High Cycle Fatigue: A Mechanics of Materials Perspective part 4 pdf

16 Introduction and Background
as a knowledge of the vibratory loading, is a viable and reliable method for designing
for pure HCF. The failures encountered also indicate that the problem is typically not
one of long-life degradation or a high number of accumulated cycles, but rather one of
shorter life including infant mortality and conditions which were not anticipated in design
or detected in developmental engine testing. The problem appears to be the synergistic
combination of HCF with other modes of initial or service-induced damage, something
that is not addressed in a Goodman diagram. As noted earlier, the HCF problem in
turbine engines provides an example of how HCF capability can be degraded by service
usage which also has to be considered in a robust design process. Although the examples
cited in this book come largely from experience with turbine engines, the problem and
approaches are felt to be quite generic and applicable to other applications where HCF is
a design consideration.
A final aspect of HCF design has to be related to the statistical distribution of fatigue
strengths. There are a number of scenarios surrounding field failures where analysis
indicates that failures should not have taken place under the assumed circumstances. On
the one hand, the circumstances may not have been properly categorized and vibratory
loading, for example, may have been greater than that determined from detailed analysis
or actual component or engine testing. On the other hand, the fatigue strength could be
shown to be adequate to prevent failure. Under both circumstances, there is little known
about the tail end of the distribution function that describes either the applied loading or
the material capability. In an attempt to shed some light on this subject, specifically in
regard to material capability, some aspects of the statistics of fatigue limit strength are
presented in Chapter 3.
1.6. DAMAGE TOLERANCE
Before discussing damage tolerance, the distinction between durability and damage tol-
erance should be established. From the original version of ENSIP [5], the following
definitions are established. Section 3.1.3 defines damage tolerance as “the ability of the
engine to resist failure due to the presence of flaws, cracks or other damage for a spec-
ified period of unrepaired usage.” Section 3.1.7 defines durability as “the ability of the
engine to resist cracking (including vibration, corrosion and hydrogen induced crack-

ing), corrosion, deterioration, thermal degradation, delamination, wear and the effects of
foreign and domestic object damage for a specified period of time.” It is Noteworthy
that damage tolerance is applied to critical structural components whose failure would
cause major damage or total failure. Durability, on the other hand, eliminates the task of
excessive and unscheduled maintenance involving part replacement or added inspections.
The remainder of this section is concerned with the concept of damage tolerance and its
potential application to HCF.
Introduction 17
While damage tolerance as applied to LCF has a limited role in HCF, the concepts and
philosophical aspects are important to grasp in understanding how HCF problems can
be addressed. Damage tolerance is a design philosophy that was adapted by the US Air
Force for both airframe structures in the 1970s and for turbine engines in the 1980s. It
evolved from experience with field failures attributable to either initial or service-induced
damage or flaws that were not accounted for initial design. It involves the assumption
of the existence of initial defects (flaws) in critical structural components combined with
inspection methods to assure flaws of a size larger than those assumed do not exist
when the structure enters service. For a comprehensive discussion of all of the aspects
of damage tolerance as well as the associated nondestructive evaluation techniques, the
reader is referred to the book by Grandt [7]. It is the intent of this section only to provide
an overview of some of the concepts involved in damage tolerant design and how they
relate to problems in HCF.
The Air Force defines damage tolerance in engines in the latest version of ENSIP [4]
in the same manner as in the original version [5] as cited above, namely “the ability of
the engine to resist failure due to the presence of flaws, cracks, or other damage. ”
Among the other guidance provided in ENSIP, the scope of the applicability of damage
tolerance is established as:
Damage tolerance requirements should not, in general, be applied to components in which
structural cracking will result in a maintenance burden but not cause inability to sustain flight
or complete the mission; i.e., durability-critical parts. However, damage tolerance require-
ments should be applied to durability-critical parts to: (1) identify components sensitive

