Fatigue properties of titanium alloys disclosed in NIMS fatigue data sheets

ABSTRACT National Institute for Materials Science fatigue data sheets disclose fatigue data on Ti-6Al-4 V alloys, pure titanium, and Ti-6Al-4 V ELI alloys. The fatigue tests applied were low-cycle, high-cycle and gigacycle types. Low-cycle tests revealed that fatigue lives evaluated by strain amplitudes were roughly the same between the alloys despite differences in tensile strength. Ti-6Al-4 V alloys revealed cyclic softening, while pure titanium revealed cyclic hardening. The cyclic yield stress of the titanium alloys was higher than that of conventional steels. In contrast to the results for pure titanium, the high-cycle fatigue tests on Ti-6Al-4 V alloys revealed internal fractures without conventional fatigue limits. Internal fractures were more frequent at high-stress ratios than at R = –1. Internal fractures from interiors created fish-eye patterns on the fracture surfaces, whereas no fish-eye patterns were observed in internal fractures from sub-surfaces. The internal crack initiation sites revealed clear facets at high-stress ratios without inclusions. The gigacycle fatigue tests on Ti-6Al-4 V alloys revealed the results of ultrasonic fatigue testing at 20 kHz to be equivalent to those for conventional fatigue testing at 120 Hz in cases where internal fractures occurred. Fatigue failures at over 109 cycles were very rare, suggesting the presence of new fatigue limits in the gigacycle region. Degradation of gigacycle fatigue strength was very minor at R = –1, while at high-stress ratios degradation was marked, with the modified Goodman line entering the danger zone, revealing this behaviour to be the main shortcoming of Ti-6Al-4 V alloys. GRAPHICAL ABSTRACT IMPACT STATEMENT This paper analyzed massive data disclosed in NIMS fatigue data sheets and disclose low-cycle, high-cycle and gigacycle fatigue properties of titanium alloys.


Introduction
NIMS fatigue data sheets [1] disclose fatigue properties of metallic materials made in Japan.All the fatigue tests were conducted by NIMS and its predecessor (NRIM: National Research Institute for Metals), meaning that the fatigue test conditions were standardized down to the smallest detail.The NIMS fatigue data sheets have a history of over 40 years and now comprise a huge database.The major materials tested include steels, aluminium alloys, and titanium alloys.This review paper focuses on the titanium alloys in the database.
Table 1 shows a list of the fatigue data sheets on titanium alloys [2][3][4][5][6][7][8][9][10][11][12], covering Ti-6Al-4 V alloys and pure titanium (JIS Class 2).The Ti-6Al-4 V alloys include conventional versions and ELI (Extra Low Interstitial) versions.Both versions included two types of materials with different tensile strength levels of 900 and 1100 MPa.These materials were selected due to their extensive range of applications in which high fatigue performance is frequently required, particularly with Ti-6Al-4 V alloys.The fatigue data sheets disclose fatigue properties at room temperature in air for these titanium alloys.
Low and high-cycle fatigue tests were conducted on these materials, with the low-cycle fatigue tests conducted under strain-controlled conditions.The results disclose not only their fatigue lives but also their cyclic softening or hardening behaviours.The high-cycle fatigue tests were conducted under load-controlled conditions.They were conducted only under uniaxial stress conditions.Rotating bending and reversed torsion fatigue tests were not conducted.Gigacycle fatigue tests were also carried out on the Ti-6Al-4 V alloys under high-stress ratio conditions to clarify stress ratio effects.
The gigacycle fatigue tests were conducted by ultrasonic fatigue testing [13][14][15][16][17] at 20 kHz.Although the conventional low and high-cycle fatigue tests conformed to standards that included JIS, ASTM, and ISO, there was at the time no standard for ultrasonic fatigue testing.However, ultrasonic fatigue testing methods have recently been standardized by the Japan Welding Engineering Society (JWES) as WES 1112 [18,19], to which our ultrasonic fatigue tests fully conformed.A point to be noted is frequency effects, which are very small in high-strength metallic materials that reveal internal fractures [20].The frequency effects are summarized in the 'Explanation' attached to WES 1112.
These fatigue data are very informative in that they clarify the characteristics of the fatigue properties of the titanium alloys in question.Although some of their unique features have already been published in regular papers [21,22], this review paper summarizes their overall fatigue properties, arrived at by analysing whole data sets.These analysis results have already been disclosed in NIMS Structural Materials Data Sheets Technical Document No. 20 [23], which is in Japanese.This paper is a re-edited and translated version for publication of the analysis results in an open-access journal.The review papers have already been published for highstrength steels [20] and aluminum alloys [24].

