High Cycle Fatigue: A Mechanics of Materials Perspective part 38 pptx

356 Effects of Damage on HCF Properties
nothing changes during the SR process other than the removal of residual stresses. This
finding is consistent with that discussed in the previous section for impact on leading
edge geometries. Of greater significance is the observation that ballistic impacts to the
same depth as pendulum or quasi-static indentations are more severe in terms of the
resulting fatigue limit strength reduction. This is especially true for the deeper indents
corresponding to ballistic impacts at 300 m/s. In the work of Peters et al. [2], the impacts at
300 m/s produced small amounts of cracking at the crater whereas the impacts at 200 m/s
produced no observable cracks. This shows that low velocity (pendulum) or quasi-static
indentation does not produce the same amount of damage as ballistic impact for this
material under the specific impact conditions (depth of indent) described, particularly at
higher velocities.
Results for the tests in torsion are summarized in Table 7.3. Here, only ballistic impacts
were evaluated at R =0 for both AR and SR samples, and R =−1 for AR only. The SR
samples show a reduction in k
f
which is equivalent to an increase in 
FLS
. This is attributed
to the implied existence of tensile residual stresses in the failure region. The value of
k
t
in Table 7.1 for a deep notch in tension indicates that fracture would be expected at
the bottom of the notch. This is confirmed by the observed location of initiation near the
notch bottom as shown in Figure 7.29(a). On the other hand, torsion tests of a specimen
Table 7.3. Experimental values of k
f
for ballistic notches under torsion
Notch type R =0 R =−1
AR shallow 131 1.62
AR deep 200 2.00

SR shallow 101 –
SR deep 147 –
200 µm
(a) (b)
600 µm
Figure 7.29. Fractographs showing initiation sites in (a) tension, (b) torsion.
Foreign Object Damage 357
with a shallow notch would be expected to produce a failure near the surface because of
the higher value of k
t
as listed in Table 7.1. The fractograph, Figure 7.29(b), confirms
such a finding. In both cases illustrated, the specimen was subjected to SR, so only
microstructural damage or hardening could account for fracture initiating at any other
location. In one extreme case initiation occurred near the surface of a deep notch from
high velocity (312 m/s) ballistic impact. While initiation would be expected to occur at
the bottom according to k
t
analysis for tension fatigue loading, damage in this case was
sufficient in the form of local tearing to reduce the fatigue strength below that of most
of the other specimens. This resulted in fracture initiating near the location of extensive
damage at the surface.
The difference in 
FLS
between AR and SR in the tension and torsion cases for ballistic
impact seems to indicate that the tensile residual stresses are somewhat higher near the
surface than at the bottom although scatter in test results makes this observation some-
what tenuous. In both the tension and torsion cases, for ballistic impact at 300 m/s which
produces the deeper crater, the debit in fatigue strength is greater than that expected due
solely to the stress concentration factor, indicating some type of microstructural dam-
age near the failure location whether it be at the bottom, for tension tests, or near the

surface, for torsion tests. Finally, for the shallow indents produced by ballistic impact
at 200m/s, there is no apparent reduction in fatigue strength under torsion testing after
SR, even though the value of k
t
is 1.32 at the failure location. This implies that some
type of strengthening mechanism is present that retards fatigue failure, most likely delay-
ing fatigue initiation. In a study of deep rolling and other surface treatments in this
same alloy, Nalla et al. [19] identified a strengthening mechanism in the form of an
induced work hardening near-surface layer that improves the fatigue resistance of the
material.
Figure 7.30 shows high resolution SEM images of a region at the deformed surface
where a different microstructure can be seen over the first several microns from the free
surface. This region of intense plastic deformation seems to have a retarding effect on
fatigue crack initiation as deduced from the experimental data, particularly from the SR
specimens.
All of the data obtained in tension at R = 01 and torsion at R = 0 are summarized
in Figure 7.31 where hollow symbols represent the SR specimens and solid symbols are
for specimens that were not stress relieved and are designated AR. The data are plotted
as a function of k
t
for the various notches, where it should be noted that k
t
is different
for the same geometry notch when tested in tension or torsion as discussed earlier. This
figure illustrates the trend of SR specimens to have higher strengths than AR specimens,
even higher than would be expected from a k
t
analysis. For reference purposes, the line
representing 1/k
t

is shown. Ideally, a line showing theoretical values of 1/k
f
, which
would be somewhat higher, should be shown. However, for the notch geometry and
loading conditions used here, there is no model for values of k
f
.
358 Effects of Damage on HCF Properties
X-section of impact site
Specimen: 04-424, Ti-6-4
Orientation imaging microscopy (OIM) image
Image Quality (IQ) image
Backscattered electron image
(BEI)
5 µm
6
µm
Figure 7.30. SEM images of region near impacted surface.
0
0.2
0.4
0.6
0.8
1
1 1.2 1.4 1.6 1.8 2
Ballistic SR
Ballistic AR
Pendulum SR
Pendulum AR
Quasi-static SR

