High Cycle Fatigue: A Mechanics of Materials Perspective part 23 pdf

206 Effects of Damage on HCF Properties
the LCF cycles can be considered to be an underload on the baseline HCF cycles. On top
of this simple spectrum, a single overload is added to the baseline LCF cycle. Defining
the overload ratio as OLR =K
max
/K
ss
, experiments were carried out to see when the onset
of HCF activity occurred. The results, based on the use of a number of values of OLR,
are presented in Figure 4.51. The curves shown are the best fit to the actual data points
which are not shown for clarity. OLR = 1 represents the case where there is no overload
in the baseline LCF–HCF cycle. The pure LCF curve is also shown. The results show
that as OLR increases, the retardation effect of the single overload diminishes the growth
rate until the minor cycles have almost no influence on the baseline LCF cycle at a value
of OLR = 2.0. This work, conducted on Ti-6Al-4V, also shows that the apparent onset of
HCF activity is delayed by the overload cycle. In this case, there is both an underload in
the baseline combined cycle as well as a superimposed overload. While the behavior of
the baseline cycle defined by OLR = 1.0 is predictable with linear summation of the LCF
and HCF cycles, the additional effect of the overload is both to reduce the minor cycle
contribution to the growth rate and to reduce the threshold where minor cycle activity
begins.
The natural conclusion arising from these studies is that growth rates and thresholds
from constant amplitude loading cannot always be used directly in spectrum loading
without consideration of interaction effects. Both retardation and acceleration effects have
been noted in various studies, with overloads usually observed to retard crack-growth
rates while underloads are found to accelerate the growth rates. While these observations
are common, the exceptions prove that a single rule cannot be applied in all cases.
In [52], HCF and LCF tests were used to establish baseline material properties, and
simple mission tests were used to assess additional failure modes that may exist if
10
–1

10
–2
10
–3
10
–4
10
–5
10
–6
8 9 10 20 30 40 50
OLR = 1.0
OLR = 1.15
OLR = 1.3
OLR = 1.45
OLR = 1.75
OLR = 2.0
LCF only
da

/dBlock (mm/block)
Ti-6Al-4V
n
= 1000
ΔK

LCF
(MPa m)
Figure 4.51. Fatigue crack growth for various overload ratios, R
HCF

=07, 1000 minor cycles per block.
LCF–HCF Interactions 207
LCF–HCF interactions are important. This was explored with mission tests at 75

F
with Ti-6Al-4V and were based on the following criteria: (a) tests that avoid specimen
ratcheting failure modes (typically high stress, high R) that are not representative of
component failures, (b) LCF stresses that are in the main regime of design interest for
turbine engines (average N
f
∼10000 cycles), (c) HCF stresses that are in the regime of
design interest (R>05 and HCF > 10
7
cycles), (d) mission histories that include LCF
+ periodic HCF cycles until mission failure, and (e) tests that can be run economically in
the laboratory. A double-edge V-notch specimen geometry was used to avoid ratcheting
for load-control testing and loads were selected to keep the fatigue lives in the regime
of design interest. Baseline notch LCF tests at R = 01 were run to identify stresses
for an LCF failure of ∼10000 cycles while baseline notch HCF tests were used to
identify the value of R for an average HCF failures of ∼10
7
cycles. All interaction tests
were missions or blocks of cycles that were repeated until failure. Missions included an
LCF load-up R =01+10000–100000 repeated HCF cycles R =07–09 +anLCF
unload reversal R =01 for each mission. The baseline and mission test conditions for
the notch geometry are given in Table 4.3. Stresses are reported in units of ksi.
The first group of mission tests was used to assess the HCF capability when minimal
LCF damage is present. This was evaluated with 10,000–100,000 HCF cycles/mission
with an HCF cycle from 56 to 80 ksi (R = 07). These conditions were intentionally
selected to avoid significant predicted LCF damage. The number of HCF cycles to failure

