196 Effects of Damage on HCF Properties
4.4.1. LCF–HCF nomenclature
Combined LCF–HCF loading has caused some confusion over the years because of
nomenclature and the differences that occur when dealing with actual usage versus
mathematical formulations involving simple linear summation concepts. Consider the
schematic of Figure 4.39 that shows the major cycles (LCF) with a hold or dwell time
in between them during which HCF cycles can occur. The problem we deal with is the
superposition of the HCF cycles on the LCF behavior. The nomenclature is that of Powell
and coworkers at University of Portsmouth, formerly Portsmouth Polytechnic.
LCF loading alone produces a stress intensity level K
major
and represents the contribu-
tion of the major throttle excursions in an engine. During dwell times, at maximum K for
the LCF cycle, a vibratory loading occurs whose total amplitude is denoted by K
minor
.
If the total contribution of the individual loading components is considered, then a linear
summation law would require that the total growth rate be the sum of K
total
+K
minor
,
not K
major
+K
minor
. This is because in the combined case, the effective amplitude of
the LCF cycles is K
total
, not K
major

stress cycles is the amplitude ratio, Q Q is defined as the ratio of the amplitude of the
minor cycles to the magnitude of the major cycles. It can also be written in terms of the
K values.
Q =
K
minor
K
major
(4.36)
Note again that the major cycle amplitude refers to K
major
as shown in Figure 4.39, not
to the value of K
total
even though the latter is used in linear damage summation. There
is no single, yet simple, way of relating the major and minor cycle ratios, other than
through the definition of Equation (4.36). The following useful expressions are easily
derived and are found frequently in the literature, particularly in the papers coming from
University of Portsmouth.
R
minor
=
2 −Q

1−R
major

2 +Q

1−R

superimposed. For the horizontal axis, K
total
or K
max
can be used to describe the block
loading. As an alternative, K
major
can be used. In the latter case, the HCF data cannot be
shown superimposed on the block loading. A similar comment can be made for the use of
K
total
. If it is desired to represent the LCF, HCF, and CCF data on the same plot, the use
of K
max
is preferable. However, if a linear superposition concept is attempted graphically,
both a vertical shift to account for n HCF cycles per LCF cycle, and a horizontal shift to
account for the different maximum values in HCF and LCF has to be used. The reader is
cautioned that there is no easy way to show LCF, HCF, and CCF data on the same (log)
plot while also demonstrating linear summation graphically.
4.4.2. Example of anomalous behavior
An illustration of the type B behavior of Figure 4.35 observed in combined LCF–HCF
testing is taken from [52] where the fracture mechanics of a nickel-based single crystal
alloy was studied. The focus was on the interaction of HCF at high stress ratio and at
198 Effects of Damage on HCF Properties
high frequency combined with LCF at low stress ratio and low frequency in combined
cycle loading. The test plan utilized previous threshold data generated at 1100

F, for
R =01 and 0.8 in the <001/010> orientation on alloy PWA 1484. After precracking,
the specimen was run at a stress ratio of 0.1 at a frequency of 10 CPM (0.167 Hz) until a

da /dN
LCF
a

o
a
f
a
i
LCF only
LCF + HCF
LCF only
σ
max
σ
max
0.1
0.1
0.8
0.1
σ
max
σ
max
σ
max
σ
max
σ
max

30
R
= 0.1 Threshold
97
K
max
(ksi in.)
Figure 4.41. LCF–HCF Interaction test results
the first test, the interaction between HCF and LCF produces an accelerated growth rate
below the HCF threshold.
To further study this unexpected crack-growth rate acceleration, five loading schemes
were devised and performed at a constant K
LCF
of 10ksi
√
in. The frequency was 10
cycles per minute (CPM) for the LCF portion and 60 Hz for the HCF portion. The loading
schemes are shown in Figure 4.42 as Case (a) through Case (f). A single sample was
again used to perform all six cases in succession with each case consuming up to 0.020 in
(0.5 mm) of specimen ligament before proceeding to the next case.
The results of the test sequence shown in Figure 4.42 are summarized in Figure 4.43.
Comparison of the various case loading blocks suggests the higher mean stress or dwell
is the significant contributor to the accelerated crack-growth behavior as opposed to the
number of HCF cycles. As shown in Figure 4.43, the application of dwell, Case (b),
increased the growth rate from the baseline without dwell, Case (a). The dwell produced
nearly the same acceleration as adding 1000R = 08 cycles, Case (c). The similarity
between Case (c) and Case (d) (1000 versus 500 HCF cycles) suggests that the sensitivity
to time-dependent behavior is inclusive of very small differences in hold times and
200 Effects of Damage on HCF Properties
= 0