Quasi-static AR
1/k
t
1/k
f
k
t
Figure 7.31. Fatigue limit strength for all tension R = 01 and torsion R = 0 tests.
Figure 7.31 shows that the ballistically impacted specimens show degradation in
strength beyond that predicted simply by k
t
. The results are in agreement with those
shown in the previous section for 2.0 mm ball indents on leading edges where damage
under ballistic impact was greater than from quasi-static or pendulum indents.
The observations discussed above indicate that FOD, even under carefully controlled
laboratory conditions, involves a number of mechanisms that contribute to the fatigue
Foreign Object Damage 359
strength of a material. Normal impacts on flat plates under ballistic and slower velocity
conditions that produce craters of a given depth produce damage involving a number
of mechanisms. The fatigue strength, that is a reflection of the damage severity, is also
a function of loading conditions under axial or torsion stress states. Residual stresses
are deduced to be tensile in most cases while some type of strengthening mechanism
from the indenting exists that is not removed by stress relief annealing. The result of
plastic deformation near the surface seems to have a beneficial retardation effect on
crack initiation. For the deeper of the impacts discussed here, the impact damage from
ballistic or lower velocity conditions reduces the fatigue strength beyond that predicted
from the geometry of the resultant crater as characterized by the equivalent elastic stress
concentration factor. However, quasi-static and low velocity pendulum indents produce
different damage mechanisms than equivalent depth craters from ballistic impacts even
though the fatigue strengths may be similar. These results, combined with observations

of damage in leading edge specimens in the previous section, indicate that simulating
FOD using quasi-static or low velocity methods may not produce identical results to true
FOD in terms of either fatigue strength or damage mechanisms.
7.9.2. Other laboratory FOD simulations
This section illustrates several methods for analyzing FOD data obtained from several
specimen geometries using different techniques based primarily on concepts developed for
notches as described earlier in Chapter 5. In the HCF program of the US Air Force [8], the
fatigue properties of specimens subjected to well-controlled laboratory FOD simulations
were deduced based on the geometry of the notch produced. An extensive experimental
investigation was conducted where the fatigue limit strength of a material subjected to
real or simulated FOD was characterized. All tests were run on Ti-17 material at room
temperature using two different test specimen geometries to simulate the leading edge of
an airfoil. The axial specimen geometry, similar to the one shown earlier in Figure 7.16
(see also Appendix G), was machined with a 12-mil root radius that simulates a blunt tip
airfoil leading edge geometry.
The bending specimen geometry is shown in Figure 7.32. This specimen is tested under
4-point bending to simulate the stress gradients in an airfoil. The use of this specimen is
described in more detail in Appendix G. The edge of this specimen was machined with
7-mil and 14-mil root radii to simulate a sharp and blunt tip airfoil geometry, respectively.
The FOD to the leading edge was simulated on the axial and bending specimens with
a steel chisel indentor fired from a solenoid gun described earlier in this chapter (see also
Appendix G). The FOD indentor had a nominal root radius of 5 mil with a 60

included
angle. Several depths of penetration were obtained at a 30

impact angle using different
energy levels on the solenoid gun. At a depth of ∼10mil, the onset of shear cracks in
the material being extruded was observed. The FOD at ∼20 mil produced more extensive
360 Effects of Damage on HCF Properties

0.2
6.00
1.0
2.0
0.6
Sharp tip
0.25
0.007R
0.014R
0.032
Blunt tip
0.014R
0.014R
0.090
0.25
Figure 7.32. Bend bar simulating sharp and blunt airfoil leading edge. All dimensions in inches.
damage as expected. Numerous shear cracks were observed on the flanks of the FOD
in the extruded material, but no tears or cracks were observed at the root of the FOD
notches.
The FOD depth was determined with a line normal to the FOD as a notch depth profile.
The FOD impact angle was determined from a line normal to the FOD impact with
respect to a line tangent to the specimen leading edge face. An example of deep FOD in
a sharp tip bend specimen is given in Figure 7.33. Lines to obtain the FOD impact angle
and depth are shown schematically in the figure.
Fatigue tests on the axial specimens were predominately run at R =−1 under step
testing to 10
7
cycles. Three different FOD impact angles were evaluated for the axial tests
in the “as-FODed” and “FODed + stress relief (SR)” conditions. Tests with FOD + SR
were used for comparison to assess the role of residual stresses in the analysis. The SR

condition was obtained on the Ti-17 material in a vacuum furnace for 8 hours at 1130