Materials
Table 2 shows the chemical compositions of the tested alloys.The materials were hot-rolled round bars with diameters of 20-30 mm and were sampled between  1998 and 2003.Table 3 shows the heat treatment conditions.The 900-MPa Ti-6Al-4 V alloys were aircooled after the solution treatment, whereas the 1100-MPa alloys were water-quenched.The aging conditions were also different between the 900-and 1100-MPa-class.The pure titanium was normalized only.Table 4 shows their mechanical properties.The Ti-6Al-4 V alloys demonstrate high strength and low ductility.The 0.2% proof stress is close to the tensile strength, so the yield ratio is very high.An examination of the differences between heats shows heats C to have slightly lower strengths in all the alloys.The Al content of heats C are slightly lower, as seen in Table 2, so the differences in the strengths are attributable to the differences in Al content.In contrast, pure titanium shows low strength and high ductility.The 0.2% proof stress is much lower than the tensile strength, so the yield ratio is low.An examination of the differences between heats shows heat C to have slightly higher strength.
Figures 1-5 show microstructures.Those of the Ti-6Al-4 V alloys are of an α-β type.The microstructures of the 900-MPa-class are different from those of the 1100-MPa-class, whereas the differences are small between the conventional and the ELI versions.The β phases are different between the 900-and 1100-MPa -class since the 1100-MPa-classes are water quenched.An examination of the differences between heats shows the grain sizes of heats B to be slightly larger in all the Ti-6Al-4 V alloys.The microstructure of the pure titanium is a single-phase α type.A comparison of the differences between heats shows the grain sizes of heat C to be slightly larger.

Fatigue testing
The fatigue tests conducted were low-cycle, high-cycle and gigacycle types.The low-cycle fatigue tests under strain-controlled conditions included not only constant-strain amplitude tests to determine fatigue lives but also incremental step tests [25] to clarify cyclic stress-strain curves.The constant-strain amplitude tests used a symmetrical triangular waveform with a strain rate of 5 × 10 −3 s −1 .Figure 6 shows the waveform used in the incremental step tests.The strain rate was 5 × 10 −3 s −1 , with one block consisting of 25 cycles.Figure 7(a) shows a specimen used in the straincontrolled tests.The specimens with a diameter of 8 mm had a straight section measuring 16 mm.The surface of the test section was finished by axial direction polishing using 600-grit papers.The strain in the axial direction was controlled by using an extensometer with a gauge length of 8 mm.Servo-hydraulic testing machines were employed.
The high-cycle fatigue tests under load-controlled conditions were an axial loading type that used electromagnetic resonance fatigue testing machines at 120 Hz up to 10 8 cycles.With the pure titanium samples, however, servo-hydraulic fatigue testing machines were additionally used, since some specimens revealed temperature increases at 120 Hz.The servo hydraulic fatigue tests were conducted at 5-20 Hz up to 10 7 cycles.Stress ratios were R = −1, 0, 0.3 and σ max = σ y .The σ max = σ y tests kept the maximal stress σ max at the yield stress σ y rather than fixing the stress ratio.The σ max = σ y test condition corresponds to the highest stress ratio condition, assuming that the materials are used in an elastic region.The 0.2% proof stress was then applied to the yield stress. Figure 7(b) shows a specimen used in these tests.
The diameter was 6 mm, and the test section was finished by axial-direction polishing using 600-grit papers.
The gigacycle fatigue tests using the ultrasonic fatigue testing were conducted up to 10 10 cycles at 20 kHz.The gigacycle fatigue tests were applied only to the Ti-6Al-4 V alloys.The stress ratios were R = −1, 0, 0.3 and σ max = σ y .The testing machine used was a Shimadzu USF2000, which has a load frame for superimposing tensile mean stress.An aircooling system was built into this system to prevent the specimens from overheating.The air-cooling system consisted of a vortex tube-type cooler and a 5.5 kW type compressor that is sufficiently powerful to counteract virtually any temperature increase in the specimens, even during continuous tests at 20 kHz.For this reason, intermittent tests [15,16] were not applied.Figure 7(c) illustrates the specimen used in ultrasonic fatigue testing.The diameter was 3 mm, and the test section was finished by axial direction polishing using 600-grit papers.

