Introduction to thermodynamics of mechanical fatigue

Michael M. Khonsari • Mehdi Amiri

Thermodynamics of

Mechanical Fatigue

Introduction to

Macroscale

Plasticity

Component Testing

Microscale

Atomic Scale

Application

Thermodynamics of

Mechanical Fatigue

Introduction to

Fatigue is probabilistic in nature and involves a complex spectrum of loading history

with variable amplitudes and frequencies. Yet most available fatigue failure prediction

methods are empirical and concentrate on very specific types of loading. Taking a different

approach, Introduction to Thermodynamics of Mechanical Fatigue examines the

treatment of fatigue via the principles of thermodynamics. It starts from the premise that

fatigue is a dissipative process and must obey the laws of thermodynamics. In general,

it can be hypothesized that mechanical degradation is a consequence of irreversible

thermodynamic processes. This suggests that entropy generation offers a natural measure

of degradation.

Drawing on recent cutting-edge research and development, the authors present a unified

entropic approach to problems involving fatigue. They introduce the fundamentals of

fatigue processes and explore a wide range of practical engineering applications.

The book reviews commonly observed failure modes, discusses how to analyze fatigue

problems, and examines the deformation characteristics of a solid material subjected to

fatigue loading. It also looks at how to use thermodynamics to determine the onset of

fatigue failure. In addition, the book presents methodologies for improving fatigue life and

for accelerated fatigue testing.

Comprehensive and well organized, this work helps readers apply powerful

thermodynamics concepts to effectively treat fatigue problems at the design stage. It

offers an accessible introduction to a new and exciting area of research in the field

of fatigue failure analysis.

MECHANICAL ENGINEERING

ISBN: 978-1-4665-1179-8

9 781466 511798

9 0 0 0 0

K14850

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Thermodynamics of

Mechanical Fatigue

Introduction to

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CRC Press is an imprint of the

Taylor & Francis Group, an informa business

Boca Raton London New York

Michael M. Khonsari • Mehdi Amiri

Thermodynamics of

Mechanical Fatigue

Introduction to

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CRC Press

Taylor & Francis Group

6000 Broken Sound Parkway NW, Suite 300

Boca Raton, FL 33487-2742

© 2013 by Taylor & Francis Group, LLC

CRC Press is an imprint of Taylor & Francis Group, an Informa business

No claim to original U.S. Government works

Version Date: 20120726

International Standard Book Number-13: 978-1-4665-1180-4 (eBook - PDF)

This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been

made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid￾ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright

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Dedicated to

Karen, Maxwell,

Milton, Mason Khonsari, and

to the memory of my father (MMK),

and to Hassan Amiri

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vii

Contents

Preface................................................................................................................................ xi

About the Authors............................................................................................................ xiii

Acknowledgments..............................................................................................................xv

Chapter 1 Introduction to Mechanical Degradation Processes........................................1

1.1 Fatigue ...................................................................................................1

1.2 Fracture..................................................................................................2

1.3 Wear ......................................................................................................2

1.4 Fretting ..................................................................................................3

1.5 Brinelling and False Brinelling .............................................................4

1.6 Corrosion ...............................................................................................5

1.7 Creep .....................................................................................................5

1.8 Thermal Shock ......................................................................................7

1.9 Impact....................................................................................................7

References .......................................................................................................9

Chapter 2 Fundamentals of Thermodynamics...............................................................11

2.1 Open and Closed Systems...................................................................11

2.2 Equilibrium and Nonequilibrium State ...............................................12

2.3 Steady and Unsteady State ..................................................................14

2.4 Stable and Unstable State ....................................................................15

2.5 First Law of Thermodynamics............................................................15

2.6 Second Law of Thermodynamics........................................................21

2.7 Entropy Flow and Entropy Generation................................................22

2.8 Entropy Balance Equation.................................................................. 24

References .....................................................................................................27

Chapter 3 Degradation–Entropy Generation (DEG) Theorem ......................................29

3.1 Thermodynamic Forces and Flows .....................................................30

3.1.1 Examples of Thermodynamic Forces and Flows ....................34

3.2 Relations between Thermodynamic Forces and Flows.......................34

3.2.1 Thermodynamic Orthogonality Principle ...............................38

3.2.2 Coupling between Plastic Deformation and Heat Flow...........41

3.3 Degradation–Entropy Generation Theorem ........................................42

3.3.1 Degradation Forces and Flows................................................43

3.3.2 Generalization: DEG Corollary.............................................. 44

3.3.3 Application: Paris–Erdogan Law.............................................45

References .....................................................................................................47

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viii Contents

Chapter 4 Fatigue Mechanisms: An Overview ..............................................................49

4.1 Multiscale Characteristics of Fatigue ..................................................49

4.2 Parameters Influencing Fatigue and Classification of Regimes...........49

4.2.1 Low-Cycle Fatigue (LCF) and High-Cycle Fatigue (HCF).....50

4.2.2 Effect of Mean Stress ..............................................................56

4.2.3 Load History............................................................................59

4.2.4 Stress-State: Torsion, Tension–Compression, Bending,

and Combined Mode ...............................................................61

4.3 Fatigue and Energy Dissipation...........................................................63

4.3.1 Micro/Nanoscale Mechanism of Energy Dissipation..............63

4.3.2 Macroscale Mechanism of Energy Dissipation .......................65

4.3.3 Prediction of Fatigue Failure Based on Energy Dissipation....65

4.4 Fatigue–Temperature Rise...................................................................67

4.4.1 Temperature Evolution during Fatigue ....................................67

4.4.2 Application to Prediction of Fatigue Failure ...........................74

References .....................................................................................................78

