High Cycle Fatigue: A Mechanics of Materials Perspective part 2 pps

Preface
The first question a prospective reader or purchaser of this book may ask is, “Why another
book on fatigue?” This is a very legitimate question because there are many books and
hundreds of journal articles dealing with various aspects of fatigue, including high cycle
fatigue (HCF). In fact, in researching various aspects of HCF, the author was drawn back
in history to works like those of Wöhler in the late 1800s as well as many related articles
on fatigue of railroad wheels and bridges. Hopefully, what makes this book both unique
and of technical interest is the background and history of recent HCF failures within the
US Air Force, and the program that evolved from the concerns raised by those failures.
This book should be of value to students, scientists, engineers, and researchers who deal
with HCF. However, the main audience for this book is the practicing engineer who has
to deal with HCF from design or analysis point of view. The book can also serve as a
supplement to graduate level courses that delve into almost any aspect of HCF or as the
basis for continuing education short courses. The book has been put together in the form
of a series of review articles on the various aspects of HCF, which are both of importance
and which have not been covered extensively in one place in the open literature. From
this perspective, it should be of use to researchers and scientists dealing with any of a
wide variety of topics associated with HCF.
It is assumed that the reader has a basic knowledge of fracture mechanics, a background
that includes mechanics of materials, and some knowledge of general fatigue concepts.
Where appropriate, the reader is referred to some general references for more complete
coverage of certain topics that cannot be covered completely in this book. The book is
written at a slightly higher level and with more detail than many books on mechanical
behavior, fatigue, design, or materials. There is no intent to duplicate the existing literature
but rather to expand the coverage at a somewhat more advanced level. For basic coverage
of some of the material contained herein, the reader is referred to, for example, the
chapter on HCF in the book by Collins.
∗
The present book addresses HCF issues from a
mechanics of materials point of view. There is no attempt in this book to deal with fatigue
mechanisms. Books such as those of Suresh and Hertzberg address fatigue mechanisms

quite extensively and are recommended to those who wish to pursue that aspect of HCF.
†
High Cycle Fatigue has been a serious engineering problem in many industries since
the 1800s. Around 1995 there were a series of gas turbine engine failures on US Air
∗
Collins, J.A., Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, Second Edition,
John Wiley & Sons, New York, 1993.
†
Suresh, S., Fatigue of Materials, 2nd ed., Cambridge University Press, New York, 1998. Hertzberg, R.W.,
Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., Wiley, New York, 1989.
x
Preface xi
Force fighter jets that caused great concern because of excessive maintenance costs and
potential costs of redesigns, but mostly because of the threat to operational readiness.
While the cause of these failures was widely attributed to HCF– the specific causes were
not known and the risk of continued operation was even less known. It is interesting
to note that, over the years, failure investigations and detailed fault tree analyses have
shown that, beyond reasonable doubt, many of these HCF failures should or could not
have occurred! Because of the concern about HCF, and even though HCF has been
studied extensively for many years, the Air Force initiated a program to deal with the
technological issues associated with HCF in gas turbine engines. The primary goal was to
reduce the incidence of HCF-related failures and to reduce the associated maintenance and
replacement costs. Another goal was to produce more damage tolerant design approaches
for HCF and apply these procedures to the next generation of engines, namely the engine
for the Joint Strike Fighter. The team that put together the HCF program included the
author and other experts from both industry and government. The program was broken
down into a number of technical areas, most dealing with propulsion. One aspect of the
program that ended up accounting for nearly a third of the overall effort was materials;
particularly the damage tolerant aspects as related to HCF. What came out early in the
program planning stages was that design for HCF is actually quite straightforward, given

