High Cycle Fatigue: A Mechanics of Materials Perspective part 3 docx

6 Introduction and Background
The Engine Structural Integrity Program (ENSIP) handbook (MIL-HDBK-1783A
dated 22 Mar 99)
∗
is used as a guide to design, develop, produce and sustain engines to
assure their structure eliminates or minimizes safety, reliability and durability prob-
lems. Many mechanical, electronic and software problems are identified and corrected in the
EMD program. At the end of the EMD program, a review of the analyses and test reports
validates the functional requirements.
Two of the challenges of the development program, which affect reliability of the field
engine, are engine to engine tolerances and variations and the required operational usage of
the engine. Test time and test hardware are expensive. The limited number of test assets limits
the tested tolerances and variations whose characteristics can account for some problems
in field operation with the hundreds of engines produced. Secondly, the original usage
projection of the engine in terms of throttle cycles, altitude profiles influences the design.
The projected usage is compiled for the engine as a set of component and engine test cycles
used to evaluate the product design. Sometimes the pilots fly the system different than
the original projection of the usage. This can result in a more severe operation of the
engine and affect different component failure modes in the engine. Modeling, simulation
and analysis improvements and application throughout the weapon system life cycle will
hopefully limit these two problems.
Once the engine goes into production for a production aircraft installation or as a spare
engine, it is released for field service evaluation. Sometimes a field service evaluation is
performed on the aircraft/engine combination in which case it is an initial operational test and
evaluation. Usually a small group of aircraft and spare engines are used, perhaps 6 aircraft/
engines and 2 spare engines. The length of the evaluation might be 1–2 years. In this time the
engines might each accrue some 300–600 flight hours or 600–1200 cycles. This represents
but 15–30% of the typical engine hot section 2000 flight hour (4000 cycle life). Oftentimes
it’s the engine’s hot section i.e. combustor and turbines that deteriorate and drive maintenance
inspection rejects. Infant mortality, manufacturing/quality, software and electronic problems
are usually the type of problems to surface in the field service evaluation. The field service

evaluation is also employed for design changes prior to approval of the engineering change
proposal for software changes to the engine control, diagnostic system or ground support
equipment. It is effective because it employs the software for several different engines.
Sometimes software problems with engine-to-engine variability surface during these tests.
Crouch [3] goes on to point out how changes are made in design based on field
problems through a Component Improvement Program (CIP), which the Air Force, Navy
and Army all have, which funds redesigns and verification tests to correct fielded engine
safety, reliability and operational support cost problems. He notes:
“Reliability analyses are also used to manage field problems. Statistical distributions
are used to predict component failure rates. These are used to perform risk management
∗
The version referenced here has been superceded by a more recent version [4] cited elsewhere in this book.
These, in turn, supercede the original version [5] adapted and published in 1984.
Introduction 7
on our aircraft engines to judge the needed frequency of part replacement, safety inspection
or retrofit of a redesign. Usually we use the Weibull distribution but sometimes other
distributions better fit the data. Also we must plan for engine support through spare part and
engine provisioning. Once again the field data for part failure or the engine shop visit rate
data and projections are used as inputs to models to estimate the number of spare parts or
spare engines needed.
One reliability limitation occurring during the operational use of the engines is
the lack of accurate and timely failure data. The Air Force has a deficiency reporting
system to identify component or system failures. Oftentimes this system is also used to
report warranty claims. After the warranty runs out often the maintenance personnel fail
to use it to report failures. Thus the engine program office may be surprised with a new
failure mode. Other factors which influence the reporting system include: reduced number of
maintenance personnel to report the faults, frustration with the shipment and transportation of
the failure exhibits, and frustration with the engine program office, repair center and engine
contractor with the length of time it takes to perform the investigation and complete the
report. Sometimes the time from initial report of failure to a report analyzing the problem and