F
after the FOD impact.
The Ti-17 bending tests were run under step loading to 10
6
cycles. Bending tests
were run at one nominal impact angle for both the sharp and the blunt tip leading
edge geometries. Tests were run for the geometries in the as-FODed and FODed + SR
conditions. The results are presented as k
f
as a function of geometry, impact angle, stress
relief, and FOD depth. To account for different values of R, k
f
is defined as S
equiv
for the
smooth specimen data normalized by S
equiv
at the specimen failure stress calculated for
the notched specimen.
Several methods were used to predict allowable HCF limits for specimens with FOD.
Crack initiation methods were used, where baseline HCF capability for Ti-17 was obtained
Foreign Object Damage 361
D
θ
D: FOD depth
θ: FOD angle
Figure 7.33. Fractography for deep FOD in the sharp tip geometry.
from the best-fit curve to the smooth specimen data using equivalent stress to consolidate

data obtained at different values of R. The first prediction ignored the FOD notch stress
concentration and damage, and was based solely on the calculated maximum stress at
the notch location. This approach is easy to implement, but is inaccurate for FOD tests
as shown in Figure 7.34. The term S
un-notched
refers to the local stress at the location of
the FOD, uncorrected for the notch effect or any stress gradient due to the notch. In this
and subsequent plots, S
curve
refers to the baseline smooth bar data. This result is generally
non-conservative as expected. This method of data analysis simply shows the debit in
fatigue strength at the notch location. By definition, k
f
is the reciprocal of the y-axis
value that appears to range from slightly over one to as high as five.
The next approach utilized the calculated local peak stresses with the smooth specimen
fatigue curve. For this approach, stress components are obtained from the measured notch
geometry with maximum and minimum load cases at the interpolated loads with 3D
elastic-plastic stress analysis. This approach is generally conservative (Figure 7.35) as
expected. There does not seem to be any trend with stress relieved specimens compared
to those without SR, indicating that residual stresses are neither compressive nor tensile
consistently. Rather, they appear to be scattered and probably depend on the specific
conditions at each impact site and the specific failure initiation location.
362 Effects of Damage on HCF Properties
0
0.5
1
1.5
2
2.5

3
3.5
4
0
5
10 15 20 25 30
Un-notched predictions
S
un-notched
/S
curve
FOD depth (mil)
Conservative
Axial S, as-FODed
Axial S, with SR
Bending S, as-FODed
Bending S, with SR
Figure 7.34. Prediction of the HCF capability of specimens with FOD using the unnotched stresses.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25 30
Peak local stress predictions
Axial S, as-FODed

Axial S, with SR
Bending S, as-FODed
Bending S, with SR
Peak S
equivalent
/S
curve
FOD depth (mil)
Conservative
Figure 7.35. Prediction of the HCF capability of specimens with FOD from the peak concentrated stress.
Machined notch data for the same material are shown in terms of equivalent peak
local stress as a function of fatigue life in Figure 7.36. In the plot, the RFL model (see
Chapter 2) was used to represent the smooth bar data. Data for specimens with very small
notches are shown along with those that were obtained for machined U- and V-notches.
The local stress approach with smooth specimen fatigue curves under-predicts the HCF
capability of specimens for small notches. On the other hand, the V-notch data are over-
predicted based on the local stress at the notch tip. The notch data and the smooth bar
Foreign Object Damage 363
40
50
60
70
80
90
10
3
10
4
10
5

