# high-cycle fatigue of beta titanium alloys

# J. O. Peters\*^+^, G. Lütjering\*, R. K. Nalla\*\*, I. Altenberger\*\*, R. O. Ritchie\*\* {#j.-o.-peters-g.-lütjering-r.-k.-nalla-i.-altenberger-r.-o.-ritchie .Author-name}

> This study compares the high-cycle fatigue (HCF) properties of the
> high-strength *β* titanium alloys *β−*Cez and Ti-6246 (in two
> distinctly different *α+β* processed and *β* processed conditions)
> with the conventional *α+β* titanium alloy Ti-6Al-4V (in a *α+β*
> processed condition). The first part of the work addresses the
> superior fatigue-crack initiation resistance and smooth-bar HCF
> strength of *β−*Cez and Ti-6246 compared to Ti-6Al-4V. In the second
> part, the problem of foreign-object damage on jet engine fan blades is
> used as an engineering example of potential HCF applications for *β*
> titanium alloys.

## Introduction

This paper compares the high-cycle fatigue (HCF) properties of the
high-strength *β* titanium alloys *β−*Cez and Ti-6246 with the
conventional *α+β* titanium alloy Ti-6Al-4V. It is motivated by an
increasing interest in replacing *α+β* titanium alloys with *β* titanium
for highly-stressed airframe and engine components. This comparative
study includes two distinctly different *α+β* processed and *β*
processed microstructures in *β−*Cez and Ti-6246, and a *α+β* processed
microstructure in Ti-6Al-4V. In the first part, the smooth-bar
stress-life (*S-N*) fatigue behavior of *α+β* and *β* titanium alloys
was investigated, with specific emphasis on the underlying
microstructural aspects of the superior high-cycle fatigue (HCF)
strength of the *β* titanium alloys.

The latter part of the paper focuses on foreign-object damage (FOD),
which has been identified as one of the prime causes of HCF failures in
military aircraft engines (e.g., Cowles \[1\]). The objective here is to
investigate the role of FOD in affecting the initiation and early growth
of small surface fatigue cracks under HCF conditions in Ti-6246 alloy
(in both microstructures), and to compare the results with previous data
for Ti-6Al-4V. FOD was simulated using high-velocity impacts of steel
shot on the flat surface of fatigue test specimens, as used in prior
work by Peters et al. \[2\] on Ti-6Al-4V. This study indicated that FOD
could severely reduce the fatigue strength due to several factors,
including the stress concentration associated with the damage site, the
formation of FOD-induced microcracks, impact induced plasticity and
tensile residual stresses resulting from the impact. In this study, we
attempt to extend the Kitagawa-Takahashi approach, which was proposed in
\[2\] to account for the effect of FOD on HCF failures in Ti-6Al-4V, to
the higher-strength *β* titanium alloys.

## Materials and EXperimental procedures

The *β* titanium alloys, *β−*Cez
(wt.%-Ti-5.0Al-1.9Sn-4.5Zr-3.9Mo-2.2Cr-1.1Fe-0.1O, produced by CEZUS,
France, and supplied by Boehler Schmiedetechnik GmbH, Austria) and
Ti-6246 (wt.%-Ti-5.8Al-2Sn-4Zr-6Mo-0.1O, produced by Timet, USA, and
supplied by Otto Fuchs Metallwerke, Germany), were *α+β *or *β*
processed to produce, respectively, fine-grained bi-modal and larger
pancake-shaped grained microstructures. The Ti-6Al-4V alloy
(wt.%-Ti-6.3Al-4.2V-0.2Fe-0.2O) was processed to a *α+β *processed
fine-grained equiaxed microstructure and supplied by the U.S. Air Force
HCF program (Eylon \[3\]). Processing details are given below and are
listed in Table 1.

For the fine-grained bi-modal microstructures of the* β−*Cez and Ti-6246
alloys shown in Figs. 1a and 1d, respectively, the as-received *α+β*
processed bar stock material was initially cross rolled (at TUHH) in the
*α+β* phase field followed by air cooling. Recrystallization at
relatively high temperatures in the *α+β* phase field resulted in a low
volume fraction of the primary *α* phase and a *β* grain size of \~40
μm. During subsequent controlled cooling, continuous *α* layers formed
at *β* grain boundaries and *α* plates precipitated within *β* grains.
To coarsen these *α* plates and to adjust the volume fraction of *α*
plates, specimen blanks were annealed below the recrystallization
temperature (Table 1), followed by controlled cooling. Finally, blanks
of the *α+β* processed material were aged to precipitate small
incoherent secondary *α* platelets between coarse *α* plates.