Fatigue life
Figure 8 shows the results of the constant-strain amplitude tests in which fatigue lives are plotted against total strain amplitude.It is clear that there are only minor differences in the fatigue lives of the alloys despite their dissimilar tensile strengths, in contrast to high-cycle fatigue test results shown later, e.g. Figure 19.
Figure 9 shows the relationships between plastic strain and fatigue lives, and between elastic strain and fatigue lives.The crossing points between the plastic and elastic strain curves are at around 10 2 − 10 3 cycles for the Ti-6Al-4 V alloys, in spite of being around 10 3 − 10 4 cycles for pure titanium.This difference is attributable to the ductility of the materials.The crossing points indicate the low-cycle fatigue region to which the Coffin -Manson rule applies.When the ductility is high, as in pure titanium, the low-cycle fatigue region is wide, whereas it is narrow for less ductile materials such as Ti-6Al-4 V alloys.
These patterns in low-cycle fatigue properties are not very different from those of steel.It is generally understood that constant-strain amplitude test results show minor differences between steel types, and that the low-cycle fatigue region to which the Coffin -Manson rule applies is a function of the ductility of the steels.In short, the low-cycle fatigue lives of these titanium alloys are similar to those of steels.

Cyclic stress-strain curves
Figure 10 shows cyclic stress-strain curves compared with the monotonic stress-strain curves of tensile tests.In this figure, the results of incremental step and constant-strain amplitude tests are plotted together, and show good agreements, meaning that the effect of the incremental step on the curves is small.The Ti-6Al-4 V alloys reveal a small degree of cyclic softening.In contrast, the pure titanium reveals evident cyclic hardening.
Figure 11 shows cyclic yield stress σ yc plotted against tensile strength σ B .The relationship between the cyclic yield stress and the tensile strength is close to σ yc = 0.61σ B in most of the steels, while that of the titanium alloy is around σ yc = 0.80σ B .On the other hand, some steels such as SUS630 (precipitation-hardened stainless steel, 17-4PH) reveal a relationship of σ yc = 0.90σ B .Consequently, the ratio of the cycle yield stress to the tensile strength is higher in the titanium alloys than in conventional steels, but lower than in precipitation-hardened stainless steels.
The cyclic softening and hardening patterns are similar to those of steels, i.e. hard materials show cyclic softening and soft materials show cyclic hardening.On the other hand, the cycle yield stresses of the titanium alloys revealed marked differences to those of steels.Figure 12(a) is the result for the 900-MPa-class Ti-6Al-4 V alloys.Heats A and B reveal internal fractures in the long-life region above 10 6 cycles.Internal fractures occur even above 10 7 cycles, meaning that conventional fatigue limits are not confirmed.In contrast, heat C reveals no internal fractures and clearly shows a fatigue limit.Despite a lack of internal fracturing, the fatigue strength of heat C is equivalent to that of the others, since the tensile strength of heat C is lower than that of the others.The 1100-MPa-class Ti-6Al-4 V alloys shown in Figure 12(b) reveal higher fatigue strengths than the 900-MPa-class, whereas the trends are very similar, i.e. heats A and B reveal internal fractures without conventional fatigue limits in contrast to heat C.

