High Cycle Fatigue: A Mechanics of Materials Perspective part 37 pot

The hollow triangles, in Figure 7.22, show the effect of removing residual stress effects from the quasi-static and pendulum indents, which indicates that the fatigue strength increases

0 0.5 1 1.5 2

Static (J) Pend KE (J) Bal KE (J)

Depth (mm)

The energy plotted in the figure represents the input kinetic energy only There was no information obtained experimentally about the residual velocity of the spheres If it is assumed that the spheres did not rebound, then the energy plotted can be considered to

be an upper bound of what went into deforming or fracturing the target At any given energy level, the figure shows that there is a lot of scatter in the permanent depth Careful examination of the individual points revealed that at the highest energy level, obtained with the 2.0 mm diameter spheres at 305 m/s impact velocity, most of the leading edge specimens were chipped or fractured and showed what has been termed loss of material (LOM) [9, 13] Such a condition is shown in the SEM photo, Figure 7.21(a) The points having such a fracture appearance lie to the right and below the trend line of the quasi-static data Some of the data points to the left had only permanent deformation

as seen in the SEM photo in Figure 7.21(b) This shows that the energy required to produce a fracture is less than that needed to produce a crater of equivalent size through

500 µ m

500 µ m

plastic deformation A similar observation was made for the data points to the right at an energy level of approximately 0.5 J which represent the 1.33 mm diameter sphere impacts

at 305 m/s Here, again, chipping and local fracture led to the formation of the crater rather than extensive plastic deformation Thus, the depth of penetration of all of the impacts can be correlated well with impact energy, as would be expected, except for cases where fracture occurred locally In that case, the depth of penetration is generally higher and represents the worst case scenario regarding fatigue strength debit as noted also in previous research [9, 13] Of significance is the observation that the two types of permanent distortion, LOM and crater formation, occur under nominally identical impact conditions In these cases, the differences were in the location of the actual impact with respect to the targeted point exactly in the middle of the airfoil leading edge

As an overall observation, for the range of conditions covered in [12], quasi-static and pendulum indenting used to produce craters of the same depth as the ballistic impacts resulted in plastic deformation in all cases While the depth of penetration was correlated

with the input energy, this quantity cannot be predicted a priori because the unloading

load-displacement curve or rebound velocity is not known for the quasi-static or pendulum indenting, respectively These types of FOD simulations that produce plastic deformation can over-predict the fatigue strength for the same depth of penetration compared to the ballistic case where LOM occurs

For different impact conditions that produce craters, the reduction of fatigue strength can

fatigue strength to that of the notched bar based on net cross-sectional area, as indicated

in earlier in the discussion of notches, Section 5.4,

kf=unnotched fatigue limit stress

In [12], predicted values of kf were calculated based on the elastic stress concentration factor, kt, through an empirical formula that fits experimental data The notch was assumed

to have a radius equal to the impacting sphere or the static indentor, an assumption that was verified in prior investigations on the same material [9, 13, 14] Finite element analyses of ideal 30notches were used to determine ktfor several different combinations

of radius and depth These values were found to be close to those calculated for a circular notch of depth, d, and radius, r, from Peterson [15],

 d

(7.2)

The fatigue notch factor used was that given by Peterson [16] in the form,

kf= 1 + kt− 1

1+ap

r

(7.3)

same material [17]

The results for the FLS, normalized with respect to the smooth bar fatigue strength

measured notch depth Most of the data in this investigation were obtained for impacts with a ball diameter of 1.33 mm and quasi-static indents with the same diameter chisel Shown also is a reference line corresponding to the fatigue notch factor as calculated for a notch radius of 0.67 mm from Equation (7.3) In the nomenclature used, hollow symbols refer to stress-relieved (SR) specimens, whereas solid symbols are for specimens tested as-received (AR) after impacting or indenting Data obtained at three different ballistic velocities (having significantly different kinetic energies) are noted, as well as results for the quasi-static and pendulum indents of similar impact depths

(Since the fatigue strength is normalized, the prediction appears as a line calculated as

FOD depth (mm)

(inches)

1.33 mm Dia.

quasi-static (AR) quasi-static (SR) pendulum (AR) pendulum (SR) machined notch 305,67,518 m/s (SR)

1/Kf

σsmooth = 568 MPa @ R = 0.1

σFOD

σsmooth

0.0 0.0

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

1.0

1.0

1/kf.) It should be noted that this line does not take into consideration any microstructural damage imparted by the impacts or any residual stresses produced during the impacts The data of the as-impacted (AR) specimens follow essentially the same trend, which is slightly lower than the prediction regardless of the impacting technique By comparison,

validity of the kf formulation for these notch geometries

The hollow triangles, in Figure 7.22, show the effect of removing residual stress effects from the quasi-static and pendulum indents, which indicates that the fatigue strength increases due to stress relief This would imply that the indenting procedures imparted

analysis can be partially explained by observing the geometry of the non-ballistic notch after indentation as compared to a machined notch, as shown in Figure 7.23 The indent produced by quasi-static methods produces substantial bulging, plastic deformation, and distortion of the notch, as shown in Figure 7.23(b) The net effect seems to be a shielding effect on the notch and invalidates the ktapproximation because of the distorted geometry