For the *β−*Cez and Ti-6246 microstructures with large pancake-shaped
*β* grains, two different *β* processing procedures were used at Boehler
Schmiedetechnik (for *β−*Cez) and at Fuchs Metallwerke (for Ti-6246)
\[4,5\]. For the *β*−Cez alloy, the bar stock material was initially
heated into the *β* phase field, which resulted in a *β* grain size of
\~400 μm, taken out of the furnace and subsequently forged through the
*β* transus (890°C) into a slab. The final temperature was \~850°C.
Using a deformation degree of *ϕ* = 0.9, the relatively large equiaxed
*β* grains were flattened into pancake-shaped *β* grains (1000 x 650 x
260 μm), as shown in Fig. 1b. During air cooling after the forging
process, a more or less continuous *α* layer formed at *β* grain
boundaries and *α* plates precipitated within the *β* grains. The
subsequent heat treatments were identical to the *α+β *process in order
to achieve the same strength level, namely annealing to coarsen the
large *α* plates and to control their volume fraction, followed by aging
step to precipitate small secondary *α* platelets. The microstructure of
the *β* processed microstructure in the *β*−Cez alloy after final heat
treatment is shown in Fig. 1c. For the Ti-6246 alloy, bar material was
also heated into the *β* field, which resulted in a *β* grain size of
\~750 μm, and then deformed in the *β* field at 965°C (*β*-transus
945°C), followed by fast cooling to inhibit the recrystallization of
deformed *β* grains (1200 x 1200 x 200 μm). Again, the final annealing
and aging treatment in the *α+β* phase field was identical to that used
for the *α+β* processed bi-modal Ti-6246 alloy to achieve the same
strength level. Fig. 1e shows the coarse *α* plates within the
pancake-shaped *β* grains and the more or less continuous *α* layer at
the *β* grain boundaries of the *β* processed Ti-6246 after final heat
treatment.

The fine-grained Ti-6Al-4V material, shown in Fig. 1f, was forged in one
stroke in the *α+β* phase field (940°C) to a plate size of 400 x 150 x
20 mm. Subsequently, the forged plates were recrystallized in the *α+β*
phase field (at 930°C) to adjust the volume fraction of primary *α*
phase to \~60% (diameter \~20 μm). During subsequent fan air cooling,
*α* lamellae precipitated within the *β* grains. Finally, the plate
material was stress relieved for 2 hr at 705°C. This fine-grained
equiaxed microstructure has been termed "solution treated and overaged"
(STOA).

The tensile properties of the *β−*Cez, Ti-6246 and Ti-6Al-4V alloys are
listed in Table 2. The pancake structures were tested in the
L-direction. Further details on the tensile and fatigue testing are
given in \[2,4\], and on the FOD simulation in \[2\].

## Smooth-bar Fatigue properties

Smooth-bar stress-life (*S-N*) fatigue data (*R* = -1) for both *α+β*
and *β* processed *β−*Cez and Ti-6246 alloys, are compared with results
on Ti-6Al-4V in Fig. 2. All tests were performed on
electrolytically-polished hourglass-shaped specimens.