the actual loading (which is an entire problem in itself). However, the HCF capability of
a material in a real environment, where it is simultaneously subjected to “damage” from
other operational conditions, is a subject that has received little or no attention historically.
HCF – in conjunction with three real-world conditions, low cycle fatigue, contact fatigue,
and foreign object damage – was defined as the major problem and formed the basis of a
research and development program that was originally forecast to last for 5 years or more.
It is largely the works associated with that program that is the theme of this book. As with
many other authors, the present book relies heavily on the author’s own publications. The
background notes and studies, many of which did not get included in published papers
for reasons of length limitations, are included along with works from many colleagues
and other authors who have contributed so much to this field. Finally, the author has
to look back and give credit to a group of individuals, universities, and companies, that
made up the team which worked on the HCF program. Like a mini-Manhattan project,
one of the finest and most talented teams in history was formed and worked together
to advance the state of the art in HCF and provide the technology which has advanced
our capability to deal with the perplexing problem of materials damage tolerance under
HCF in gas turbine engine environments. The present book documents some of those
advancements and expands the problem to include materials and applications beyond
turbine engines, which involve rotating machinery or any structural components subjected
to high frequency vibratory loading.
While much of this book deals with HCF of turbine engine components, it was the
intent to make the application of the relevant technologies much broader to include all
xii Preface
applications where cyclic loading at high frequencies for a large number of cycles is
involved. Thus, rotating machinery in general produces conditions where HCF can be a
problem and the technologies addressed in this book are applicable. Interaction of low
cycle fatigue (LCF) with HCF, for example, is a condition that occurs under almost any
simple spectrum loading in a rotating component. Just bringing a component up to a
steady rotational speed and occasionally shutting it down constitutes a condition where
LCF–HCF interactions have to be evaluated. As pointed out in the beginning of Chapter

6, whenever two bodies in contact undergo relative motions with superimposed contact
loading, conditions are favorable for fretting fatigue, a type of HCF, to occur.
Another aspect of this book is the extensive reference to Ti-6AI-4V as a material for
HCF data. In the Air Force HCF program, a decision was made to use a single material
as a “model” material to study various features of HCF behavior. The choice of a single
material was made so that everyone working on the program would have access to the
same material as well as the database accumulated by all participants in the program.
A very large number of forgings were produced from the same heat under nominally
identical and carefully controlled and monitored conditions. The data obtained and trends
in HCF behavior were felt to be rather generic and applicable to other materials. The
advantage of the use of a single model material was the ability to generate a large database
from which comparisons could be made on any aspect of HCF behavior by anyone
conducting research on the program. For this reason, the reader will come across many
examples that use Ti-6AI-4V forged plate as the reference material to point out specific
behavior. Similar to the use of aluminum to study crack closure, steels to study gigacyle
fatigue, or aluminum to study overload effects in crack growth, the use of titanium to
study HCF is felt to be representative of the generic behavior of other materials. To apply
the findings to another material, however, a database for that material would have to be
established. That is not a small task when dealing with long life or very high cycle counts
that are typical of HCF.
A comment is in order regarding the length and detail contained in Chapter 7 and the
accompanying Appendix G on the subject of foreign object damage (FOD). While the
original intent was not to write a book or even have a detailed discussion of FOD as an
issue in HCF, it became obvious as this book was being written that the discussion of
FOD in the open literature is extremely sparse. That, combined with the many questions
and issues that were raised during the Air Force HCF program (and are still being raised),
led to the detailed discussion of the subject presented in this book. Similar comments
are in order regarding the extensive coverage of statistics. With increased emphasis on
statistics of HCF data and use of a probabilistic type of approach in HCF design, extensive
coverage has been given to statistical aspects of HCF data since such details are not

