certain way and another piece fails differently; and will provide engineering tools for analyzing these failures, and ultimately, preventing failure. This book can be used as a desktop reference book or as a self-study book, and can be used by engineering students and practicing engineers with or without some prior training in solid mechanics and/or mechanical metallurgy. I want to sincerely thank the reviewers at ASM for their constructive comments. A special thanks to Steve Lampman for his effort in integrating handbook content in the area of brittle and ductile fractures, and the mechanism of intergranular fracture, into Sections 2.4.3 and 2.4.4. Last but not least, I wish to acknowledge the excellent work that Kathy Dragolich put in the coordination of this book. vi www.asminternational.org A.F. Liu West Hills, California

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    Chapter 2: Deformation and Fracture

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    Chapter 2: Deformation and Fracture

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    2.3 Fracture Criteria Chapter 2: De

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    or Chapter 2: Deformation and Fract

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    Mechanics and Mechanisms of Fractur

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    companied only by plastic strain lo

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    obtained by using Eq 1.77 with h 0

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    Fig. 4.6 Effect of strain-hardening

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    the plate normal to the crack front

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    ther increased until final fracture

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    Chapter 4: Static and Dynamic Fract

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    Chapter 4: Static and Dynamic Fract

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    granular or transgranular for a cer

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    way. A second look shows another tr

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    Chapter 4: Static and Dynamic Fract

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    V-notch at one end. The specimen is

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    els were made from the same materia

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    DWTT. Details about the DT test are

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    tangential lines: one drawn from th

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    lations were made only for limited

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    Chapter 4: Static and Dynamic Fract

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    According to Irwin (Ref 4.49), KIC

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    ometry, initial crack length, loadi

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    quent crack extension (i.e., beyond

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    Chapter 4: Static and Dynamic Fract

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    Fig. 4.58 Behavior of K1 and K2 int

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    4.33. W. Server and A.S. Telelman,

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    Mechanics and Mechanisms of Fractur

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    This proportional relation can be u

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    The Paris and Sih solutions along w

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    1/2 3/2 5/2 F( 1) 29.6 185.5 655

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    2c and a, respectively. The crack s

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    of the highest K value is at the ma

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    Fig. 5.19 Front-face geometric coef

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    However, so far, a good method of h

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    Comparison of Eq 5.30(b) with Eq 5.

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    The Williams, or Westergaad, stress

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    K values for a given panel would be

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    Fatigue crack propagation is a phen

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    sity at the crack tip (Ref 5.40, 5.

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    Chapter 5: Damage Tolerance of Meta

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    Fig. 5.42 Typical shape of a fatigu

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    a curve-fitting equation capable of

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    To demonstrate the usefulness of th

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    no point in reviewing or evaluating

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    KC 65.93 MPa m. Then select severa

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    scatter exists. Therefore, the fair

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    zone, approximately one-eighth to o

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    or spectrum loading, a crack-tip pl

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    epresentation of the material crack

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    imum load level set to zero). In a

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    embrittlement. Most engineering all

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    line through all the experimental d

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    alloys. This section briefly summar

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    tensity factor in one case is below

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    through-thickness crack. Thus, the

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    comparing the predictions with actu

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    0.01 Hz (i.e., tr 50 s), tH 50 s.

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    5.34. P. Tong, T.H.H. Pian, and S.

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    on Threshold and Growth Mechanisms,

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    Mechanics and Mechanisms of Fractur

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    Appendix 1: Lattice Structure and D

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    Appendix 1: Lattice Structure and D

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    Appendix 1: Lattice Structure and D

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    Appendix 1: Lattice Structure and D

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    Appendix 1: Lattice Structure and D

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    Appendix 1: Lattice Structure and D

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    Appendix 1: Lattice Structure and D

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    Mechanics and Mechanisms of Fractur

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    Appendix 2: Close-Form Representati

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    where K t Appendix 2: Close-Form Re

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    Mechanics and Mechanisms of Fractur

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    Appendix 3: Nonarbitrary Crack Size

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    Mechanics and Mechanisms of Fractur

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    divided by the average bearing stre

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    Mechanics and Mechanisms of Fractur

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    REFERENCES Appendix 7: Mechanical P

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    Appendix 7: Mechanical Properties D

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    Table A7.4 Tensile strength and pla

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    Appendix 7: Mechanical Properties D

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    Appendix 7: Mechanical Properties D

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    Fig. A7.16 Strain-life data for D35

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    412 / Mechanics and Mechanisms of F

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    Mechanics and Mechanisms of Fractur

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    Appendix 9: Mechanical Properties D

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    Appendix 9: Mechanical Properties D

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    Appendix 9: Mechanical Properties D

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    Mechanics and Mechanisms of Fractur

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    Mechanics and Mechanisms of Fractur

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    terial is subjected to a sustained

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    generally occurs at loads that, app

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    value is equivalent to fracture tou

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    structure or specimen that contains

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    tangent modulus. The slope of the s

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    Index A © 2005 ASM International.

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    © 2005 ASM International. All Righ

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    © 2005 ASM International. All Righ

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    © 2005 ASM International. All Righ

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    © 2005 ASM International. All Righ

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    © 2005 ASM International. All Righ

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    © 2005 ASM International. All Righ

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    © 2005 ASM International. All Righ

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    ASM International is the society fo

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