It can be seen that the *β−*Cez and Ti-6246 conditions show a much
higher 10^7^-cycle HCF endurance strength (*σ*~HCF~ = 575-625 MPa)
compared to Ti-6Al-4V (*σ*~HCF~ = 375 MPa). The superior HCF strength of
the *β* alloys is primarily due to their higher yield strength. HCF
strength is primarily controlled by resistance to fatigue-crack
nucleation, i.e., to first dislocation slip, although microstructure and
texture can play an important role. Crack-initiation sites in the *α+β*
processed and *β* processed *β* alloy microstructures are shown for
*β−*Cez in Fig. 3 in comparison to Ti-6Al-4V. In the Ti-6246 and *β−*Cez
alloys, fatigue cracks preferentially initiated along the *α*/*β*
interfaces of coarse *α* plates within the *β* grains, as shown in Fig.
3a (*α+β* processed) and Fig. 3b (*β* processed). These interfaces can
be identified as microstructurally-weak crack-initiation sites because
of the incompatibility of strains at the interface. (A thin volume of
*β* matrix adjacent to the *α* plates is plastically deformed by a
slip-band mechanism, as there are no hindering secondary *α* platelets
within this thin volume and the coarse *α* plates remain undeformed).
The higher HCF strength of the *α+β* processed structure can be
attributed to the smaller *β* grain size (which effectively limits the
maximum length of the *α* plates), in comparison with the larger
dimensions of the *β* grains in the *β* processed structures (even in
the thickness direction). The continuous *α*-layer at *β* grain
boundaries, which is the weakest crack-nucleation site in the *β*
alloys, apparently was very difficult to activate because the pancake
structure was tested in L-direction and in the bi-modal structure the
*β* grain-boundary length is smaller than the *α* plate length. In the
*α+β* processed Ti-6Al-4V microstructure, fatigue cracks tend to
initiate within the primary *α* phase along planar slip bands (Fig. 3c).
Whereas the lower HCF strength of the Ti-6Al-4V alloy may be primarily
controlled by the lower yield strength (*σ*~0.2~), the low
*σ*~HCF~/*σ*~0.2~ ratio of \~0.41 (Table 2) can be explained by the high
volume fraction of interconnecting primary *α* grains, which show strong
crystallographic texture and which increase the effective maximum slip
length from a single *α* grain diameter to several grain diameters.

To investigate the role of mean stress in Ti-6246 (as an example of *β*
Ti alloys), smooth-bar *S-N* fatigue tests were performed at higher load
ratios of *R* = 0.1 and 0.5 and compared to results for the *α+β*
Ti-6Al-4V alloy. Resulting *S-N* curves for these alloy conditions are
shown in Fig. 4, and indicate that increasing the load ratio, and hence
the mean stress, results in a higher limiting value of applied maximum
stress necessary to cause HCF failure; the corresponding limiting stress
amplitude is decreased. Generally, the Ti-6246 microstructures show
superior HCF strength at higher load ratios compared to the *α+β*
processed Ti-6Al-4V alloy. Whereas at load ratios of *R* = -1 and 0.1,
both Ti-6246 microstructures show effectively the same HCF strength, at
*R* = 0.5 the *β* processed condition clearly has a much higher HCF
strength than the *α+β *processed condition. Typical crack-initiation
sites at *R* = 0.5 are illustrated in Fig. 5 for both Ti-6246
microstructures. Of particular note is the observation that the
preferred sites for crack initiation changed from the interface of the
coarse *α* plates at low *R-*ratios to the interface of the *α* layers
at *β* grain boundaries at *R =* 0.5. Apparently, the higher maximum
stress at *R* = 0.5 can cause the coarse *α* plates to plastically
deform, which reduces the incompatibility strains at the *α* plate
interface. Indeed, this explanation should also apply for the *α+β*
processed bi-modal condition. The lower HCF strength at *R* = 0.5 of the
bi-modal structure, compared to that of the *β* processed structure
(Fig. 4), indicates that the next crack-nucleation site which would then
be activated is much weaker in the former condition. Because of the
fineness of the bi-modal structure, however, it is difficult to identify
an alternative crack-nucleation site unambiguously, and further work is
necessary before definitive conclusions can be made.