commonly found in the fatigue literature.
While some topics such as FOD and statistics are given extensive coverage in this
book, other topics such as HCF under multiaxial stresses are neglected completely. For
Preface xiii
this topic, experimental data into the long life (HCF) regime are essentially non-existent.
Thus, much of the limited work in this area is somewhat speculative and is an extension
of work dealing with LCF that is covered extensively in the open literature.
The nomenclature used in this book may differ somewhat from what is considered
standard or common usage. In such instances, this has been noted in a footnote. Addition-
ally, units of measurement are not standard in many cases. While technical publications
typically adhere to SI units these days, much of the work published by the engine man-
ufacturers in the United States is presented using English units (pounds, inches, for
example), because these are the units used as standard practice in that industry. The
graphs and calculations came in those units and no attempt was made to convert to SI
units. A similar situation arises when dealing with data from older publications. In most
of the cases, the absolute numbers are not important but rather the concepts conveyed are
what matters.
It will become apparent in reading this book that the references are not as complete as
they would be in a comprehensive review article. Rather, references have been chosen, in
many cases from the authors’ own works, to illustrate certain points. Many appropriate
and relevant references are not included. For this the author apologizes with no intent to
slight anyone who has contributed to the HCF field and whose work is not referenced.
The book is arranged into three Parts consisting of eight Chapters. Part one deals
with the background related to HCF and includes chapters on the history of the subject,
methods for presenting data, and test techniques. Part two covers damage states that
affect HCF behavior, namely LCF and its influence, notches, fretting, and FOD. The final
chapter addresses a number of issues related to HCF design and includes discussion of
crack growth thresholds and effects of residual stresses among other topics. The text is
supplemented by nine Appendices.
I would like to acknowledge the support of many that contributed to this book. The

reviewers for Elsevier helped and encouraged me to get this book into a presentable form.
My greatest appreciation goes to the authors of the various appendices that supplement
the contents of the book. These appendices were not just taken from existing documents.
Rather, they were put together by the individual authors to provide insight into specific
subjects that could not be easily incorporated directly as part of the text. To these authors
– Otha Davenport, George Sendeckyj, Major Randall Pollak, Alan Kallmeyer, Bence
Bartha, Narayan Sundaram, Thomas Farris, Jeffrey Calcaterra, and Joseph Zuiker – go my
sincerest thanks. I would also like to thank the following individuals who read different
sections of the book and provided suggestions that led to improvements in the text in the
specific areas indicated: Prof. Skip Grandt of Purdue University (Chapters 1–3), Mr Steve
Thompson of the Air Force Research Laboratory (FOD), Dr Michele Ciavarella, CNRITC,
Bari, Italy (fretting and notches), Prof. Tom Farris of Purdue University (fretting), Mr
Rick Wade formerly in the Air Force Research Laboratory Propulsion Directorate (FOD),
Mr Patrick Conor of the New Zealand Defence Technology Agency (FOD), Dr Pat
xiv Preface
Golden of the Air Force Research Laboratory (fretting), Mr Charles Annis of Statistical
Engineering, Mr Jerry Griffiths of General Electric Corp., and Mr Al Berens of University
of Dayton Research Institute (accelerated test techniques and statistics). The support of the
US Air Force in my positions at the Air Force Materials Lab and, more recently, at the Air
Force Institute of Technology (AFIT) is gratefully acknowledged. This last assignment
was through my employment at the University of Dayton Research Institute under the
US Government IPA program, which allowed me to accomplish a substantial part of the
writing of this book while at AFIT. Finally, I would like to thank Mr Ted Fecke, Director
of Engineering, Propulsion Product Group, Wright Patterson AFB, and his predecessor,
Mr Otha Davenport for their support in establishing and guiding the Air Force HCF
program and for the many opportunities they have given me to be involved in Air Force
HCF problems and to learn about the real world of HCF in turbine engines.
Part One
Introduction
and Background