Fatigue life
Figure 12(c) shows the results for pure titanium.The heat C specimen reveals higher fatigue strengths than the others, since the tensile strength of heat C is higher.No internal fractures are observed in the pure titanium.
Fatigue limits are very clear in heats A and B but not in heat C. One reason for the unclear fatigue limit of heat C is that the fatigue tests were terminated at 10 7 cycles.The heat C specimen showed a temperature increase at 120 Hz, so the maximum test frequency was decreased to 20 Hz, a frequency too low to allow fatigue tests to be conducted up to 10 8 cycles.Moreover, several of heat C specimens failed at over 10 6 cycles.It is thus not known if heat C has a fatigue limit.
Figure 12(d,e) are the results for Ti-6Al-4 V ELI alloys.The fatigue limits are not clear, since many specimens fail at around 10 7 cycles.Despite these unknown fatigue limits, internal fractures are rare, i.e. most specimens ended via surface fractures.The fatigue strengths of heats B are slightly lower than those of heats C, whereas the tensile strength of heats B was higher.These differences in fatigue strengths are likely attributable to differences in grain size, i.e. the large grain sizes of heat B appear to decrease their fatigue strengths.Grain size effects will be discussed in Section 5, since they are more visible in gigacycle fatigue test results.
Figure 13 shows high-cycle fatigue test results at high-stress ratios, which were conducted only for 900-MPa-class Ti-6Al-4 V alloys.The Ti-6Al-4 V ELI alloys were newly sampled because of a shortage of test materials.Details of the newly sampled materials can be found in Fatigue Data Sheet No. 115 [12].The Ti-6Al-4 V alloys also reveal internal fractures at highstress ratios.The internal fractures are more frequent at high-stress ratios than at R = −1.Even heats C of the Ti-6Al-4 V alloy, which reveal no internal fractures at R = −1, show internal fractures at the high stress ratios.As a result of the internal fractures, fatigue limits are not confirmed in all materials at the high stress ratios.The fracture surfaces reveal typical transgranular fatigue fracture morphologies, which are characteristic fatigue fracture surfaces.When the crack initiation sites are located in the interiors, it is very easy to identify the internal fractures, as seen in Figure 15(b).In these cases, fish-eye patterns are frequently identifiable on a macroscopic scale.For sub-surface crack initiations, identification of internal fractures is, however, not always easy.The crack initiation sites of internal fractures are greater than 100 μm in size, and the sub-surface crack initiation sites are located very near the surfaces.No fish-eye pattern is thus observed for sub-surface crack initiations.The internal crack initiation sites occasionally reveal facets, as indicated by the arrows in Figure 15(c), whereas these facets are not identifiable in most cases at R = −1.Figure 16 shows the internal fracture surfaces at high stress ratios.On these fracture surfaces, clear facets are observed at the internal crack initiation sites.The internal crack initiation sites are not a single facet but a cluster, with the sizes of these facets close to the grain sizes.Accordingly, the facet sizes are larger in coarse-grain materials such as heat B of Ti-6Al-4 V ELI in Figure 16(b).The reason why the facets are unclear at R = −1 is not known, but one possibility is damage by compressive stress, as suggested by Figure 15(b).Another possibility is that the crack initiation mechanisms are different between at R = −1 and at high stress ratios.Note that no inclusions were observed at the internal crack initiation sites of the Ti-6Al-4 V alloys, unlike those of high-strength steels [20].

Fracture surfaces
Figure 17 shows a cross-sectional view of an internally fractured specimen beneath the facet [22].This specimen was cut along a cross section that divided the facet to be able to observe the microstructure where the facet had formed.It is confirmed that the facet is formed in the α-phase in an inclined direction, suggesting the facets to be shear-type fatigue cracks initiated in the α-phase.Moreover, there is a subcrack that is formed in the α-phase in an inclined direction.This sub-crack also indicates the existence of the shear-type fatigue cracks initiated in the α-phase.