for these mission tests is compared to the number of cycles to failure for HCF alone
with probability plots shown in Figure 4.52. Given the similarity of these distributions
Table 4.3. Baseline and LCF–HCF mission tests
LCF LCF HCF HCF HCF/mission Freq Expt HCF Expt missions Pred life
S
min
S
max
S
min
S
max
(Hz) cycles with Fs
9 90 NA NA LCF 0.5 NA 9963 11365
8 80 NA NA LCF 0.5 NA 10766 16489
8 80 NA NA LCF 0.5 NA 10821 16489
NA NA 56 80 HCF 1k 234894301 234894301 6370632
NA NA 56 80 HCF 1k 11694364 11694364 6370632
NA NA 56 80 HCF 1k 2613654 2613654 6370632
8805680 10000 0.5/1k 16400000 1640 613
8805680 10000 0.5/1k 71682975 7168 613
8 80 56 80 100000 0.5/1k 14298296 142 63
8 80 56 80 100000 0.5/1k 9312872 93 63
8 80 56 80 100000 0.5/1k 405933382 4059 63
8807280 10000 0.5/1k 142814
527 14281 16222
8806580 10000 0.5/1k 94130587 9413 16222
208 Effects of Damage on HCF Properties
HCF + LCF
HCF

1.00E5 1.00E6 1.00E7 1.00E
+ 08 1.00E + 09
99
95
90
80
70
60
50
40
30
20
10
5
1
HCF cycles to failure
Percent
Figure 4.52. Capability of notched HCF tests compared to the HCF capability of LCF–HCF mission tests
when HCF damage dominates.
for the small set of data presented, a significant LCF–HCF interaction does not seem to
be present for cases when HCF damage dominates.
The second group of tests was run to assess if LCF failure modes are influenced
when minimal predicted HCF damage exists. Minimal HCF damage was evaluated with
mission tests that included an LCF load-up reversal R = 01 +10 000 repeated HCF
cycles (S
max
=80 ksiS
min
=72 for R =09 or 65ksi for R =082). The HCF parameters
were selected near the minimum allowable stress for a 10

7
HCF limit so that HCF could
be ignored as a contributing factor, assuming no LCF–HCF interactions. The number
of LCF cycles to failure for the notch mission tests as compared to N
f
for the notch
specimens with LCF alone is shown in Figure 4.53. The values for predicted N
f
used
an average smooth specimen S
equiv
fatigue curve with the modified Manson-McKnight
fatigue parameter. The local stresses from the notch were obtained from elastic-plastic
analysis and notch life was predicted with the local notch stresses and notch gradients
using the effective stressed area, Fs approach described in Appendix E. (see Chapter 5
for a detailed discussion of notch fatigue). The tests are seen to be well predicted within
the 2X scatter bands that are representative of a reasonably accurate LCF life method.
Neglecting LCF–HCF interactions is shown here to be a reasonable assumption for these
mission tests where the predicted HCF damage is minimal. From the viewpoint of design,
it appears that one can use an HCF limit based on minimum properties such that HCF
can be ignored as a failure mode in the type of mission used here that contains HCF and
LCF conditions.
LCF–HCF Interactions 209
Ti-6Al-4V notches with LCF + Min allowable HCF
(predictions with smooth specimen curve plus Fs)
1,000
1,000
10,000
10,000
100,000

100,000
Observed LCF to failure
Predicted LCF to failure
LCF Only
LCF + min HCF
Figure 4.53. Notched LCF tests compared to the LCF of LCF–HCF mission tests with minimal HCF damage.
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th
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LCF–HCF Interactions 211
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212 Effects of Damage on HCF Properties
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Chapter 5
Notch Fatigue
5.1. INTRODUCTION
A notch in a component can be considered to be a defect since it produces a local stress
concentration or stress raiser that can ultimately be the location of an HCF failure. Thus,
it is important to understand the effect of a notch on the FLS and to be able to predict
the strength without having to conduct extensive experiments for each notch geometry.
An alternate reason for understanding and modeling notch behavior is that it represents
a condition where there are stress gradients in going from maximum stress at the notch
root to lower stress at locations beneath the notch. Stress gradients also arise in fretting
fatigue, discussed later in Chapter 6. Additionally, FOD, discussed later in Chapter 7,
often produces some type of geometric discontinuity. To be able to predict the effect of
the discontinuity or damage to stresses induced by vibratory HCF loading requires an