In the first three Chapters we present some of the historical background on high cycle
fatigue (HCF) to introduce the reader to some of the concepts and approaches that were
developed over a century ago. The primary reason for presenting this material is to
illustrate the many concepts that formed the basis for what now constitutes the basis of
modern-day procedures that have not changed, or are very similar, to what was introduced
when HCF was first developed. Moreover, it is important to recognize the limitations
and intended applications of some of these technologies as pointed out by the original
developers. With the exceptions of modern-day experimental methods and instrumentation
as well as today’s powerful computational tools, HCF has not seen what could be labeled
tremendous advancements over many years.
In Chapter 1, the reader is exposed to the history of development of HCF as well
as some of the more recent trends based on experience within the US Air Force which
precipitated a major program on HCF to improve the damage tolerance of aircraft engines
to HCF. In Chapter 2, the methods for representing data from HCF tests are presented,
again with a strong historical perspective. In Chapter 3 methods for obtaining HCF
data are reviewed. Here, both traditional methods and, some recent developments are
presented.
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Chapter 1
Introduction
1.1. HISTORICAL BACKGROUND
Fatigue has not always been a technical subject or consideration in the disciplines of solid
mechanics or strength of materials. In fact, one of the earliest researchers to address the
topic was Wöhler [1], who, in 1870, gave a general law which may be stated as:
Rupture may be caused, not only by a steady load which exceeds the carrying strength,
but also by repeated application of stresses, none of which are equal to this carrying
strength. The differences of these stresses are measures of the disturbance of the continu-
ity, in so far as by their increase the minimum stress which is still necessary for rupture
diminishes.
Wöhler performed many experiments that eventually were used as the basis for much of

the fatigue modeling that was carried out in the late 1800s and beyond. In researching
the contributions of August Wöhler, one should not be confused with Friedrich Wöhler,
a distinguished and well-published German chemist, nor with Karen Wöhler who wrote
extensively about preventing pain and fatigue in people, both of whom were active in the
same time period as August Wöhler.
This book deals with a specific portion of the general problem of fatigue, namely high
cycle fatigue (HCF). Any book on HCF should begin with a short introduction to the
history of fatigue. Fatigue is not a technical subject that has been around hundreds of
years. In fact, it came into being in the 1800s because of numerous accidents associated
with railroad axles and railroad bridges, both of which were subjected to repeated loading.
Although the terminology “high cycle fatigue” (HCF) was not used in connection with
these accidents and the subsequent investigations, the high cycle counts associated with
some of these incidents put them in the high cycle category. Most of the early papers on
fatigue (see, for example, the works of Wöhler cited in Appendix A) dealt with tests to
failure and an attempt to establish an endurance limit, a term now associated with HCF.
The British work (in the commission report discussed in Appendix A) dealt with shorter
life comparative tests of rails, that is which rail design was best based on shorter life tests.
The railroad industry had adopted a definition of service life and used it for scheduling
replacement or repair of axles and wheels. This was a modern concept used quite early
by the railroad people.
The origins of the history of fatigue, particularly with respect to railroad accidents,
have been documented in a heretofore unpublished article by Dr George Sendeckyj, a
former colleague of mine at the Air Force Research Laboratory. This article, with his
3
4 Introduction and Background
permission, appears as Appendix A in this book and provides the reader with some very
interesting documentation of the history of the subject of this book. Additionally, the
history of fatigue, particularly the efforts in Germany, is presented in an extensive review
article by Schütz [2]. There, the enormous and significant contributions of Wöhler are
reviewed. Wöhler, who is often cited in discussing the beginnings of fatigue, was the Royal

