86 Introduction and Background
0
20
40
60
80
100
Percentage of last
loading block complete
Pure HCF With LCF cracks
Figure 3.16. Comparison of number of cycles in last loading block of step test for HCF with and without LCF
precrack.
uncracked specimen. This observation is similar to the speculation in Chapter 2 where
tests at negative R are thought to initiate cracks at stresses below the failure stress when
using step loading.
Additional data are available on the number of cycles on the last loading block in the
step-loading tests when a crack is present. The data of Figure 3.16 are supplemented
with additional data on precracked notch specimens and replotted in Figure 3.17 as
a function of crack size. While very small crack lengths did not show a very well
0 × 10
0
2 × 10
6
4 × 10
6
6 × 10
6
8 × 10
6
1 × 10
7

Figure 3.18. Number of cycles in last block for C-specimens with LCF cracks.
defined threshold, the longer crack lengths showed that specimens typically failed early
in the block, within a million cycles, indicating that the precrack eliminated some of
the initiation life. A similar observation can be made for the data in Figure 3.18 which
are obtained on a C-shaped specimen which was originally a pad in a fretting fatigue
experiment where cracks were formed on the pad in the contact region [31]. From
earlier observations, the HCF load block was reduced from 10
7
to 2 ×10
6
cycles. Here,
again, most of the failures occur within a million cycles, indicating that initiation life
in the step tests is reduced or eliminated. Of significance is the observation that in
both series of tests, uncracked specimens failed at a random number of cycles up to
10
7
, which was the loading block used in the step tests in both cases for uncracked
specimens.
Another example of the small number of cycles in the last block of step testing can
be seen in the work by Caton [32] on commercially cast aluminum alloy W319. In
this material, porosity plays the role of initial defects and, in that work, is treated as
an initial crack. Experiments were performed on three solidification conditions referring
to average secondary dendrite arm spacing (SDAS) of approximately 23 m 70m and
100 m denoted by low, medium, and high, respectively. The step-loading technique
to determine the FLS involved increments that were typically under 10% of the pre-
vious step stress and each step was carried out to 10
8
cycles or until failure occurred.
The number of cycles in the last block is plotted in Figure 3.19 for the three material
solidification conditions. With the exception of one data point, the results show that the

machine, fatigue life and run-out data [33] are shown in Figure 3.20. It appears that
there is a small degree of scatter in the data, but the fatigue limit at 10
9
cycles can be
established as approximately 1020 MPa. It remains to be shown if a similar number can
be obtained using the step-test method using fewer specimens.
10
5
950
1000
1050
1100
10
6
10
7
10
5
10
9
10
10
Failure
Run-out
Maximum stress (MPa)
Number of cycles
1800 Hz
R = 0.8
Figure 3.20. S–N data for establishing N
f

cycles. Such a value would appear to be
somewhat below 110 ksi as seen in the figure. No attempt was made to obtain a specific
10
4
10
5
10
6
10
7
10
8
90
100
110
120
130
140
150
No step data
Step data
Run-out
Step interpolated
Cycles to failure
Maximum stress (ksi)
PWA 1484
1100 F
R
= 0.1
Figure 3.21. Experimental data on PWA 1484 from step test series.

In addition to their statistical studies of number of cycles to fracture at each of a number
of stress levels, Ransom and Mehl [8] introduced a new abbreviated statistical method
known as “staircase testing.” which is still widely used today. In a series of tests, the
stress level for the next test is determined by whether the previous specimen failed or
ran unbroken for 10
7
cycles (survived). If the specimen failed, the stress on the next test
is reduced by one step. If the specimen survived, the stress on the subsequent specimen
is raised by one step, and so on. Statistical methods, described below, are then used to
determine the average endurance limit as well as the standard deviation. The results of
such tests on an SAE 4340 steel are shown in Figure 3.22 which includes the values of
the mean stress, 
0
, and the range ±2 where 95% of the values would fall.
Accelerated Test Techniques 91
40
42
44
46
48
50
52
54
56
10 20 30 40 50 60
Failure
Non-failure
Stress (ksi)
Specimen number
95%

cycles or
less) is assumed to be large enough to produce an endurance limit, but data show that
an endurance limit may not exist for most materials. Nonetheless, the FLS is a useful
number for many applications, particularly when the cycle count exceeds the number
of cycles that may be reasonably expected in the lifetime of a given application. In the
staircase method, the stress increment from one test to another is kept a constant.
∗
3.4.1. Probability plots
At the end of the up-and-down method, there are data at each stress level that was reached
which contain either failures or run-outs. Thus, for each stress level, the test data can
be used to calculate the percent of tests in which failure occurred. These data are used,
in turn, to compute a mean stress level at which 50% fail, 50% survive (run-out) and a
standard deviation about the mean. Some of the earliest data on the statistical nature of
FLSs, or endurance limits, were presented by Epremian and Mehl [9]. Based on a limited
number of staircase tests, the data shown in Figure 3.23 were obtained. They are plotted
on a linear scale as percent failures against stress for SAE 1050 steel. This type of plot
shows the cumulative distribution of percent failures for discrete values of stress level as
used in the staircase tests. If, as was done at the time, a normal distribution is assumed,
then a probability plot will produce a straight line as is illustrated for the same data in
∗
The staircase method was referred to as the “up-and-down” method in the early days of its development and
usage.
92 Introduction and Background
0
20
40
60
80
100
36 38 40 42 44 46

0
20
40
60
80
100
40 42 44 46 48 50
Percent failures
Stress (ksi)
Ransom and Mehl
(1949)
Figure 3.25. Experimental data of Ransom and Mehl [8].
44.5
45
45.5
46
46.5
47
47.5
48
48.5
.01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99
Stress (ksi)
Percent failures
s = mean
Ransom and Mehl
(1949)
Figure 3.26. Probability plot of data from Ransom and Mehl [8].
specimens were obtained (27 each). Figure 3.25 shows that a simple distribution function
would not be able to represent these data to any reasonable extent. The plot includes the

65
70
75
80
85
90
.01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99
Stress (ksi)
Percent failures
s = mean
Ti-6Al-4V
R = 0.1
Figure 3.28. Probability plot of data on Ti-6Al-4V from National HCF program.
Accelerated Test Techniques 95
3.4.2. Statistical analysis
Data from staircase tests can be analyzed statistically by assuming any type of statistical
distribution for the percent failure data. Normal and Weibull distributions are the most
commonly used, but lognormal and smallest extreme value (SEV) distributions are also
found to be useful. If the stress increments are not constant, or data are obtained at lives
beyond the defined life used for the endurance limit definition (10
7
, for example) then
statistical analysis of the data becomes more complicated and other methods have to be
introduced [34]. An example of such data can be found in the final report on the National
HCF Program [24] where staircase tests, using 10
7
as the reference, often continued
beyond that cycle count because there was no automatic shutoff at 10
7
cycles if failure

∗
Carnegie Institute of Technology.