to manufacturing variables and pre-damage which could cause noneconomical maintenance
(e.g., blades), or (2) aid in the establishment of economic repair time or other maintenance
actions.
Damage tolerance is the only one method used in design to assure structural integrity.
Other methods include safe-life design or fail-safe design (see [7], for example). One of
the reasons that damage tolerance is not used universally for critical structural components
is the maintenance burden and associated cost for the required inspections. Nonetheless,
the requirement by the US Air Force provides details on how to achieve a damage tolerant
design. In ENSIP [4] it states
Damage tolerance will be achieved by proper material selection and control, control of
stress levels, use of fracture-resistant design concepts, manufacturing and processing con-
trols, and the use of reliable inspection methods. The design objective will be to qualify
components as in-service noninspectable to eliminate the need for depot inspections prior
to achievement of one design lifetime. As a minimum, components will be qualified as
depot- or base-level inspectable structure for the minimum interval. Damage tolerance can
be achieved by performing crack growth evaluation as an integral part of detail design
of fracture-critical engine components. Initial flaws (sharp cracks) should be assumed in
highly-stressed locations such as edges, fillets, holes, and blade slots. Imbedded defects
18 Introduction and Background
(sharp cracks) should also be assumed at large volume locations such as live rim and bore.
Growth of these assumed initial flaws as a function of imposed stress cycles should be
calculated. Total growth period from initial flaw size to component failure (i.e., the safety
limit) is thus derived. Trade studies on: (1) inspection methods and assumed initial flaw
size, (2) stress levels, (3) material choice, and (4) structural geometry can be made until the
safety limit is sufficiently large such that the need for in-service inspection is eliminated or
minimized. Damage tolerance design procedures which account for distribution of variables
that affect growth of imbedded defects are permitted (e.g., probability of imbedded defects
associated with the specific material and manufacturing processes). Specific requirements
on initial flaw sizes, residual strength, critical stress intensities, inspection intervals, damage
growth limits, and verification are contained elsewhere in this document. Damage tolerance

requirements may be applied to durability-critical parts to: (1) identify components sensitive
to manufacturing variables and pre-damage which could cause non-economical maintenance
(e.g., blades), or (2) aid in the establishment of economic repair time or other maintenance
actions.
The concepts embodied within a damage tolerant approach to structural integrity can
be illustrated with the aid of several figures. In Figure 1.2, the traditional design approach
to LCF is illustrated schematically and shows that fatigue life, being a statistical variable
in life for a given stress level, has to be treated with enough of a factor of safety (or
uncertainty) to account for a worst case scenario in terms of material capability. The
shape of the S–N curves depicted in Figure 1.2 has no physical meaning and is used
merely to illustrate the concept of having both an average and a design curve. Since
these curves are different, the resultant design allowables can then severely underestimate
the average behavior of the material. Because of the conservative nature of this design
Applied Stress
Number of Cycles to Crack Initiation
Average
Design
Allowable
Distribution
Of Lives
Figure 1.2. Schematic of S–N curve with illustration of scatter.
Introduction 19
approach, the US Air Force implemented a program called “Retirement for Cause (RFC)”
on some of their engines that had not been designed using damage tolerance procedures.
RFC was actually an early application of damage tolerance to an existing design. The
RFC approach allowed the Air Force to keep in service components that had reached their
design life (see Figure 1.2) but had not developed any signs of fatigue cracking. Since only
a small fraction of components would be expected to show signs of failure at the design
lifetime because of the conservatism in the design, inspection procedures coupled with
crack growth analyses based on fracture mechanics were implemented on the remaining