Data analysis
Table 5 shows the numerical values of the high-cycle fatigue strengths that are used in these data analyses.The fatigue strengths are average values between the maximum stress amplitude at which no specimen is fractured, and those just above it.Figure 18 shows comparisons of the fatigue strengths between titanium alloys and steels at R = −1.The fatigue strengths of the titanium alloys reveal linear relationships with tensile strength and cyclic yield stress.The relationship of fatigue strength σ W with tensile strength σ B is σ W = 0.53σ B for the quenched and tempered steels and σ W = 0.39σ B for the normalized steels and stainless steels.In this case, the fatigue strengths of titanium alloys are close to those of the quenched and tempered steels, i.e. σ W = 0.53σ B .On the other hand, the relationships with cyclic yield stress σ yc are σ W = 0.87σ yc for the quenched and tempered steels and σ W = 0.69σ yc for the normalized steels and stainless steels; and in this case, the titanium alloys are close to the latter, i.e. σ W = 0.69σ yc .
Figure 19 shows S-N curves connecting low-and high-cycle fatigue data at R = −1.The stress amplitudes of the low-cycle fatigue tests are evaluated at half of the fatigue life.The high-cycle fatigue data form a smooth continuum with the low-cycle fatigue data.The Ti-6Al-4 V alloys reveal much higher fatigue strength than that of pure titanium, since the tensile strength and cyclic yield stress of the Ti-6Al-4 V alloys are higher than those of pure titanium.The scattering among the Ti-6Al-4 V alloys is also dependent on differences in tensile strength and cyclic yield stress.
Figure 20 shows S-N curves normalized by tensile strength and by cyclic yield stress at R = −1.The difference between the Ti-6Al-4 V alloys and pure titanium is dramatically reduced by these normalizing processes.The scattering is reduced more by tensile strength than by cyclic yield stress, suggesting that tensile strength has the greater effect on fatigue strength.This also indicates the comparison in Figure 18(a) to be more appropriate than that in Figure 18(b), i.e. evaluation using tensile strength is more appropriate than that using cyclic yield stress.According to this view, the fatigue strength of   titanium alloys is close to that of quenched and tempered steels, which is higher than that of normalized steel and stainless steel.In short, the titanium alloys show outstanding high-cycle fatigue performance.

Fatigue life
Figure 21 shows gigacycle fatigue test results for the 900-MPa-class Ti-6Al-4 V alloys.In most cases, the results at 20 kHz show good agreement with those at 120 Hz.The exception is for heat C at R = −1, in which the 20 kHz tests show longer fatigue lives than at 120 Hz.In this case, no internal fracturing occurs, meaning that the frequency effects are visible as surface fractures.In other words, the frequency effects are negligible for internal fractures.Similar trends are reported in steels [18], pointing out that the presence or absence of the frequency effects may be related to the crack initiation mechanism.In short, slip bands are formed prior to the surface crack initiation, while the slip bands are not formed in case of the internal crack initiation.Heat C at R = −1 shows only surface   fractures and reveals a clear fatigue limit at 10 7 cycles, while internal fractures occur at high-stress ratios and the conventional fatigue limit disappears.The reason why the internal fractures are more frequent at highstress ratios may be related to the internal crack initiation mechanism as discussed in Section 5.3.The occurrence of internal fractures and disappearance of the conventional fatigue limit are thus characteristics of the Ti-6Al-4 V alloy's fatigue properties.On the other hand, no specimen fails at over 10 9 cycles.This suggests the presence of new fatigue limits in the gigacycle region [26].
Figure 22 shows gigacycle fatigue test results for the 1100-MPa-class Ti-6Al-4 V alloys.Although the results are only seen at R = −1, the patterns are very similar to those of the 900-MPa-class alloys: the results at 20 kHz show good agreement with those at 120 Hz for heats A and B for occurrence of internal fractures, while for heat C, the frequency effects are visible without the occurrence of internal fractures.A notable point is the relatively large degradation of the fatigue strength of heat B at over 10 7 cycles.This is likely due to the negative effects of coarse grain sizes, since the grain sizes of heats B are larger than those of other heats.
Figures 23 and 24 show gigacycle fatigue test results for the Ti-6Al-4 V ELI alloys.The patterns seen in the Ti-6Al-4 V ELI alloys are similar to those of the Ti-6Al-4 V alloys.Many internal fractures occur at high-stress ratios, eliminating conventional fatigue limits.For the internal fractures, the results at 20 kHz show good agreement with those at 120 Hz.Minor frequency effects are visible at R = −1 due to the occurrence of many surface fractures.Moreover, fatigue failures at over 10 9 cycles are very rare, suggesting the presence of new fatigue limits in the gigacycle region.