10
–6
10
–5
10
–4
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
(a)
(b)
(c)
(d)
(e)
(f)
da /dN (in./cycle)
Crack length (in.)
Figure 4.43. Test plan 2 results. Legend refers to loading blocks shown in Figure 4.42.
or cyclic frequency. In fact, threshold testing done previously on that program clearly
showed a pronounced frequency effect between 20 Hz, 1 Hz and 10 CPM (0.167 Hz).
An interesting aspect of these findings is that the results indicate that there is a dwell
effect present in a temperature regime well below what has typically been called the creep
regime. The significance of this finding is that very small decreases in frequency that is
10 CPM alone versus 10 CPM with as little as an 8-second dwell at maximum load, cause
up to a 2X–3X acceleration in crack-growth rate. One possible explanation proposed for
the LCF–HCF interaction effects was oxidation at the crack tip. Tests in vacuum were
recommended.
4.4.3. Another example of anomalous behavior
Another observation of the interaction of LCF and HCF and the subsequent growth rate
behavior is that of Russ [45] who conducted studies on Ti-17, a  processed titanium
alloy. In that work, LCF cycles with R =01 were superimposed on what are referred to
LCF–HCF Interactions 201

202 Effects of Damage on HCF Properties
10
–6
10
–5
10
–4
10
–3
10
–2
68910
P
max

=

1.77

kN
P
max

=

0.86

kN
Linear summation
da

LCF–HCF Interactions 203
crack and compressive residual stresses develop ahead of the crack tip after the R =01
underloads. It should be pointed out that, consistent with FEM results by Sehitoglu et al.
[53], compressive residual stresses were observed even in the absence of closure during
the R =07 cycles. The distances over which the closure and residual stresses develop are
only a few microns, inviting speculation as to whether such phenomenology could affect
the net growth rate behavior. However, as in the previous examples of Type B behavior
as defined in Figure 4.35, the observed behavior is non-conservative when compared to
the predictions of a linear summation model.
Another observation by Russ [45] was on the threshold for crack propagation and the
differences in the growth rate behavior in the near-threshold regime. For a constant value
of K
max
= 8 MPa
√
m, Figure 4.47 shows the combined-cycle growth rate for different
numbers of HCF cycles per block (1 LCF cycle) as well as the results from a simple linear
summation of the individual contributions of LCF and HCF. For the maximum number
of HCF cycles per block, 1000, the growth rate is dominated by the HCF cycles. For
all conditions other than 10 HCF cycles per block, the experimentally measured growth
rates are higher than those predicted by the linear summation model. These differences
are approximately a factor of two or more. Equally important from a life prediction
point of view, the threshold for combined cycle loading is lower than predicted by linear
summation. For the spectrum illustrated in Figure 4.44, where the ratio of HCF to LCF
cycles is 10,000, the threshold value of K
max
for pure HCF is 727 MPa
√
m whereas,
during increasing loading for the combined cycle, the threshold at which crack growth

R
LCF
= 0.1
Figure 4.47. Fatigue-crack-growth rates for LCF–HCF spectrum of Russ [45].
204 Effects of Damage on HCF Properties
4.5. COMBINED CYCLE FATIGUE CASE STUDIES
There are other examples of combined cycle loading where HCF at stress levels below
their constant amplitude threshold appear to contribute to the combined cycle growth
rate. An example is the study by Zhou and Zwerneman [54] where the cycle block
contains small amplitude cycles with periodic overloads. Denoting the major cycles as
“overload” (ol) cycles and the other as minor cycles, the ratio K
minor
/K
ol
was chosen
as 0.3 and R
ol
= 01. A schematic of the block loading is shown in Figure 4.48. Using
ASTM A588 steel as the test material, values of the number of minor cycles per block,
n, were chosen as 0, 4, 9, 49, 99, and 999. The results, presented in terms of growth
rate per block, are shown in Figure 4.49. The number of cycles per block includes one
Time
K
n cycles
Minor
cycles
R
= 0.27
Overload
cycle

experimentally observed block growth rate is higher than predicted by a linear summation
rule. It is clear that the threshold is reduced by the overload cycles, an effect similar
to the acceleration of crack growth due to underload cycles observed by Russ [45],
described above. Further evidence of the growth due to the minor cycles was obtained
from acoustic emission (EM) monitoring. The intensity of the AE signals was observed
to increase with increasing numbers of minor cycles per block. The authors concluded
that the increase in AE activity indicated that “the minor cycles below the threshold
contribute to fatigue damage.” It certainly is possible that the threshold obtained under
constant amplitude loading is not applicable to the block-loading situation, an example of
load-history effects. Alternatively, the determination of the threshold could be incorrect,
also due to load-history effects. This latter condition is discussed in Chapter 8. In both
cases, the growth rate of the minor cycles under combined LCF–HCF block loading is
affected by the major cycles, whether they are of the overload or underload variety. In
both cases, the linear summation approach is non-conservative.
Another example of an LCF–HCF interaction is the overload study of Byrne et al.
[55] on a slightly more complicated load spectrum as shown in Figure 4.50. In this case,
overloads were superimposed on a baseline LCF–HCF block which combined a major
cycle with a number of minor cycles having the same maximum K value. In this block,
Time
K
Kol
Kss
Baseline
block
Overload
block
Figure 4.50. Schematic of block loading with superimposed overload cycles.