components. The procedure is shown schematically in Figure 1.3, which incorporates the
fundamental philosophy of damage tolerant design. If the inspection capability to reliably
detect a flaw of a given size is available, then all inspected parts will have flaws no
larger than those shown as “inspection capability” in the figure. The worst case, shown
as curve “A,” would then have the crack growth behavior shown and would fail after
two inspection intervals if the interval was chosen as half of the predicted crack growth
life as shown. The interval could be chosen as one-third to be more conservative. For the
worst case, A, the crack would be found at the first inspection and the part removed from
service. All remaining parts where no crack was found could be kept in service for another
inspection interval and the new worst case component would follow curve “C” as shown.
The procedure could be repeated for curve “D” as many times as practical. Note that as
the life increases, the probability of a crack developing increases as the average life is
approached (see Figure 1.2). Note also that an average part, denoted by curve “B,” would
be retired when a crack above the inspection limit was detected and that, in the example
Crack Length
Number of Cycles
Inspection limit
Critical crack size
Inspection
interval
A
B
C
D
Figure 1.3. Schematic of crack growth in damage tolerant design.
20 Introduction and Background
cited, there would be two inspections available to find the crack if it was missed at the first
inspection.
∗
The applicability of damage tolerance to HCF, discussed in Chapter 8, is severely

limited because of the rapid growth of cracks under HCF where large numbers of cycles
can be accumulated in a short period of time. This would require unacceptably short
inspection periods, some of which could be shorter than a single mission. Another aspect
of damage tolerance applied to HCF is illustrated in Figure 1.4 where, as an example,
a single event such as FOD can cause a level of damage that is severe compared to an
inspection level and can occur at any time. It is the possibility of such damage occurring
and the concurrent rapid rate of crack growth under HCF that precludes the applicability
of damage tolerance to HCF in many cases as discussed below.
1.6.1. Application to HCF
A damage tolerant design approach for HCF must take into account both potential
initial (manufacturing) and service-induced damage in order to be successful. Further,
the margin of safety must be determined for any operating condition in order to know
how close to the “edge of the cliff” one is operating. The types of damage that must
be addressed, if relevant, include fretting, galling, FOD, combined LCF–HCF, corrosion
pitting, thermomechanical fatigue, creep, and their combinations. It is of interest to note
the limited scope of requirements, especially details, for HCF that were contained within
the original ENSIP [5], the document which governs the design and development of US
D
N
Design
life
Actual
life
Critical
damage
state
Remove from
service or
inspect
LCF

FOD
Figure 1.4. Schematic of damage accumulation applicable to HCF.
∗
Figures 1.2 and 1.3, and many variations thereof, were used numerous times as an illustration of how a damage
tolerant approach could save costs in not having to replace engine components when they reached their design
lifetimes. These schematic plots were created and used by Dr Walter Reimann of the Air Force Materials
Laboratory many times to champion the Retirement for Cause (RFC) program that was eventually adopted by
the US Air Force and produced cost savings approaching a billion dollars.
Introduction 21
Air Force engines. The following sections are extracted from that original version of
ENSIP and deal specifically with, or are applicable to, HCF:
Section 4.6.2 defines initial flaw size: “Initial flaws shall be assumed to exist as a
result of material, manufacturing and processing operations. Assumed initial flaw sizes
shall be based on the intrinsic material defect distribution, manufacturing process and the
NDI methods to be used during manufacture of the component.”
Section 4.7.4 addresses HCF design requirements: “Engine components shall be capable
of withstanding combined steady and high cycle fatigue stresses, including vibratory
stresses that occur at sustained power conditions, for the required design service life.”
Section 5.7.4 requires: “The HCF life of engine components shall be evaluated by
analysis and measurement of vibratory stresses during the engine tests. ”
Appendix Section 5.6b “Certain levels of vibratory stress, e.g., 10 ksi, should be
assumed to exist on each fracture critical part to identify sensitive components.”
Appendix Section 4.7.4  “it is recommended that vibratory or high cycle stress
be restricted to a value of 40% of that allowed by the minimum value material
property allowable due to the sensitivity of high cycle stresses to damping variabil-
ity, part to part resonance variation, unknown excitations, etc. An alternative design
approach to achieve margin is to limit the steady stress such that a significant level of
vibratory stress (e.g., 30 ksi peak-peak) will not exceed the minimum value material
allowable.”
It is important to recognize that ENSIP was written and implemented at a time when