## EFFECT OF FOD ON Fatigue properties

To investigate FOD-induced HCF failures in *β* titanium alloys and to
compare with previous results \[2\] for Ti-6Al-4V, FOD was simulated
using high velocity (200 and 300 m/s) impacts of 3.2 mm diameter steel
spheres on the flat surface of fatigue test specimens. It was found that
both microstructures in Ti-6246 showed similar states of damage. A
typical impact damage site after a 300 m/s impact for the *α+β*
microstructure in Ti-6246 is shown in Fig. 6. Although impact craters in
Ti-6246 were \~5% smaller in size than in Ti-6Al-4V (due to higher
strength of Ti-6246), once again similar states of damage were observed.
Specifically, impact velocities greater than 200 m/s caused
circumferentially-oriented intense shear bands to form, which emanated
from the surface of the impact crater; in addition, a pronounced plastic
pile-up of material occurred at the crater rim, resulting in the
formation of multiple notches and microcracks. These small cracks, which
were \~5 to 70 μm in surface length, were found to act as the preferred
initiation sites for fatigue cracking during subsequent cycling.
Consequently, the smooth-bar *S-N* fatigue life is significantly reduced
by prior high-velocity impact damage (Fig. 7). Although the presence of
the FOD-induced microcracks represents the primary cause of the reduced
fatigue resistance, the stress concentration factor associated with the
indent (*k*~t~ \~ 1.25), the deformed microstructure beneath the indent
and the tensile residual stresses resulting from the impact are
contributing factors.

Although only seven Ti-6246 specimens were tested, two groups of
failures could be identified (Fig. 7). As noted, for 300 m/s impacts,
FOD caused the formation of microcracks at the crater rim, which served
as the initiation sites for subsequent fatigue cracking (the surface
crack lengths are indicated in Fig. 7). Fatigue-crack initiation after
slower 200 m/s impacts occurred at locations remote for the indent
crater (Fig. 8), specifically in regions where numerical computations
\[6\] have confirmed the existence of relatively high (\~350 MPa)
tensile residual stresses.[^1] These tensile stresses act to elevate the
*local* load ratio when simply superimposed on the applied fatigue
loading. For applied cyclic maximum stresses of 500 MPa, superimposing a
tensile residual stress of \~350 MPa causes an increase in the local
load ratio from 0.1 to about 0.5, assuming no relaxation; the
corresponding increase in the maximum stress is indicated by arrows in
Fig. 7. From these *S-N* results, it is clear that the simple
superposition of the applied and initial tensile residual stresses
contributes significantly to the reduction in fatigue life from FOD
through a local elevation in the *R*-ratio.

For 300 m/s impacts, all Ti-6246 and Ti-6Al-4V microstructures studied
showed comparable fatigue strengths following simulated FOD (Fig. 7),
presumably because similar-sized impact-induced microcracks were formed
and served as initiation sites for fatigue cracking. In contrast, for
200 m/s impacts where microcracks were not formed, the Ti-6246 alloy
exhibited a higher fatigue strength than the Ti-6Al-4V material
investigated; this relates to its superior intrinsic resistance to
fatigue-crack initiation, as evidenced by its higher smooth-bar HCF
strength (Fig. 4).

Based on recent work on Ti-6Al-4V \[2,7\] where a modified
Kitagawa-Takahashi approach \[8\] was proposed for the characterization
of a threshold envelope for FOD-induced HCF failures, Fig. 9 shows a
similar characterization (at *R* = 0.1) for both microstructures in
Ti-6246, with results compared to *α+β* processed Ti-6Al-4V. Failure
points are corrected for the stress concentration from the indent and
can be seen to be bounded by threshold envelopes defined at small crack
sizes in terms of smooth-bar fatigue limit (for Ti-6246: ∆*σ*~HCF~ = 630
MPa; for Ti-6Al-4V: ∆*σ*~HCF~ = 450 MPa), and at large "continuum-sized"
crack sizes in terms of the "worst-case" fatigue-crack growth
threshold.[^2]^\*^ Small crack threshold results would be preferred here
to define these threshold envelopes, e.g., in the Ti-6Al-4V material
investigated, ∆*K*~th~ values as low as 1.0-1.5 MPa√m have been measured
at 10^-10^ m/cycle \[9\], but such data in general are difficult to
collect experimentally. However, the worst-case threshold concept \[10\]
provides a reasonable and sound engineering alternative.

## conclusions 

Based on a study of high-cycle fatigue in high-strength *β* titanium
alloys *β−*Cez and Ti-6246 (in both *α+β* and *β* processed conditions),
as compared to conventional *α+β* titanium alloy Ti-6Al-4V (in an *α+β*
processed condition), the following conclusions can be drawn:

1.  The smooth-bar high-cycle fatigue strength of the *β−*Cez and
    Ti-6246 alloys at *R* = -1 (*σ*~HCF~ = 575-625 MPa) was found to be
    superior to that of the *α+β* processed Ti-6Al-4V material (*σ*~HCF~
    = 375 MPa), primarily because of the higher strength of the *β*
    titanium microstructures. The Ti-6246 microstructures also displayed
    higher HCF strengths at *R* = 0.1 and 0.5. This is reflective of an
    increased resistance to fatigue crack initiation in Ti-6246.