recommending a corrective action takes well over a year. A video made on the deficiency
reporting system will hopefully raise awareness of the importance of the system and address
the problem.
Other data systems are used to report aircraft and engine problems as well. Lack of
complete reports with proper malfunction codes result in both over and under reporting of
field problems. Correlation with engine contractor reports from their service representatives
with data from their daily reports has produced variance in engine shop visit and line
replaceable unit rates of about 50%. Thus the engine problems histories and reliability trends
can be suspect.
Secondly many high cycle fatigue problems have affected engine safety, reliability,
readiness and support cost problems over the recent decade. We do not understand
the phenomena well nor have the design tools to analyze it nor the test equipment to
measure it. With the help of the National High Cycle Fatigue Initiative these deficiencies
will be eliminated.”
The diagram used most commonly in LCF is generally referred to as an S–N curve
which is a plot of maximum stress (S) as a function of number of cycles to failure (N )as
depicted in Figure 1.1(a). This diagram is also referred to as a stress-life curve or a Wöhler
diagram, after the famous scientist August Wöhler who conducted the first extensive
series of fatigue tests and is often referred to as the father of fatigue. The diagram is
drawn for test data obtained at a constant value of stress ratio, R. For each value of
R, a different curve is drawn. Many attempts have been made and models developed to
consolidate data at different values of R with a single parameter based on combinations
of stress amplitude and maximum stress or other functions of stress. In this book, we will
deal with such models only as they pertain to the values of stress at or near the fatigue
limit corresponding to a large number of cycles in the HCF regime, typically 10
7
cycles
or greater.
8 Introduction and Background
(a)

(b)
Maximum Stress (S )
Cycles to Failure (N )
R
= constant
10
7
10
7
cycles
Alternating Stress
Mean Stress
R
= constant
Figure 1.1. Schematic of fatigue diagrams: (a) S–N curve for LCF and (b) Goodman diagram for HCF.
For HCF, the emphasis is on the value of stress at the fatigue limit and the data are
represented on a Goodman diagram which is a plot of alternating stress against mean
stress as shown in Figure 1.1(b). Each value of R is represented as a straight line drawn
radially outward from the origin and the plot is the locus of points having a constant life
in the HCF such as 10
7
cycles. The Goodman diagram, which should correctly be called
a Haigh diagram, is discussed in Chapter 2.
With this as a background for engine design practices, we focus on aspects of design
specifically for HCF and the associated problems that arose based on field experience.
Design for constant amplitude HCF loading can be rather straightforward when there are
no other factors involved. The procedure involves the generation of fatigue limit data at
different values of stress ratio, R, and plotting them on, for example, a Goodman diagram
as shown above. This plot of alternating stress against mean stress is a constant life
diagram and can be made for any number of cycles (Constant life diagrams are discussed

in detail in Chapter 2). Typically 10
7
cycles or higher is used, which is the traditional
maximum number of cycles that a component may be subjected to in its design life. It may
be more of a convenience in balancing testing time and expense with what a component
actually may see in service (see the discussion on gigacycle fatigue in Chapter 2). It is
Introduction 9
normally difficult to produce sufficient data at these long lives to be statistically signif-
icant, even with some of the newer high frequency machines being used. If the product
form, machining technique, and surface finish are identical for the laboratory samples
and the component for which the data are to be used, the behavior should be identical.
However, there are many instances where the component validation uses a geometry or
surface finish that does not conform to the laboratory test conditions. Many components
are shot peened or subjected to surface treatments (see Chapter 8) that are different than
those used on laboratory specimens. This is representative of the potential problems that
face designers involving transferring data from laboratory size samples to components,
especially if the components experience a multi-axial stress state [2]. A primary issue
in HCF design, one that has not been commonly addressed adequately, is the material
capability after it has been subjected to service conditions. For rotating components
in gas turbine engines, damage due to ingestion of foreign objects, fretting fatigue or
wear, and LCF can reduce the HCF capability of the material and must be considered in
design. These are some of the issues discussed in Part III (Chapters 4–7) of this book.
The stress corresponding to HCF design life is defined in various manners throughout
the literature. For cycle counts that are below the region that we classify as HCF, the term
“fatigue strength” is generally used. This is best defined as the stress that causes failure in
a set number of cycles, usually in the LCF regime. It is sometimes used for higher number
of cycles. We prefer the terminology fatigue limit or fatigue limit stress (or strength) to
indicate stress to cause failure at a fixed (large) number of cycles, typically 10
6
or 10