LCF failures were the major concern of the US Air Force. While ENSIP was establishing
a damage tolerant approach to LCF, it was also recognized that HCF is another problem
of great concern, but no approach as detailed as that developed for LCF was suggested for
addressing HCF design at that time. It is of interest, therefore, to examine a more recent
approach to HCF through the use of a Goodman diagram in the light of the requirements
and intent specified in the ENSIP document.
∗
The approach to HCF in a more recent
version of ENSIP is documented in Appendix B.
It can be seen from the above requirements and specifications that HCF design
does not address some of the aspects of field service–induced damage and does not
present any methodology for doing so. The requirements, like a 40% allowable of
∗
Subsequent to the original ENSIP document in 1984 [5], several revisions have taken place. Many of these
revisions deal with HCF and are the result of the Air Force National Turbine Engine High Cycle Fatigue
program. Appendix C presents some of the sections that were revised or added to deal specifically with HCF
issues.
22 Introduction and Background
the Goodman vibratory stress or an absolute limit on allowable alternating stress, are
based on experience and may have little applicability to newer designs, materials, or
operating conditions. In particular, one can note that the guidelines proposed in the
original ENSIP become less conservative at higher mean stresses because the frac-
tional approach is based on lower vibratory stress allowables at high mean stress (see
Chapter 2) or an absolute vibratory level which eventually intersects the Goodman allow-
able if mean stress is allowed to increase. What is not specified or accounted for in
design is any in-service damage including that caused by loading such as LCF. Most
components that are subjected to HCF are not designed based on HCF considerations
alone. In general, they are checked for tolerance to HCF, or an allowable vibratory
stress level is specified. What governs the design, for example LCF, is addressed sep-
arately and then the HCF resistance is evaluated by itself. There does not appear to be

any systematic approach to designing for the combination of HCF and another dam-
age mechanism. If interactions occur, the synergism might cause failure even though
failure is not predicted by any one mode individually. This is particularly true for
combined LCF–HCF loading which is discussed below and in Chapter 4 in greater
detail.
One of the key parameters which must be considered in damage tolerant design for
HCF is mean stress. Mean stress, resulting primarily from the rotational speed of an
engine in the form of centrifugal loading, has a very significant influence on the fatigue
limit of a material. For example, Greenfield and Suhr [8] show data for a low alloy
steel which has a tensile strength of 840 MPa and a yield strength of 700 MPa. For this
material, which exhibits a true run-out stress, the increase in mean stress from zero up to
775 MPa reduces the fatigue strength by greater than a factor of four. They observe that,
for design purposes, “a reduction in the level of mean stress may be regarded as almost
as important as a reduction in the level of fatigue stress in reducing the risks of failure
by fatigue.” Similarly, in fracture mechanics, the threshold stress intensity, which is the
value below which cracks will not propagate at a very low chosen value of growth rate
(10
−10
m/cycle in some standards), is a decreasing function of stress ratio or mean stress.
Under combined LCF–HCF loading, for example, it has been shown that the threshold at
which HCF influences the growth rate under LCF, denoted by K
onset
, is not a material
constant, but rather it is a function of stress ratio, R [9]. In one specific example, the
value of K
onset
was found to decrease by over a factor of two in Ti-6Al-4V when R
increases from 0.1 to 0.7 whereas it remains nearly constant for R>07 [9] (HCF crack
growth thresholds are discussed in Chapter 8). From the preceding, it appears that a
margin of safety which is either a fixed fraction of the allowable alternating or vibratory