By comparison, the fatigue strength of specimens with machined notches of depths of

Another possible contribution to the apparent strengthening effect on the SR samples

is the strain hardening that takes place during the deformation process when the crater

is formed Both the quasi-static and pendulum impacts show an apparent strengthening effect when stress relieved, but the net effect produces fatigue strengths above that predicted solely by the geometry In addition to the difference in deformation pattern discussed above, it is thought that some strengthening in fatigue from strain hardening in compression during the impact event may have occurred

(a)

(b)

∗

The machined notches were not stress relieved because low stress grinding (LSG) was used in machining the notches It was assumed that LSG produced little or no residual stress and that final polishing reduced any

Stress relief of the specimens that were ballistically impacted, on the other hand, produced little or no change in fatigue strength as shown by the hollow circles and crosses in Figure 7.22 Here it would appear that the ballistic impacting produces minimal residual stresses and perhaps beneficial compressive stresses dominate (A downward arrow in a data point indicates that it failed during the first loading block of the step test procedure.) This observation of apparent compressive residual stresses is consistent with observations from numerical simulations of spherical ball impacts on this leading edge geometry, which show tendencies for compressive stresses to develop near the exit side

of the crater for an ideal impact [8]

Data for the impacts with the 2.0 mm diameter spheres/indentor is shown in Figure 7.24

over-predict the FLSs, particularly when the notch depth approaches 1 mm Here, for the ballistic impacts, the stress relief procedure has little or no effect on the fatigue strength, indicating the absence of significant residual stresses in the vicinity of the damage site The quasi-static indented specimens, on the other hand, exhibit the same type of behavior

as seen in the 1.33 mm diameter specimens described above Again, this may be attributed

to some combination of the deformation pattern observed (Figure 7.23) and possible strain-hardening effects

Data from the impacts using the 0.5 mm diameter spheres, Figure 7.25, show that these smaller diameter spheres produce FLSs which are higher in the stress relieved case than

0.0 0.0 0.2 0.4 0.6 0.8

1.0

0.01

FOD depth (mm)

open symbols: stress-relieved

(inches)

1/Kf

2.0 mm Dia.

quasi-static pendulum

σFOD

σsmooth

FOD depth (mm) 0.0

0.0

0.2 0.2

0.4 0.4

0.6 0.6

0.8

0.8 1.0

1.0

σFOD

σsmooth

0.00

(inches)

0.5 mm Dia.

quasi-static (AR) pendulum (AR) pendulum (SR)

1/kf

0.04

for those without SR This would tend to indicate that some residual tensile stresses were present in the impacted specimens, the opposite of which was observed for the 1.33 mm diameter sphere impacts (Figure 7.22) Note that for the 0.5 mm case, the depths of craters are less than 0.1 mm whereas for the 1.33 mm case, the depths are typically five times as large

One reason for the lower strength of ballistic damage after stress relief is attributable

to the physical appearance of the damage sites For the impacts with the larger ballistic damage sites, most of the leading edge specimens were chipped or fractured and exhibited what has been termed LOM, discussed earlier (see Figure 7.21a) Some of the specimen impacts had only permanent deformation (dents) (see Figure 7.21b)

A general observation that can be made is that residual stresses that are produced by ballistic impact depend on the size and velocity of the impacting sphere These stresses may be different in magnitude and type (tension versus compression) depending on their appearance when going from ballistic impacts to quasi-static indentation One significant observation is that the FLS of a ballistically impacted leading edge specimen can be reduced by as much as 70–80% in the specimens that have the largest amount of damage While these were the most severe impact conditions in the reported experiments, they

sand particles that have caused FOD in gas turbine engines in both military and civilian aircraft

We can conclude that the fatigue limit strength of a ballistically impacted leading edge specimen is influenced not only by the geometry of the notch produced by the impact, but by the residual stress field and mechanisms producing the notch For notches with lesser amounts of damage, the impact site was predominately plastic deformation that resulted in a notch fatigue strength that was reasonably predicted by conventional notch analysis using kf Some strengthening effect, observed after stress relief annealing, was attributed to possible strain hardening Residual stresses, which tend to alter these strengths somewhat, are very sensitive to the nature of the impact and can be either tensile

or compressive and very hard to predict For larger ballistic damage levels, the notch crater exhibited damage such as chipping, local failure, and LOM In these cases, the

absorbed was lower than for a similar geometry notch caused by plastic deformation The fatigue strength was degraded most when LOM occurred The types of FOD simulations that provide low impact velocities (pendulum) or are quasi-static, where only plastic deformation occurs, can slightly over-predict the fatigue strength for the same depth of penetration when compared to the ballistic case where LOM occurs While some of the quasi-static and pendulum impacts produced fatigue strengths that were similar to those from ballistic impacts of the same depths, the mechanisms producing the altered strengths were not always the same in the ballistic case compared to the simulated indents at much lower velocities Of greatest concern, however, is the scatter in fatigue strengths that is attributed to the sensitivity of deformation and damage to the exact location of impact in