Fracture surfaces
Figure 25 shows fracture surfaces of internal fractures at 20 kHz.The morphologies of the fracture surfaces at 20 kHz are identical to those at 120 Hz.The internal fractures originate from the interiors and sub-surfaces, and identifiable fish-eye patterns disclose interiororiginating internal fractures.Clear facets are observed at high-stress ratios, unlike at R = −1.In conclusion, no frequency effects are observed on the morphologies of the fracture surfaces.

Data analysis
Figure 26 shows comparisons of gigacycle fatigue strengths of the Ti-6Al-4 V alloys with the fatigue  strengths of the steels.The gigacycle fatigue strengths of the Ti-6Al-4 V alloys are close to the fatigue strengths of the quenched and tempered steels at R = −1.This means that the degradation of fatigue strength in the gigacycle region is minimal at R = −1, resulting in outstanding fatigue performance being maintained.Conversely, the gigacycle fatigue strengths at R = 0 are clearly lower than the fatigue strengths of the quenched and tempered steels.The Ti-6Al-4 V alloys reveal large degradations of gigacycle fatigue strength at high stress ratios, with the occurrence of many internal fractures.
Figure 27 shows endurance limit diagrams which compare the fatigue test results with modified Goodman lines.Although the fatigue strengths at 10 7 cycles are almost identical to the modified Goodman line, the gigacycle fatigue strengths at 10 10 cycles are clearly lower at around R = 0.This means that the degradation of gigacycle fatigue strength at around R = 0 causes the modified Goodman line to enter the danger zone.This trend requires careful attention, since the modified Goodman line usually provides predictions with a wide safety margin.The significant degradations of the gigacycle fatigue strengths at highstress ratios are thus a shortcoming of the Ti-6Al-4 V alloys.
The reason for the large degradations of the gigacycle fatigue strength at high-stress ratios remains unknown, while different mechanisms of internal crack initiation may take place between at R = −1 and at higher stress ratios.Ono et al. analysed the internal fracture surfaces of Ti-5Al-2.5SnELI alloy  tested at R = 0.01 at cryogenic temperatures [27].They reported that the fatigue cracks that formed the facets were initiated at twin/matrix interfaces and that the twin-induced fatigue cracks were detrimental to fatigue strength.Twinning is generally suppressed in Ti-5Al-2.5SnELI alloy by the addition of Al and Sn, but it will still occur under extreme conditions, such as at cryogenic temperatures.Twinning is successfully suppressed at room temperature in the high-cycle region, although it may perhaps occur in the gigacycle region.If this is the case, twinning will occur only at highstress ratios, since the facets on the fracture surfaces are not clear at R = −1.The gigacycle fatigue strength is, therefore, degraded only at high-stress ratios.
Next is a discussion of the grain size effects on the gigacycle fatigue strength of Ti-6Al-4 V alloys.Table 6 shows the gigacycle fatigue strengths of Ti-6Al-4 V alloys evaluated at 10 10 cycles.The gigacycle fatigue strengths are average values between the maximum stress amplitude, at which no specimen is fractured, and that just above it.When the fatigue strengths tested at 20 kHz are higher than those at 120 Hz, the fatigue strengths at 120 Hz are adopted since it is not logical that the 10 10 cycles fatigue strengths are higher than the 10 8 cycles.Heats B of each alloy tend to have larger grain sizes than the other heats, while the tensile strength of heats C tends to be lower than those of other heats.Therefore, a comparison of the gigacycle fatigue strengths between heats B and C allowed the grain size effects to be clarified.
For 900-MPa-class Ti-6Al-4 V alloys, the differences between heats B and C do not follow a logical pattern: heat B reveals lower gigacycle fatigue strengths at some stress ratios but not at other stress ratios.Based on these results, our previous paper reported that no grain size effect was observed [22].For other Ti-6Al-4 V alloys, however, heats B clearly reveal lower gigacycle fatigue strengths, suggesting grain size effects.It is, therefore, more logical to conclude that the grain size effects are present in the gigacycle fatigue strength of the Ti-6Al-4 V alloys.In short, large grain sizes are detrimental to the gigacycle fatigue properties of the Ti-6Al-4 V alloys.