stress or a fixed value of vibratory stress, independent of mean stress, becomes smaller
as mean stresses become higher. This is true whether a total life criterion, such as the
Goodman diagram, or a damage tolerant approach based on an initial flaw size is being
used. Given this observation, in an Air Force review of root causes of HCF failures,
Introduction 23
it was not surprising to find that designers from the major engine companies identified
components with high mean stresses to be the most likely candidates for potential HCF
problems.
1.7. CURRENT STATUS
The Goodman diagram is still considered to be an acceptable design tool for HCF
provided it is applied correctly. Two aspects which may not yet be handled adequately are
the presence of initial damage and the accumulation of service-induced damage. Initial
damage, such as rogue flaws or inclusions, for example, would have to be found in
laboratory or component testing and taken into account in establishment of the minimum
design allowables. An alternate approach would be to characterize initial damage in terms
of an expected statistical distribution of defects, a process now employed for internal
defects in LCF design. One could question how many organizations or laboratories use
data from a specimen or component which was clearly defective as part of their database,
even though the defect is discovered only after performing the test! It is this situation,
where defects appear only occasionally, that has led the USAF to adapt the damage
tolerant approach to engine structures because defects are not always found in baseline
testing for LCF. Good statistics on the presence of defects from specimen testing would
require an inordinate number of tests. Thus, the assumption of the presence of initial
damage is a logical approach to avoid potential failure due to the occasional defect.
∗
A similar approach based on damage tolerant concepts could also be warranted for HCF.
The second aspect, service-induced damage, is not addressed in a Goodman diagram.
Illustrative calculations for combined LCF–HCF clearly indicate that service life and safe
design space under pure HCF is affected by the superimposed presence of LCF loading,
and a potential methodology for considering this damage is presented in Chapter 4. It

remains to be seen if a similar approach can be developed for constructing a damage
tolerant Goodman diagram for other types of field-induced damage such as fretting, FOD,
corrosion pitting, and others. Certainly this would appear to be a more rational approach
than limiting allowable vibratory stresses to some percentage of the Goodman diagram or
∗
It should be noted that in LCF design, the assumption of initial flaws in a damage tolerant design did not
add weight to components. In the latest version of ENSIP [4], referring to historical experience with engines
designed using damage tolerance, it states: “These design configurations have shown that damage tolerance
requirements can be met with small or modest increases in overall engine weight, will have little impact on
engine performance, and will provide greatly-improved engine durability while weapon system life cycle cost
is significantly reduced.” In pure LCF design assuming no initial flaws, the use of design allowables based
on extensive testing which provides data representing the lower bound on a distribution curve, similar lives
are predicted. In other words, the lower bound on the LCF database reflects the existence of the same type of
flaws that are assumed in damage tolerant design. It was cases where the occasional flaws or defects were not
discovered in specimen testing that led to problems when such flaws appeared in component hardware.
24 Introduction and Background
some absolute magnitude. For both cases where the Goodman diagram does not handle
design adequately, the requirement in the 1984 ENSIP document [5] defining initial flaw
size should be noted again. Section 4.6.2 of that document states that initial flaw size can
be based on inherent material defect distribution. This indicates that perhaps inspection
for initial or in-service damage may not be necessary but, rather, calculations or statistical
data on damage accumulation could be substituted in an HCF design life methodology.
In these summary observations, it should be noted that a Goodman diagram is a total
life diagram even though most of the life under HCF is attributed to the initiation phase.
Initiation, or nucleation, in fatigue is defined in various manners in the technical literature.
One of the more common engineering definitions is the time (number of cycles) it takes
for a crack to form and grow to a detectable or observable size. Dependent upon the
inspection capability, this crack size can become large and initiation can then become
a dominant portion of the entire fatigue life. The second part of total life is the crack
propagation portion which can be determined using fracture mechanics principles (which