a leading-edge geometry

7.9.1 Simulations using a flat plate

While it is both common and desirable to study FOD and the resulting fatigue strength in actual components, the extreme difficulty and variability in results led to the use of simple leading edge geometries under axial fatigue loading to better understand the problem While the use of axial loading as opposed to axial and bending loads in a real component simplified the problem, and complexities such as twist and camber in real blades were avoided, variability in results due to extreme sensitivity to the impact conditions has made

a thorough understanding of the FOD event rather difficult as noted above Noting this large amount of scatter in evaluating FOD in leading edge geometries, simpler geometries were evaluated by Nicholas et al [18] They followed the procedure of Peters et al [2] who investigated the ballistic impact damage on the same Ti-6Al-4V alloy in a flat plate geometry under normal impact and tensile fatigue loading However, they extended the study to a wider range of test conditions involving both axial and torsional loading on rectangular specimens as well as introducing extensive use of stress relief (SR) annealing

to separate out the role of residual stresses as was done in the LE studies described above The conditions chosen covered those found to impart deformation only at low velocities as well as microcracking under higher velocity ballistic impact [2] In addition, low velocity pendulum impacts and quasi-static indenting were used Because of the simple impact geometry of a flat plate impacted normally, as opposed to impacting a leading edge at a non-zero angle of incidence, the scatter in material behavior was reduced somewhat The procedures that were followed are close to those described in the previous section for leading edge impact studies where ballistic impact, pendulum impact, and quasi-static indentation were used to produce damage of similar depths For the ballistic impacts, steel spheres, 3.18 mm in diameter, were impacted normally at velocities of either 200

or 300 m/s onto 3.18 mm thick flat plates Half of the specimens were stress relief (SR) annealed in order to eliminate any residual stresses produced during the impact event For either the quasi-static ball indentation or the low velocity pendulum, the ball used for producing the indent was of the same diameter and material as that used in the ballistic impacts The depth of indent for the quasi-static and pendulum indents was chosen to be the same as the average value for the ballistic impacts, 0.22 and 0.41 mm for the 200 and

300 m/s impacts, respectively

All of the plate specimens were fatigue tested in tension or torsion using the step-loading technique to determine the FLS, FLS, corresponding to a life of 106cycles The torsion tests were added to axial testing previously performed on airfoil samples in order

to produce different failure locations where residual stresses might be different

For the simple plate geometry with an indent, the stress distribution and a modified elastic stress concentration factor were determined for the two notch depths using FEM

In the analysis it was assumed that the notch had a spherical surface with a radius of one-half of the impacting sphere whose diameter was 3.18 mm A schematic of the cross section at the indent or notch is shown in Figure 7.26

Results for the axial stresses on the notched specimen due to an average axial stress

of 100 MPa or a torque that produces 100 MPa at the surface were calculated and are presented in Figure 7.27 for the deep notch as a function of the y-axis location, denoted

y

s

z

r

d

s

A

B C

100 120 140 160 180 200

Tension Torsion

y-coordinate from edge of plate (mm)

Edge of notch

Large notch

1 1.2 1.4 1.6 1.8 2

Axial Torsion

kt

Edge of notch

Small notch

in Figure 7.26 The stresses for the shallow notch are shown in Figure 7.28 The center of

the edge of notch using a dotted line in the figures

factor: the actual stress at a location divided by the stress at that same location if the notch were not present For axial loading, this is no problem since the smooth bar stresses are uniform across the cross section However, for bending or torsion where the stresses

in a smooth bar vary linearly through the cross section, the value of the smooth bar stress decreases from the surface towards the notch bottom A better measure of the notch effect

is to use an effective stress concentration factor, denoted by kt, defined as the local stress

in the notched specimen divided by the maximum stress at the surface in the smooth bar The value of ktis then simply the value of the stress, shown in Figure 7.27 for the deep notch or in Figure 7.28 for the shallow notch, divided by the reference far field stress,

100 MPa in this case Values for the effective stress concentration factor are summarized

in Table 7.1 For most cases, the locations for the maximum value of the local stress concentration are either at A along the surface at the edge of the notch or at B at the root

of the notch as shown in Figure 7.26 However, for the deep notch under torsion, the maximum value of ktoccurs at point C at the interior of the notch as seen in Figure 7.27

It is slightly higher than the value at point A on the surface for the torsion case

as-received material (material as tested without stress relief after the indents were put in) while “SR” denotes samples that were stress relieved after indentation Three types of indentation are represented in this database: ballistic, pendulum, and quasi-static, all to the same depth The results of the tensile fatigue tests show that SR improved the fatigue strength in all cases, although the improvement was not very large This implies that some tensile residual stresses were present after all three indentation procedures, since

∗@y= 425 mm, ∗∗@y= 400 mm