7
.
This implies that it is not quite an endurance limit because of either material behavior
(a non-horizontal S–N curve), or limitations on either testing or expected number of usage
cycles. More recent work in the field called gigacycle fatigue extends conventional testing
and material characterization into the regime encompassing 10
9
cycles. This subject is
addressed in Chapter 2. The terminology endurance limit, therefore, is reserved for the
case of “infinite life,” referring to a stress level at which the material will never fatigue.
Since such experiments are never conducted, it is an engineering approximation to the
fatigue limit and the two terms are commonly used interchangeably. Thus, the term
endurance limit can be used for cases where the expected number of cycles in service
does not exceed the number of cycles applied in laboratory testing.
1.4. HCF DESIGN REQUIREMENTS
High cycle fatigue was identified as a primary cause of a number of failures in USAF
fighter engines in the 1990s. While the number of failures has been reduced since then,
they have not been eliminated. Failure due to HCF is not unique to USAF engines but,
rather, has been encountered in commercial engines in this country as well as abroad.
The concern over HCF failures led the Air Force to convene a team of government and
10 Introduction and Background
industry experts to determine the root cause of these failures and to review the entire
design process for HCF in order to identify potential weaknesses. At the same time,
several independent review teams composed of experts from government and academia
were evaluating causes of individual HCF failures.
The combined findings of these teams centered around many aspects of the design,
field usage, and materials and their characterization. In particular, the use of the Goodman
diagram
∗
in the design process was evaluated extensively. Because of the number and

type of failures, it was generally concluded that the design process is flawed, and that
the usage of the Goodman diagram had to be modified or replaced by a more robust and
damage tolerant design methodology.
These conclusions further strengthened the findings of separate studies by two Air
Force Scientific Advisory Board (SAB) teams. In 1992, an SAB team evaluating failures
in titanium components in turbine engines recommended that the Air Force should expand
its ENSIP to extend the application of fracture mechanics to structural problems arising
from HCF. Further, they recommended that the Air Force should initiate a substantial
research program to increase the understanding of HCF in gas turbine engines because
they felt that this was essential to decrease the frequency of such in-service failures. In
1995, another SAB team reviewing the design process and failures in propulsion systems
found that although basic technology work cannot be expected to provide near-term
solutions to current field problems, the critical questions that must be answered before
HCF can be dealt with systematically have been identified. Most of these questions
centered around the ability of a Goodman diagram to account for in-service damage
and the ability to use damage tolerance in HCF design. Among other components of
a program, this team strongly favored the development of prediction methods for the
HCF of titanium parts in the belief that they must be included in any rational HCF
program.
The Air Force, therefore, committed to developing a damage tolerant approach to
design for HCF, although the definition of damage is broader than an inspectable crack,
and the use of conventional fracture mechanics principles and approaches may not be
the final approach adapted. The situation with HCF is analogous, in some ways, to the
scenario in the 1960s when structural failures in USAF aircraft were occurring and in the
1970s when LCF failures were much too common in USAF turbine engine components to
be acceptable. Both of these scenarios led to the development and adaptation of damage
tolerant design procedures for airframe and engine components which are now required
through the USAF Aircraft Structural Integrity Program (ASIP) specifications and the
ENSIP specifications, respectively. In both cases, design is based on the assumption of
the existence of defects, and a combination of the ability to calculate remaining life and to