are not addressed to any significant extent in this book). If crack initiation is defined as
the formation of a crack-like defect at the microstructural level, then crack-propagation
life can become a larger fraction of total life. This latter interpretation of crack initiation
is more commonly referred to a crack nucleation. In this book, we lean more toward an
engineering definition for initiation and find, in general, that very long-life fatigue tests
have a minimal fraction of their lives associated with crack propagation. For this reason,
the Goodman diagram is often used interchangeably as a total or infinite life criterion as
well as an initiation criterion. The fraction of life that is initiation to a specific crack size,
however, may differ with change in mean stress. Crack propagation life from the defined
initiation crack size to failure would have to be subtracted from total life to come up with
a true initiation diagram. The addition of fracture mechanics principles to the construction
and use of Goodman diagrams, discussed in Chapter 8, would help separate the initiation
and propagation stages in the plot and provide a better indication of the inherent damage
tolerance of the material to HCF. This is shown clearly in the calculations for HCF
loading only where there are regions where a crack will not grow if initiated (damage
tolerant) and other regions where the crack will grow at stresses below those needed
for initiation (damage intolerant). It is possible that a true initiation diagram combined
with a superimposed fracture mechanics–based plot will give better insight into the stress
states where such behavior can be expected. Analyses, such as that by Barenblatt [10]
which deals with crack propagation within the grain and between grains in a material,
can then be interpreted better from a design point of view when they demonstrate the
potential for cracks to initiate but subsequently either slow down or arrest, a phenomenon
commonly associated with small crack behavior [11, 12]. It is possible, for example, that
the propensity for this phenomenon to occur may be constrained to certain combinations
of mean and alternating stresses, based on the information contained in a combination of
a Goodman diagram and fracture mechanics–based analysis.
Introduction 25
From the analysis of the conditions under which initiation and propagation under
HCF, LCF, or combined HCF/LCF can occur, it appears that a very important design
consideration for any component is a realistic estimate of the number of LCF as well as

HCF cycles to which it will be subjected in service. This could result in drastic changes
in the allowable design space, for example, if the component is potentially subjected to
some type of steady state or resonant vibratory loading as opposed to transient vibratory
conditions which may only produce a limited number of HCF cycles per mission or per
LCF cycle.
Any component designed for anything other than HCF alone will generally undergo
some degree of damage from that design consideration (e.g., LCF, TMF, creep). Even
though the condition on which design is based will not cause component failure during
the design life, some degree of subcritical damage or degradation may occur and that,
in turn, can result in less resistance to HCF. Thus, the Goodman diagram may not be a
valid indicator of HCF resistance if these other damage modes exist. Further, the HCF
resistance will decay with life and this decay should be taken into account by combining
the effects of HCF with any other mechanism which is the basis for design. The use of a
damage tolerant Goodman diagram, therefore, is recommended.
1.8. FIELD EXPERIENCE
In HCF, as in other modes of failure, field experience tends to improve our knowledge
base. “Lessons learned” are often the basis of new approaches, and many of these are
documented in guide specifications such as ENSIP. On the other hand, I have had
experience in several investigations where closure cannot be reached on the root cause or
exact scenario under which an HCF failure occurred. We still have much to learn about
HCF material behavior and design.
∗
I can recall many meetings where, as a group of
technical experts, we went through a systematic analysis of the conditions leading to an
HCF failure and can prove, through existing data, knowledge, and analysis, that a failure
could not have occurred. Only the failed parts in our hands were able to convince us of our
inability to completely describe the event accurately. Eventually, we arrive at an unlikely
∗
In a recent revision, dated 22 September 2004, to ENSIP [4], under VERIFICATION LESSONS LEARNED
(A.5.13.3.2), the following appears: “The most significant lessons learned for this requirement is that, for almost

every field failure experienced by the USAF over the last decade, the test data showed the failure should not
have occurred. This experience conclusively demonstrates that a deterministic approach to verification of HCF
capability cannot succeed. One statistical study by a major engine manufacturer estimated that a deterministic
process (analysis and testing) could at best discover less than forty percent of the HCF failures that would occur
over the life of the program.” The document goes on to recommend that a new approach must recognize “the
stochastic nature of the material strength, the component behavior and the operational usage.” The statistical
aspect of HCF design is discussed briefly in Chapter 8.