2.  For *β* titanium alloys, principally at a low *R-*ratio of -1,
    fine-grained *α+β* processed bi-modal microstructures were found to
    exhibit higher smooth-bar HCF strengths than coarse-grained *β*
    processed microstructures with pancake-shaped grains (tested in
    L-direction). However, this ranking was reversed at higher load
    ratios (*R =* 0.5), where the *β* processed microstructure showed
    the superior HCF properties.

3.  Both the investigated microstructures in Ti-6246 showed similar
    states of damage and similar reductions in HCF strength following
    simulated FOD. Although impact sites were \~5% smaller than in
    Ti-6Al-4V (due to the higher strength of Ti-6246), the nature of the
    damage and the resulting effect on fatigue strengths were similar in
    both alloys.

4.  The principal effect of FOD in reducing the HCF strength was to
    introduce preferential sites for the premature initiation of fatigue
    cracks. However, other factors include the interplay of (i) the
    stress concentration due to the indentation, (ii) the creation of
    microcracks at the damage site (for higher impact velocities), (iii)
    the deformed microstructure beneath the indent, and (iv) the
    presence of localized tensile residual stresses around the impact
    site.

5.  For both Ti-6246 and Ti-6Al-4V alloys, two groups of failures could
    be identified. At 300 m/s impact velocities, where FOD induced
    microcracks were formed, fatigue cracks initiated from these
    microcracks at the crater rim. However, for 200 m/s impacts, fatigue
    cracks were found to initiate away from the indent crater, in
    regions of relatively high tensile residual stresses (\~300-350
    MPa).

6.  Threshold conditions for FOD-induced HCF failures in both Ti-6246
    and Ti-6Al-4V titanium alloys were proposed based on a modified
    Kitagawa-Takahashi diagram, where the limiting conditions are
    described in terms of the smooth-bar fatigue limit at small crack
    sizes and the "worst-case" (large-crack) fatigue-crack growth
    threshold.

7.  For high-stress HCF and FOD-critical applications, such as fan and
    compressor blades, where critical crack sizes can be as small as 500
    μm or less, the use of high-strength *β *titanium alloys, such as
    Ti-6246, appears to be preferable choice to the currently used
    Ti-6Al-4V alloys. This is because of their superior fatigue-crack
    initiation resistance (in the form of a higher smooth-bar HCF
    strength) and only marginally lower fatigue-crack propagation
    resistance (in terms of a slightly lower "worst-case" large-crack
    threshold).

***ACKNOWLEDGEMENTS***

Work on Ti-6Al-4V was supported by the Air Force Office of Science and
Research, Grant No. F49620-96-1-0478, under the Multidisciplinary
University Research Initiative on "High Cycle Fatigue" to the University
of California, Berkeley. Special thanks are due to Prof. J. W.
Hutchinson, Dr. X. Chen and Dr. B. L. Boyce for helpful discussions and
providing us with their results.

## References

(1) Cowles, B.A., *Int. J. Fract.*, Vol. 80, 1996, pp. 147-63.

(2) Peters, J.O., Ritchie, R.O., *Eng. Fract. Mech.*, Vol. 67, 2000, pp.
    193-207.

(3) Eylon, D., Summary of the available information on the processing of
    the Ti-6Al-4V HCF/LCF program plates., University of Dayton Report,
    Dayton, OH, 1998.

(4) Peters, J.O., Lütjering, G., *Metall. Mater. Trans. A*, Vol. 32A,
    2001, pp. 2805-15.

(5) Sauer, C., Lütjering, G., *Mat. Process. Tech.*, Vol. 117, 2001, pp.
    311-17.

(6) Chen, X., Hutchinson, J.W., unpublished research, Harvard
    University, 2001.