10
6
10
7
10
8
Local stress approach (w = 0.445)
Median RFL Fit
90% RFL Fit
10% RFL Fit
Smooth bar failure
Smooth bar run-out
Small notch
V-Notch
U-Notch
S
equiv
(Ksi)
N
f
(cycles)
Figure 7.36. Smooth and notched bar fatigue results with the peak local stress approach.
data would match on this plot if k
f
=k
t
. As seen, the small notch data exhibit a size effect
that would produce higher strengths as the notch size became smaller. The V-notch data
indicate that the notch may be sharper at the tip than measured.
Local stress approaches were modified with notch fatigue stress concentration q–k

f

and feature stress (Fs) approaches. Both methods try to account for stress gradients at the
notch root by recognizing that fatigue in that location is not governed solely by the peak
stress. The first notch method evaluated is a q–k
f
approach, alternately referred to simply
as the q approach. This approach is used to predict FOD capability from the combination
of k
t
and an equation for k
f
. Note that this approach is essentially an empirical approach
using the fatigue notch factor, k
f
, applied to notch geometries. It is summarized by the
following three equations:

equivqadj
=k
f

equiv unnotched
 (7.4)
q =
k
f
−1
k
t

−1
(7.5)
q =
1

1+
a


(7.6)
where 
equiv unnotched
is calculated at the critical location without the notch present, k
t
=
notch concentrated stress/unnotched stress,  is the notch root radius, and “a” is a material
constant. Equation (7.6) is the empirical equation for k
f
, shown earlier as Equation (7.3).
k
t
can be difficult to define for 3D component geometries, but the approach is well suited
364 Effects of Damage on HCF Properties
40
50
60
70
80
90
10

3
10
4
10
5
10
6
10
7
10
8
Notch methods approach (w = 0.445)
Median RFL Fit
90% RFL Fit
10% RFL Fit
Smooth bar failure
Smooth bar run-out
Small notch with Fs
Small notch with q
Fs Adj. S
equiv
(ksi)
N
f
(cycles)
Figure 7.37. Small notch correlation with Fs and q–k
f
approaches as compared to smooth specimen fatigue
curves.
to small FOD or machined notches where the local stress can be referenced to the stresses

in the unnotched geometry. For this approach, the material constant a =18 mil was found
to best correlate small machined notch test data as shown in Figure 7.37.
The Fs approach or equivalent stressed surface area takes into account the stress
distribution about the peak stress at a notch root. This approach is described in Appendix E.
Both the q and the Fs approaches do a credible job of consolidating small notch data
with smooth bar data as shown in Figure 7.37. Since the two approaches produced almost
equivalent results, the q approach was used to consolidate the FOD test results because
it is much simpler to apply than the Fs approach described in Appendix E.
The results of the axial and bend specimen FOD tests for the various impact angles
(in the axial tests) and the different tip radii (for the bend tests), modified using the q
approach, are presented in Figures 7.38 through 7.42. In all cases, the notch geometry was
measured as described above. The predictions for a constant notch root radius of 4.4 mil
are represented with solid black lines for the different geometries and impact angles.
Significant scatter exists in the FOD test results, but calculated k
f
with the q approach
generally provides a reasonable prediction of the mean HCF behavior of specimens with
FOD for different impact angles and FOD depths. For reference purposes, the k
t
values
are also shown in the plots.
Results are summarized for tests in the “as-FODed” and “as-FODed + stress relief
(SR)” conditions in Figures 7.43 and 7.44. The predictions are best with a reduction in
test scatter when the stress relief cycle is employed after FOD to reduce residual stresses
(Figure 7.44).
Foreign Object Damage 365
1
2
3
4

5
6
7
0 5 10 15 20 25
Axial specimens (R = –1, 10° impact angle)
Pred K
t
K
t
Correlation
K
f
as FODed
K
f
with SR
Pred K
f
with q
K
t
or K
f
FOD depth (mil)
Conservative
Figure 7.38. Predicted and experimental k
f
for FOD tests in the axial specimen geometry with a 10

impact

angle.
1
2
3
4
5
6
7
Axial specimens (R = –1, 30° impact angle)
Pred K
t
K
t
Correlation
K
f
as FODed
K
f
as FODed
(R
= 0.5)
K
f
with SR
Pred K
f
with q
K
t

or K
f
0 5 10 15 20 25
FOD depth (mil)
Figure 7.39. Predicted and experimental k
f
for FOD tests in the axial specimen geometry with a 30

impact
angle.
Results with both the q and Fs approaches for the axial and bend specimens are similar
as summarized in Figures 7.45 and 7.46. For the axial specimens, the SR samples appear
to have less scatter and consolidate better with smooth bar data than those without SR.
While the authors of this report [8] propose implementation of these approaches for design
applications, it should be noted that the indentor geometry and notch conditions covered
only a limited range of FOD variables. As noted in the previous notch section, extending