∗
The Goodman diagram should correctly be called a Haigh diagram. This will be explained in the next chapter.
For the present, this chapter will use (misuse) the “Goodman diagram” terminology.
Introduction 11
inspect for defects. Whether or not such an approach is applicable to HCF because of the
long initiation and short crack propagation lives under HCF remains to be determined but
is highly doubtful (see Chapter 2). Nonetheless, an approach which is an improvement
over the existing use of Goodman diagrams was needed. The applicability of a new
approach for HCF design to other industries dealing with rotating machinery and vibratory
problems for very long lives (large number of cycles) is apparent.
1.5. ROOT CAUSES OF HCF
At the start of the Air Force National Turbine Engine High Cycle Fatigue program around
1995, each of the major engine manufacturers in the United States was queried about what
they felt had been the root causes of HCF. Their responses were based on both observed
and suspected causes of specific field incidents as well as some general speculation about
the closeness of operating conditions to the “edge of the cliff” as well as areas where data
and information were quite limited. In addition, government engineers summarized these
inputs and speculated on their own experience with HCF as a pervasive problem. The
following is a summary of the root causes of HCF at that time, before the major HCF
program was initiated. Many of the root causes led to research and developments in HCF
that is discussed in subsequent chapters. While the findings below are specific to gas
turbine engines, they appear to be generally applicable to any type of rotating machinery
where vibratory and cyclic loading and response occur.
HCF–LCF interactions: There was great concern for the scenario where LCF could cause
damage or fatigue cracking that, in turn, would alter the HCF capability of a material.
If the sizes of such cracks were sufficiently small, then the applicability of long crack
fracture mechanics and thresholds to a propagating LCF crack was questionable. Crack
orientation and mixed mode loading, particularly for small cracks and in anisotropic
materials such as single crystals, were also a concern. It was also not clear if LCF or
HCF could be the primary cause of crack initiation or whether there was a synergistic

effect between them. Debit in LCF life due to HCF was also a concern.
Fretting Fatigue: Fretting fatigue had been experienced in dovetail slots and was consid-
ered to be the cause of several HCF failure incidents. There was little understanding of
contact mechanics or tribological effects in these contact regions, let alone any systematic
design procedure beyond taking some empirical debit for fatigue strength in these regions.
While fretting fatigue was recognized as an extremely important issue, it was also antic-
ipated to be a very complicated issue. Solutions to this problem were acknowledged to
require a good understanding of how LCF–HCF interaction and residual stresses affect
HCF capability as well as an understanding of how the state of stress (normal, shear,
combined, etc.) in the contact region affects HCF capability.
12 Introduction and Background
Foreign object damage (FOD): FOD was a common occurrence in fan and compressor
blades. While bird ingestion was treated empirically through actual bird ingestion testing
in engines, the effects of hard objects such as sand or stones was not treated in design
much beyond the establishment of an empirical value of stress concentration factor, k
t
,to
account for the potential debit in fatigue strength. Empirical rules for blending out damage
or removing components from service have been in use for a very long time, but the
basis for these rules was not very scientific. It was recognized by the engine community
that the effect of notches on fatigue strength was an important first step toward treating
FOD, but that FOD was far beyond a simple notch problem because of residual stresses
and material damage resulting from the FOD event.
Manufacturing/handling damage: Concern was expressed on how damage in the form
of manufacturing defects such as machining marks, inclusions, pores, surface hardening,
or hard alpha particles (in titanium) effect the HCF strength of materials and how these
could be taken into account in the design phase. Handling damage as well as unfavorable
residual stresses can aggravate the situation as well.
Reliability of threshold and fatigue limit properties: One of the greatest concerns in
trying to establish a design methodology for HCF was the general lack of sufficient

data with which to establish material capability including the reliability (scatter) of
such data. In addition, data in the high mean stress regime were found to be severely
lacking, partially because of the difficulty of conducting smooth bar tests in that region
without introducing net-section plasticity or ratcheting. There was also a general feeling
that fatigue limits up to 10
7
cycles, common in some databases, was not sufficient for
HCF resulting from resonant vibrations that could produce far more than 10
7
cycles in
service.
Overloads and spectrum loading: Recognition was given to the fact that engine usage is
different than what is anticipated in the design phase and spectrum loading including surge
levels are not well known. While this is not specifically a materials problem, accounting
for such loads in material capability assessments is necessary.
No book on HCF, particularly from a USAF perspective, would be complete without
a quote from or acknowledgement of Otha Davenport who was responsible for leading
the USAF National Turbine Engine High Cycle Fatigue program. His work included
formulation as well as implementation of the program. The results of that program are
quoted throughout this book. In a short document, the genesis of the program and some
summary statements about accomplishments as of 1994 are presented as a draft final
report. That report appears as Appendix B and, although some of the material duplicates
what appears elsewhere in this book, the document serves to summarize the events that
led to one of the most challenging and exciting technology programs in history.
Introduction 13
1.5.1. Field failures
HCF failures in USAF fighter engines are probably no more common today than they
have been over many years. In the 1950s, creep in turbine components was a primary
cause of failure, and the associated design stresses were relatively low, so LCF failure
was not a concern. With the introduction of creep-resistant superalloys, operating stresses