(7) Peters, J.O., Boyce, B.L., Chen, X., McNaney, J.M., Hutchinson,
    J.W., Ritchie, R.O., *Eng. Fract. Mech.*, Vol. 69, 2002, in press.

(8) Kitagawa, H., Takahashi, S., *Proc. 2^nd^ Int. Conf. on Mechanical
    Behavior of Materials,* Metals Park, OH; ASM, 1976, pp. 627-31.

(9) Hines, J.A., Peters, J.O., Lütjering, G., *Titanium´99, Science and
    Technology, Proc. 9^th^ World Congress on Titanium*. Edited by
    Gorynin, I., Ushkov, S.S., Central Research Institute of Structural
    Materials (CRISM) "Prometey", St. Petersburg, Russia, 2000, pp.
    433-40

(10) Boyce, B.L., Ritchie, R.O., *Eng. Fract. Mech.*, Vol. 68, 2001, pp.
     129-47.

TABLE 1 Processing and heat treatment of the titanium alloys studied

+----------+-----------------+-------------+-----------------+--------+
| # Alloy  | # Microstructu  | #           | #               | # Coo  |
|          | re (Processing) | Deformation |  Heat Treatment | ling R |
|          |                 |             |                 | ate (° |
|          |                 |             |                 | C/min) |
+----------+-----------------+-------------+-----------------+--------+
| *β*-Cez  | Bi-modal        | 850°C,      | 1 hr 870°C, 1   | 100    |
|          |                 |             | hr 820°C, 8 hr  |        |
|          | *α+β* processed | ϕ = -1.3    | 580°C           |        |
+----------+-----------------+-------------+-----------------+--------+
| *β*-Cez  | Pancake         | 9           | 1 hr 820°C,     | 100    |
|          | *β              | 20°C→850°C, |                 |        |
|          | → α+β *deformed | ϕ = -0.7    | 8 hr 580°C      |        |
+----------+-----------------+-------------+-----------------+--------+
| #        | Bi-modal        | 905°C,      | 1 hr 935°C, 1   | 50     |
|  Ti-6246 |                 |             | hr 910°C, 8 hr  |        |
|  {#ti-62 | *α+β* processed | ϕ = -1.0    | 595°C           |        |
| 46 .Auth |                 |             |                 |        |
| or-name} |                 |             |                 |        |
+----------+-----------------+-------------+-----------------+--------+
| # T      | Pancake         | 965°C,      | 1 hr 915°C,     | 50     |
| i-6246 { |                 |             |                 |        |
| #ti-6246 | *β *deformed    | ϕ = -1.0    | 8 hr 595°C      |        |
| -1 .Auth |                 |             |                 |        |
| or-name} |                 |             |                 |        |
+----------+-----------------+-------------+-----------------+--------+
| # Ti-    | Equiaxed        | 940°C,      | 1 hr 930°C,     | 100    |
| 6Al-4V { |                 |             |                 |        |
| #ti-6al- | *α+β* processed | ϕ = -1.2    | 2 hr 705°C      |        |
| 4v .Auth |                 |             |                 |        |
| or-name} |                 |             |                 |        |
+----------+-----------------+-------------+-----------------+--------+

TABLE 2 Tensile properties, fatigue ratios, and "worst-case"
fatigue-crack growth thresholds

+----------+----------+-------+-------+-----+---------+--------------+
| Alloy    | C        | *σ*   | ###   | *   | *σ*     | worst-case   |
|          | ondition | ~0.2~ | # UTS | RA* | ~HCF~/* | ∆*K*~TH~     |
|          |          |       |       |     | σ*~0.2~ |              |
|          |          | #     | (MPa) | (%) |         | # (MPa       |
|          |          | (MPa) |       |     | (*R* =  | √m) {#mpam . |
|          |          |  {#mp |       |     | -1)     | Author-name} |
|          |          | a .Au |       |     |         |              |
|          |          | thor- |       |     |         |              |
|          |          | name} |       |     |         |              |
+----------+----------+-------+-------+-----+---------+--------------+
| *β−*Cez  | *α+β*    | 1200  | 1275  | 34  | 0.52    | \-           |
|          | proc.    |       |       |     |         |              |
+----------+----------+-------+-------+-----+---------+--------------+
| *β−*Cez  | *β*      | 1190  | 1275  | 16  | 0.48    | \-           |
|          | proc.    |       |       |     |         |              |
+----------+----------+-------+-------+-----+---------+--------------+
| Ti-6246  | *α+β*    | 1050  | 1155  | 42  | 0.55    | 1.5 (*R* =   |
|          | proc.    |       |       |     |         | 0.94)        |
+----------+----------+-------+-------+-----+---------+--------------+
| Ti-6246  | *β*      | 1055  | 1170  | 15  | 0.55    | 1.5 (*R* =   |
|          | proc.    |       |       |     |         | 0.94)        |
+----------+----------+-------+-------+-----+---------+--------------+
| T        | *α+β*    | 915   | 965   | 45  | 0.41    | 1.9 (*R* =   |
| i-6Al-4V | proc.    |       |       |     |         | 0.95)        |
+----------+----------+-------+-------+-----+---------+--------------+