“Obermaschinenmeister” of the “Niederschlesisch-Mährische” Railways in Frankfurt an
der Oder. Also included in that review are the details of the contributions of Thum, who,
with coworkers, authored no less than 574 publications on the subject of fatigue [2]. The
extensive review by Schütz is recommended reading for anyone with an interest in the
history of the subject.
1.2. WHAT IS HIGH CYCLE FATIGUE?
A number of years ago I was preparing to give a briefing to some high-level managers at
Air Force headquarters. It was for the purpose of informing them of the program that was
being put together to address issues related to HCF in turbine engines, particularly with
respect to material behavior. Since this was a high-level briefing, the charts had to be
reviewed by the appropriate staff members to make sure it had the proper length, format,
and content. My briefing charts were all found to be satisfactory, with no changes, except
for one additional chart that they felt I needed at the beginning. I was asked to define HCF.
I was partially stumped because I had never seen a good formal definition of HCF. I don’t
remember what I put together for the briefing, but it centered around the premise that HCF
involved longer lives than low cycle fatigue (LCF), which I also had to explain, and it
generally involved high frequencies in excess of around 1000 Hz (cycles per second, which
I also had to explain!). Perhaps a better definition would be a fatigue condition where the
number of cycles between possible inspections is too large to be able to do anything about
it in a practical sense. I avoided a popular definition where purely elastic behavior is
associated with HCF while LCF involves cyclic plasticity. What if someone asked “How
much plasticity?” LCF is usually conducted under strain-controlled conditions while HCF
generally involves load control, but this also is a rather vague way to define the difference
between the two. There is no formal definition in my mind, but HCF generally involves
high frequencies, low amplitudes, nominally elastic cyclic behavior, and large numbers
of cycles. On a conventional stress-life curve, commonly called a S–N curve or a Wöhler
diagram, HCF occurs at the right end of the curve where the number of cycles is usually too
large to be able to obtain sufficient statistically significant data to be able to characterize
the material behavior with a very high degree of confidence. It is this hard to define
subject that will be discussed in this book, specifically from a material’s behavior point

of view.
Introduction 5
1.3. HCF DESIGN CONSIDERATIONS
Before discussing design for HCF, it is instructional to review general design procedures
for turbine engines in general with specific emphasis on structural durability and issues
dealing with fatigue. While design procedures differ from industry to industry, the specific
concern with HCF in US Air Force turbine engines makes this background relevant to many
of the subjects addressed in this book. One of the features in design which has received
increased attention inrecent years is a trend away from deterministic design to one involving
probabilistics to insure reliability of the resulting product. To address the reliability aspects
of design along with a review of general design practices, the following is cited from a
presentation given by Crouch [3] in2000. The quotedportions of the presentation by Crouch
contain many details that might be excessive for the beginning of an introductory chapter.
Rather than relegate these quotations, which are not the entire presentation, to an appendix,
the important features and main points of the article are highlighted in bold below.
Aircraft turbine engine reliability and its growth are important parameters to manage
and control during development, production, fielding and sustainment. It can influence
system safety, aircraft readiness, and operational support costs. Its roots are early in the
development phase with the operational requirements. Operational requirements flow down
to weapon system, air vehicle and propulsion system requirements. Next there occurs a
functional requirements allocation, the engine manufacturer’s design synthesis, analysis,
and the development of a failure modes and criticality effects analysis. In the past, engine
reliability requirements are spelled out in a table in the specification. There have been
goals for the in-flight shutdown rate; shop visit rate and line replaceable unit rate
per 1000 engine flight hours. Although all problems occurring during the Engineering
and Manufacturing Development (EMD) activity are corrected, they are also tracked and
categorized in one of these three categories. In this way the demonstrated reliability of the
development engine can be monitored. After hardware and software are produced; component
tests, bench tests, rig tests and finally ground and altitude engine tests are performed to
assure the engine meets performance, operability, functionality and durability requirements.

The general basis for aircraft turbine engine design requirement and verification
processes is resident in the Joint Service Specification Guide for Aircraft Turbine
Engines (JSSG-2007 dated 30 October 1998). In the course of EMD, distress and/or
failures occur which indicate potential reliability problems. These are corrected iteratively
and are verified to eliminate the problems. The analysis and tests feature both loading and
operating environments representative of the projected usage and in some cases severe
loading and environment beyond the expected level of usage to evaluate robustness.
The tests and analyses include compressed usage cycles such that one hour of tests might
equal 4–10 hours of usage. In this way test time is minimized to reduce the development
cycle time and the development cost. We refer to such full-scale engine tests as accelerated
mission tests (AMT). These are usually accomplished in sea level and altitude engine test
cells. In addition product variability is studied analytically with the limited test components
and engines.