Summary
This paper reviewed fatigue data on titanium alloys disclosed in NIMS fatigue data sheets.The materials tested were Ti-6Al-4 V alloys, pure titanium and Ti-6Al-4 V ELI alloys.The Ti-6Al-4 V and the Ti-6Al-4 V ELI alloys were prepared with two tensile strength levels, 900-MPa and 1100-MPa.The fatigue tests applied were low-cycle, high-cycle and gigacycle types.The low-cycle fatigue tests applied  under strain-controlled conditions included not only constant-strain amplitude tests but also incremental step tests.The high-cycle fatigue tests were of the axial loading type, mainly at 120 Hz.The gigacycle fatigue tests were conducted by ultrasonic fatigue testing at 20 kHz for the Ti-6Al-4 V and the Ti-6Al-4 V ELI alloys only.The results are summarised as follows.

Low-cycle fatigue tests
(1) The constant-strain amplitude test results showed that differences in fatigue lives were very small between the alloys in spite of differences in tensile strength.(2) The width of low-cycle fatigue regions over which plastic strain exceeded elastic strain depended on the ductility of the alloys, i.e. it was wide in pure titanium (a ductile metal), but narrow in Ti-6Al-4 V alloys (less ductile alloys).(3) Ti-6Al-4 V alloys showed cyclic softening, while pure titanium showed cyclic hardening.(4) The cyclic yield stress of the titanium alloys was higher than that of conventional steels and was dissimilar to all steels.
(5) These low-cycle fatigue properties of the titanium alloys were similar to those of steels except for high cyclic yield stress.

High-cycle fatigue tests
(1) In most cases, Ti-6Al-4 V alloys revealed internal fractures from interiors or sub-surfaces without showing conventional fatigue limits.(2) Pure titanium revealed no internal fractures and showed clear fatigue limits in most cases.(3) The internal fractures of Ti-6Al-4 V alloys were more frequent at high-stress ratios than at R = −1, and fatigue limits were not confirmed in any cases at high-stress ratios.(4) The internal fractures from interiors created fish-eye patterns on the fracture surfaces, but no fish-eye patterns were observed in the internal fractures from sub-surfaces due to the proximity of the surfaces to the crack initiation sites.(5) The internal crack initiation sites revealed clear facets at high-stress ratios, whereas few were identifiable at R = −1.Note that no inclusions were observed at the internal crack initiation sites.(6) A cross-sectional observation of an internally fractured specimen revealed the facets to have formed in the α-phase in an inclined direction.(7) The fatigue strengths of the titanium alloys at 10 7 or 10 8 cycles revealed a linear relationship with tensile strength and cyclic yield stress.(8) The S-N curves revealed differences among the titanium alloys, whereas the differences were dramatically reduced by the normalizing process using tensile strength or cyclic yield stress.(9) It appeared that tensile strength had a greater effect on fatigue strength than did cyclic yield stress, and if this was the case, the fatigue strength of titanium alloys was closer to that of quenched and tempered steels than to that of normalized steels and stainless steels, revealing the outstanding high-cycle fatigue performance of titanium alloys.