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height="1.1783464566929134in"}

  ---------------------- --------------------------- ---------------------
  a\) *β−*Cez, *α+β*     b\) *β−*Cez, *β* proc.      c\) *β−*Cez, *β*
  processed              pancake grains              processed

  ---------------------- --------------------------- ---------------------

  -------------------------- --------------------- -----------------------
  d\) Ti-6246, *α+β*         e\) Ti-6246, *β*      f\) Ti-6Al-4V, *α+β*
  processed                  processed             processed

  -------------------------- --------------------- -----------------------

FIGURE 1 Microstructures of titanium alloys studied.

FIGURE 2 *S-N* curves of the *β*-Cez, Ti-6246, and Ti-6Al-4V
microstructures studied.

FIGURE 3 Fatigue crack initiation sites (*R* = -1) for a) *β*-Cez
(*α+β* processed), b) *β*-Cez (*β* processed), and c) Ti-6Al-4V (*α+β* 
processed) alloys.

![](media/image11.jpeg){width="2.3838582677165356in"
height="1.5354330708661417in"}![](media/image12.jpeg){width="1.9409448818897639in"
height="1.455511811023622in"}![](media/image13.jpeg){width="1.589763779527559in"
height="1.1783464566929134in"}![](media/image14.jpeg){width="1.589763779527559in"
height="1.1783464566929134in"}![](media/image15.wmf){width="3.216535433070866in"
height="2.116535433070866in"}![](media/image16.wmf){width="3.205511811023622in"
height="2.1251968503937007in"}![](media/image17.wmf){width="3.277165354330709in"
height="2.3661417322834644in"}

  ----------------------------------- -----------------------------------
  FIGURE 4 Smooth-bar *S-N* data of   FIGURE 5 Fatigue crack initiation
  Ti-6246 microstructures at *R* =    sites in Ti-6246 in the a) *α+β*,
  -1, 0.1, and 0.5, as compared to    b) *β* processed states.
  Ti-6Al-4V.                          

  ----------------------------------- -----------------------------------

+-----------------------------------+-----------------------------------+
| FIGURE 6 300 m/s FOD              | FIGURE 7 *S-N* data of FOD        |
|                                   | impacted and smooth-bar specimens |
| impact in Ti-6246,                | for all alloys.                   |
| *α+β *processed.                  |                                   |
+-----------------------------------+-----------------------------------+

  ---------------------------------- ------------------------------------
  FIGURE 8 Residual stress-induced   FIGURE 9 Kitagawa-Takahashi diagram
  fatigue failure of a FODed sample. for FOD-affected HCF thresholds.

  ---------------------------------- ------------------------------------

[^1]: ^\*^ This peak tensile residual stress in Ti-6246 was higher than
    the corresponding value of 300 MPa computed for Ti-6Al-4V, the
    latter value being experimentally verified using synchronous X-ray
    diffraction measurements \[7\].

[^2]: ^\*\*^ "Worst-case" ∆*K*~TH~ values can be considered as
    lower-bound large-crack thresholds; they are measured with large
    through-thickness cracks on compact-tension specimens at load ratios
    approaching unity, i.e., as *K*~max~ → *K*~Ic~, in order to minimize
    any role of crack closure \[10\]. Values are listed in Table 2.