were increased and LCF soon became a major cause of failure. The introduction of
retirement-for-cause as a life management philosophy, utilizing fracture mechanics, and
the adaptation of a damage tolerant design requirement through ENSIP [5] have led to
a significantly reduced incidence of LCF failures. The result has been that HCF is left
as the last remaining major mode of failure. With the commonality of parts in engines
on many different aircraft, combined with a draw down in the number of field assets,
the existence of HCF failures becomes a problem of immediate and critical concern. It is
certainly difficult to describe and document the exact scenario under which HCF failures
have occurred in USAF assets because of the proprietary nature of the design and usage
specifications and, in many instances, insufficient information to pinpoint root causes.
While there is no single general theme that is common to all failures, some aspects share
a degree of commonality. Additionally, failures have not been confined to one type of
component, one class of material, one particular engine, or one specific manufacturer.
The widespread nature of HCF failures is what has raised the question of the adequacy
of the design process.
Consider the following instances of field failures due to HCF. In one case, a single
crystal turbine blade failed below the platform in a contact area near a stress con-
centration, with the failure initiating slightly subsurface at very small pores which are
characteristic of this class of materials. The crack propagated as a stage I crack along
a crystallographic plane before changing to stage II and propagating along a plane nor-
mal to the loading direction. In addition to the very high vibratory amplitudes that are
assumed to have occurred, an unusual aspect of this class of failures was the appar-
ently small number of HCF cycles within any given mission. This indicates that the
resonance, whatever the cause, is not a steady-state phenomenon but, rather, a tran-
sient phenomenon which occurs only under specific operating conditions and which does
not persist very long. The hypothesis of this scenario was developed partly through
fractographic examination of failed blades. What is of significance from a material’s
characterization point of view is that failure was not caused by an unusually large num-
ber of HCF cycles, but a smaller number of high frequency, low amplitude cycles. It is
of importance to point out that little is known about the Mode II crack initiation and

crack growth characteristics of single crystal alloys, particularly along crystallographic
planes. Work at the time by John et al. [6] showed that growth rates are higher and
thresholds are significantly lower in Mode II and mixed mode I and II compared to
pure Mode I in certain crystallographic directions in a single crystal nickel-base superal-
loy at room temperature. Certainly, design methodology such as the Goodman diagram
14 Introduction and Background
does not consider all possible combinations of mode mixity and crystallographic plane
orientation.
Another source of field failures attributed to HCF is related to FOD through the
ingestion of debris into engines. Titanium fan and compressor blades with thin leading
edges have been shown to be especially susceptible to FOD along the leading edge and, in
some newer engines, along very thin trailing edges. This service-induced type of damage,
combined with vibratory loading from forced response resonances, has led to HCF failures
in several components and engines. The vibratory stresses, as in the previous example,
were transient rather than steady state and occurred only during specific conditions in the
flight and operational envelope. The design of such a component for HCF in the presence
of FOD was based, in part, on the use of a Goodman diagram which had been modified
to account for FOD through the use of an equivalent stress concentration factor k
t
 or
through the use of a limiting level of vibratory stress. The various types and levels of
FOD, which includes a surrounding region of residual stresses, is not handled well in
a Goodman diagram combined with an equivalent k
t
in terms of its total HCF life. In
analysis of field failures, it is still not apparent whether the failures were due to extremely
high stresses due to excessive vibrations, or that the FOD on the components severely
degraded the HCF capability of the material. This is particularly true in several instances
where the fracture surface indicated a fatigue initiation site that was in the form of a dent
or ding, but of an unusually small size. Such incidents have been classified as involving