Chapter 5 Basic Thermodynamic Framework for Fatigue Analysis..............................83

5.1 Entropy Balance Equation of a Deformed Body .................................86

5.2 Entropy Change Due to Thermal Deformation ...................................91

5.3 Clausius–Duhem Inequality ................................................................95

5.4 Thermodynamic Forces and Flows in Processes Involving Fatigue ......97

5.4.1 Legendre–Fenchel Transformation..........................................99

References ...................................................................................................100

Chapter 6 Thermodynamic Assessment of Fatigue Failure .........................................103

6.1 Limitation of Conventional Methods and the Need for Further

Advances ...........................................................................................103

6.2 Evaluation of Entropy Generation and Entropy Flow........................103

6.3 Time to Failure ..................................................................................107

6.3.1 Failure Criterion Based on Accumulation of Entropy

Generation .............................................................................108

6.3.2 Coffin–Manson Equation and FFE........................................ 110

6.3.3 Fast Prediction of Fatigue Failure.......................................... 111

References ...................................................................................................113

Chapter 7 Damage Mechanics: An Entropic Approach...............................................115

7.1 Introduction to Damage Mechanics...................................................115

7.1.1 Entropy-Based Damage Variable........................................... 116

7.2 Continuum Damage Mechanics (CDM)............................................120

7.2.1 Damage Variable, D(n)..........................................................121

7.2.2 CDM and Fatigue Damage....................................................123

7.2.3 CDM and Fretting Fatigue.....................................................124

7.2.4 CDM and Sliding Wear.........................................................124

References ...................................................................................................126

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Contents ix

Chapter 8 Self-Organization in Fatigue .......................................................................129

8.1 Introduction to Self-Organization......................................................129

8.2 Effect of Electric Current on Fatigue Life.........................................132

8.3 Effect of Magnetic Field on Fatigue Life...........................................133

8.4 Effect of Environment (Surface Cooling) on Fatigue Life ................133

8.5 Self-Organization and Complexity ....................................................134

References ...................................................................................................135

Chapter 9 Entropic Fatigue: In Search for Applications..............................................139

9.1 Application to Variable-Loading Amplitude and Structural

Health Monitoring .............................................................................139

9.2 Accelerated Fatigue Testing............................................................... 141

9.3 Concluding Remarks .........................................................................144

References ...................................................................................................145

Index................................................................................................................................147

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xi

Preface

The subject of fatigue degradation and the methodologies for its treatment span multitudes

of scientific disciplines, ranging from engineering to materials science and mechanics

to mathematics.

Fatigue is probabilistic in nature. For example, fatigue tests performed on the same

material subjected to the same operating conditions can yield different results in terms of

the number of cycles that the system can withstand before failure occurs. Such uncertainties

affect the system design, structural integrity, and operational reliability. Yet the majority

of available methods for prediction of fatigue failure—cumulative damage models, cyclic

plastic energy hypothesis, crack propagation rate models, and empirically derived relation￾ships based on the curve fitting of limited laboratory data—require many unknown input

parameters that must be experimentally determined.

There are other complications. All of the above-mentioned methods concentrate on very

specific types of loading and single fatigue modes, that is, bending, torsion, or tension–

compression. In practice, however, fatigue involves simultaneous interaction of multimode

processes. Further, the variability in the duty cycle in practical applications may render

many of these existing methods incapable of reliable prediction. It is, therefore, no sur￾prise that the application of these theories often leads to many uncertainties in the design.

Further, their use and execution in practice require one to implement large factors of safety,

often leading to gross overdesigns that waste resources and cost more.

In reality, the science base that underlies modeling and analysis of fatigue processes

has remained substantially unchanged for decades, leaving a significant gap between the

available technology and the science that effectively captures the dynamics of degradation.

The premise of this textbook is that fatigue is a dissipative process and must obey the laws

of thermodynamics. In general, it can be hypothesized that the degradation of machinery

components is a consequence of irreversible thermodynamic processes that disorder a com￾ponent, and that degradation is a time-dependent phenomenon with increasing disorder.

This suggests that entropy—a fundamental parameter in thermodynamics that character￾izes disorder—offers a natural measure of component degradation.

Although an entropic approach to problems involving degradation is gaining momen￾tum, its practical applications have not yet become widespread. This concept offers new

and exciting research in the field of fatigue fracture analysis for years to come. We hope

this introduction to the treatment of fatigue via the principles of thermodynamics serves as

a useful contribution to the science of degradation.

Michael M. Khonsari and Mehdi Amiri

Baton Rouge, Louisiana

Note: This book contains information obtained from authentic and highly regarded sources.

Reprinted material is quoted with permission, and sources are indicated. A wide variety of

references are listed. Reasonable efforts have been made to publish reliable data and infor￾mation, but the author and the publisher cannot assume responsibility for the validity of all

materials or for the consequences of their use.

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xiii

About the Authors

Michael M. Khonsari is the holder of the Dow Chemical Endowed Chair and professor

of the Mechanical Engineering Department at Louisiana State University, where he directs

the Center for Rotating Machinery. Professor Khonsari is a fellow of the American Society

of Mechanical Engineers (ASME), the Society of Tribologists and Lubrication Engineers

(STLE), and the American Association for the Advancement of Science (AAAS). He holds

several patents and has authored two books and over 200 archival journal articles. He is

currently the editor of the ASME Journal of Tribology.

Mehdi Amiri earned his PhD in mechanical engineering from Louisiana State University,

where he is currently a research associate in the Center for Rotating Machinery. His area of

research is in the field of fatigue and fracture analysis. He holds one patent and has authored

several journal publications. His research interests include thermal/fluid mechanics, ther￾modynamics, tribology, and failure analysis.

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