understanding of notch effects in fatigue. For these reasons, we present an overview of
notch fatigue as related, primarily, to the fatigue limit or threshold for crack propagation.
5.2. STRESS CONCENTRATION FACTOR
In notch fatigue, the primary aim is to be able to predict the fatigue behavior of a material
or component with a stress concentration from smooth bar data. The majority of fatigue
data available is in either the LCF regime or corresponds to fatigue lives below the
endurance limit, if such a limit exists at all. The first aspect of addressing notch fatigue
strength is to define the severity of the notch or stress concentration. To do this, the
elastic stress concentration factor, k
t
, is used.
∗
Here, k
t
is defined as the ratio of the peak
stress at the root of a notch to the average stress over the net cross section:
k
t
=
peak stress at notch root
average stress over the net cross section
∗
The symbol used for the elastic stress concentration factor throughout the literature is either K
t
or k
t
. The
former definition was commonly used before fracture mechanics was developed, when K was introduced as
the stress intensity factor. However, K
t

is still widely used. In this book, the term k
t
will be used wherever
possible for consistency. Note, however, that many drawings made early in the preparation of this manuscript
or taken from the literature will still show K
t
as the stress concentration factor. For this inconsistency and
possible confusion, the author expresses his sincere apologies.
213
214 Effects of Damage on HCF Properties
Values of k
t
can be found in tables or handbooks and have been obtained from closed-
form elastic solutions for simple geometries, photoelasticity experiments in the early
days, and finite element calculations in the more recent literature. The value of k
t
is a
measure of the severity of the notch or discontinuity and is used to predict fatigue lives in
many engineering applications. There are numerous cases in components with complex
geometries where k
t
cannot be defined as stated above because there is no well-defined
“net-section.” An example of such a geometry would be at the root of a notch in a dovetail
attachment region where the cross section has a continuing variable geometry. In such a
case, the net-section stress is hard to define because a section is difficult to be identified
uniquely. Similarly, a notch in a complex 3-d geometry has an undefined value of k
t
when the cross-section stresses, wherever the cross section is defined, are highly variable
in all directions. Even if k
t

is formally defined, it may have no meaning for engineering
and design purposes for HCF applications.
In Figure 5.1, three geometries are shown schematically under far-field uniform tensile
loading. In (a), a mild notch is depicted, and the stress at the notch tip is slightly
higher than the net-section stress over the width, w. Note that if the gross cross section
width =d is used (incorrectly), then a large stress concentration factor will result with
resulting misleading approximations for the fatigue strength. All calculations for k
t
are
based on linear elastic material behavior and are independent of material and depend only
on geometry. In (b) and (c), two identical notch radii are shown, but the two do not have
the same value of k
t
. In (b), the average stress is more influenced by the local notch
field than in (c) which is closer to that of an infinite body. The stress concentrations are
w
d
(a)
(c)
(b)
d
d
Figure 5.1. Three geometries illustrating the definition of k
t
.
Notch Fatigue 215
different, therefore, and this demonstrates that both the notch geometry and the overall
geometry are important in determining k
t
.

5.3. WHAT IS K
t
?
There are a number of industrial applications where accounting for damage is necessary,
even though the amount and severity of such damage is hard to quantify. In cases such
as those with FOD, discussed later in Chapter 7, a knockdown factor in the form of an
equivalent value of k
t
is often used. While the design procedure may quote k
t
= 3, for
example, as the guideline, the intent seems to be to reduce the fatigue limit by a factor
of 3 in this example, so the guideline should be k
f
=3 instead.
∗
The fatigue notch factor,
k
f
, is defined and discussed later in Section 5.4.
The ambiguous meaning of quoting a value of k
t
to represent damage is illustrated in
a simple example here. Not only is k
t
not unique in terms of the geometry it represents,
but for a given geometry the value of k
t
also depends on the loading condition. In this
example, a rectangular plate with a U-shaped notch is loaded in tension or bending,

as shown in Figure 5.2. With the nomenclature and loading as depicted in the figure,
values of k
t
are presented for several r/d ratios for tension as well as bending loading
in Figure 5.3. For a fixed value of k
t
, any of a number of values of r/d can be used to
produce that value. Further, for a fixed geometry with specified values of D/d and r/d, the
value of k
t
is different under axial load than under pure bending. Thus, the specification
of a value of k
t
to represent a damage state is rather ambiguous and, as mentioned
above, is a misuse of the term when a fatigue notch factor, k
f
, is probably what was
intended.
M
r
d/2
d/2
D
d
P
M
P
Figure 5.2. Nomenclature for plate with U-shaped notch under tension and bending.
∗
In recognition of the intent to reduce fatigue strength for FOD damage in ENSIP in preliminary design, k

t
=3
was introduced in the original document. The latest versions of ENSIP now use k
f
=3 as the guideline.