Gigacycle fatigue tests
(1) All materials revealed internal fractures at highstress ratios, eliminating conventional fatigue   limits, even though some materials revealed no internal fractures at R = −1.(2) When internal fractures occurred, the results at 20 kHz showed good agreement with those at 120 Hz, meaning that frequency effects were negligible; whereas for surface fractures, only minor frequency effects were visible.(3) Fatigue failures at over 10 9 cycles were very rare, suggesting the presence of new fatigue limits in the gigacycle region.(4) The morphologies of the fracture surfaces at 20 kHz were identical to those at 120 Hz, indicating no frequency effects on the morphologies of the fracture surfaces.(5) Degradation of gigacycle fatigue strength was very small at R = −1, maintaining excellent fatigue performance, whereas major degradation occurred at high-stress ratios.(6) The degradation of gigacycle fatigue strengths at around R = 0 was so great that the modified Goodman line entered the danger zone, revealing a shortcoming of the Ti-6Al-4 V alloys.( 7) Grain size effects were present in the gigacycle fatigue strength results of the Ti-6Al-4 V alloys, indicating large grain sizes to be detrimental.

Disclosure statement
This paper analyzed massive data disclosed in NIMS fatigue data sheets and disclose low-cycle, high-cycle and gigacycle fatigue properties of titanium alloys.

Figure 12
Figure 12 shows high-cycle fatigue test results at R = −1.The symbols with a vertical bar indicate surface fractures, and those without a vertical bar indicate internal fractures.Surface fracturing, which is a conventional fracture mode of fatigue failure, indicates that fatigue cracks initiate from surfaces, whereas for internal fractures, the crack initiation sites are located in interiors or at sub-surfaces.

Figure 6 .
Figure 6.Waveform used in incremental step tests.

Figure 7 .
Figure 7. Profiles of fatigue test specimens in mm.Figure 8. Constant-strain amplitude test results.

Figure 8 .
Figure 7. Profiles of fatigue test specimens in mm.Figure 8. Constant-strain amplitude test results.

Figure 9 .
Figure 9. Plastic and elastic strain curves plotted against fatigue lives.

Figure 11 .
Figure 11.Relationship between cyclic yield stress σ yc and tensile strength σ B .

Figures 14 and 15
Figures 14 and 15 show fracture surfaces at R = −1.The fracture surfaces reveal typical transgranular fatigue fracture morphologies, which are characteristic fatigue fracture surfaces.When the crack initiation sites are located in the interiors, it is very easy to identify the internal fractures, as seen in Figure15(b).In these cases, fish-eye patterns are frequently identifiable on a macroscopic scale.For

Figure 13 .
Figure 13.High-cycle fatigue test results at high stress ratios for the 900-MPa-class Ti-6Al-4 V alloys.

Figure 16 .
Figure 16.Typical fracture surfaces of internal fractures at high stress ratios at 120 Hz.

Figure 17 .
Figure 17.Cross-sectional view of an internally-fractured specimen beneath a facet (heat A, 120 Hz, R = 0, σ a = 340 MPa, N f = 1.68 × 10 7 ).The observed specimen was cut crosssectionally across a facet on the fracture surface, as indicated by the broken line in the upper photo [22].Reproduced with permission from Materials Science and Engineering A, 598, Yoshiyuki Furuya, Etsuo Takeuchi, Gigacycle fatigue properties of Ti-6Al-4V alloy under tensile mean stress, 135-140.Copyright (2014), with permission from Elsevier.

Figure 18 .
Figure 18.Comparisons of fatigue strengths between titanium alloys and steels at R = −1.

Figure 19 .
Figure 19.S-N curves from low-to high-cycle fatigue regions at R = −1.The stress amplitudes of the low-cycle fatigue tests are evaluated at half the fatigue life.

Figure 20 .
Figure 20.Normalized S-N curves from low-to high-cycle fatigue regions at R = −1.

Figure 25 .
Figure 25.Typical fracture surfaces of the internal fractures at 20 kHz.

Table 1 .
List of fatigue data sheets on titanium alloys.

Table 3 .
Heat treatment conditions.

Table 5 .
Numerical values of the high-cycle fatigue strengths at R = −1.

Table 6 .
Numerical values of the gigacycle fatigue strengths of Ti-6Al-4 V alloys.