“micro FOD” because of the extremely small size of the initiation site that is too small to
measure or detect in the field. Other incidents, involving small FOD, have led to the use
of techniques such as dental floss being rubbed along the leading edge to detect damage
of the order of 0.5 mm or less in depth. These are not small enough to classify as micro
FOD, but they are very difficult to detect. Various aspects of FOD and related analysis
and design issues are discussed in Chapter 7.
In other instances, titanium fan and compressor blades, and the disk lugs which support
them, have experienced HCF failures due, in part, to fretting which occurs in service
under vibratory loading from a steady state or transient resonance or from a forced
response. These types of failures, where the HCF resistance of the material is degraded
significantly due to fretting, are not confined solely to the contact region. In some
instances, failure occurs just outside the fretted region and may be due to the redistribution
of stresses because of the uneven wear due to fretting. Here, again, the vibratory stresses
causing failure are not necessarily steady-state stresses but, rather, the result of transient
phenomena which occur only under certain engine operating conditions. The use of
the Goodman diagram under conditions of fretting fatigue is based, traditionally, on
knockdown factors to account for the reduction in HCF resistance and is based, almost
exclusively, on empirical data. Developments in this area are contained in Chapter 6.
A most unusual failure scenario developed in the HCF of a rotating seal which experi-
enced resonances causing bending stresses superimposed on high centrifugal stresses from
Introduction 15
the very high engine speeds. In a series of these types of failures, there were no failed
parts recovered from which to deduce the failure scenario in terms of number of cycles,
HCF or LCF, or initial defects, the type of information which might be available from
fractographic analysis. It was only on the chance discovery of cracks in an identical part
during an overhaul inspection that the cause of these failures became more apparent. It
now appears that during the initial break-in operation, some of these rotating seals experi-
enced transient resonances which led to excessive rubbing, heating, and the development
of very small cracks on the outer edge of the seal. When subjected to normal service,
these slightly damaged seals were again subjected to vibratory loading through bending

resonances and the cracks propagated. It appears from limited data that the amount of
crack extension per flight was slight and that the resonances were transient rather than
steady state in nature. Although the operating conditions, including the fatigue loading,
were within the design envelope of the Goodman diagram, the damaged material had
HCF resistance substantially below that determined from a Goodman diagram which is
based on tests of undamaged material.
Another example of failures in engines involved what appeared to be LCF. Yet testing
and analysis showed no defect in the material taken from the region around the cracked
part, and LCF analysis showed stress levels that were nowhere near the level to produce
failure in the number of cycles to which the engine was exposed. Assuming that a
vibratory component had to be present, extensive testing and fractography led to the
conclusion that some HCF vibratory stresses had to be present. Questions as to the HCF
capability of the material at very high mean stresses, the effect of dwell times (hold
at constant stress) on the fatigue behavior of titanium alloys, or the interaction of LCF
and HCF still have not been adequately answered in order to adequately explain the
failures.
While no one common thread connects all these failures with one another, a common
feature of many of them is the presence or development of damage from sources such as
fretting, FOD, LCF, and others. These types of damage are not all handled adequately
with a Goodman diagram, or they are handled in a highly empirical fashion. Another
point of commonality among many of the failures is that the number of HCF cycles is
not extremely large, but rather that a limited number may occur within a given mission
due to transient phenomena which occur for short durations. Thus, concern over a run-out
stress equivalent to 10
8
or 10
9
cycles in an S–N plot may not be justified for some cases.
Finally, two aspects of field failures seem to be common among the many cases involved.
First, many of the failures involved new designs, materials, and operating conditions

(steady stress, temperature, geometries), which are somewhat new and slightly outside of
the envelope of operating experience. The second is that many of the failures appear to
be occurring at high mean stresses associated with high engine speeds.
What operational experience shows, in summary, is that pure HCF is generally not the
primary problem and that the use of a Goodman diagram, given appropriate data as well