# Fileset

[Fatigue Fract Eng Mat Struct - 2023 - Yoshinaka - Characterization of internal fatigue crack initiation in Ti‐6Al‐4V alloy.docx](https://mdr.nims.go.jp/filesets/49889fc0-43ed-4df9-b07c-7d78a4b27f49/download)

## Creator

[Fumiyoshi Yoshinaka](https://orcid.org/0000-0003-0534-7815), [Takashi Nakamura](https://orcid.org/0000-0001-9673-7768), [Hiroyuki Oguma](https://orcid.org/0000-0003-1104-7317), [Nao Fujimura](https://orcid.org/0000-0002-3310-6894), [Akihisa Takeuchi](https://orcid.org/0000-0001-7693-9928), [Masayuki Uesugi](https://orcid.org/0000-0001-6261-9034), [Kentaro Uesugi](https://orcid.org/0000-0003-2579-513X)

## Rights

This is the peer reviewed version of the following article: Characterization of internal fatigue crack initiation in Ti-6Al-4V alloy via synchrotron radiation X-ray computed tomography, which has been published in final form at https://doi.org/10.1111/ffe.13957. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Characterization of internal fatigue crack initiation in Ti-6Al-4V alloy via synchrotron radiation X-ray computed tomography](https://mdr.nims.go.jp/datasets/38d6a014-951a-46e0-b1ed-2b064de95723)

## Fulltext

Characterization of internal fatigue crack initiation in Ti-6Al-4V alloy via synchrotron radiation X-ray computed tomographyFumiyoshi Yoshinakaa, Takashi Nakamura*, b, Hiroyuki Ogumaa, Nao Fujimurab, Akihisa Takeuchic, Masayuki Uesugic, and Kentaro Uesugica National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japanb Division of Mechanical and Aerospace Engineering, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japanc Japan Synchrotron Radiation Research Institute, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hyogo, 679-5198, Japan* Corresponding author. Takashi NakamuraTel: +81-11-706-6419, E-mail address: nakamut@eng.hokudai.ac.jpAbstractThe initiation of internal fatigue cracks in very high cycle fatigue of Ti-6Al-4V alloy was investigated using synchrotron radiation X-ray computed tomography (SR-CT). Micro-CT detected 28 cracks that were distributed across the examined volume of Ф1.8 × L 2.5 mm. No apparent correlation was observed between the spatial distribution, initial lengths, and initiation lives of cracks. The crack growth rate of the facet-sized crack varied widely; some cracks propagated rapidly, whereas no crack growth was observed for other cracks over a specific period of time after detection. Using nano-CT, the several grain-sized internal cracks and their microstructures were clearly and non-destructively visualized. In the field of view, many primary α phases were detected; however, no other cracks were observed. The multiple facet initiation site, which are commonly observed for titanium alloys, might not be due to the concurrently initiated facets but may be caused by the small crack growth accompanied by facet formation.KeywordsGigacycle fatigue; Internal fatigue crack; Non-destructive inspection; Synchrotron radiation light; Computed tomography; Titanium alloy1. IntroductionFatigue fracture characteristics of structural metallic materials in the very high cycle fatigue regime with numbers of cycles of over 107 have attracted significant attention because of the growing demand for long-term and high-speed operation of mechanical components. This type of fatigue fracture is called the very high cycle fatigue (VHCF) or giga cycle fatigue (GCF). Fatigue data in the very high cycle regime have been accumulated for various metal types 1-3. In particular, the advances in high-speed fatigue testing methods including ultrasonic fatigue testing have played an important role in effectively obtaining VHCF data, and the development of testing methods is an important topic in research on VHCF 4. Duplex S-N curves that include S-N curves for conventional surface-initiated fracture in the high stress / low and high cycle regime and those for subsurface-initiated fracture in the low stress / very high cycle regime were observed along with data accumulation 2. The occurrence of an internal fracture in the very high cycle regime indicates that the conventional fatigue design based on the fatigue limit for surface fractures leads to an overestimation of the long-term strength. Therefore, to reduce the dangers caused by VHCF, the mechanism of internal fracture must be clarified. For titanium alloys, no nonmetallic inclusions or other defects are observed at the origin site of internal cracks. Chai called such type of crack initiation “subsurface non-defect crack origins” to distinguish it from crack initiation due to subsurface defects mainly observed in high strength steels 5. Crystallographic flat areas, which are called facets, are observed at the origin sites of both surface and internal fatigue fractures in titanium alloys 6-9. To understand fatigue fracture in titanium alloys, the formation mechanism of facets must be studied. Facets are generally formed in the primary α phase in the near-α and α+β titanium alloys and have a near-basal orientation 10. However, Sackett et al. concluded that basal slip is not necessarily involved in facet formation 11. As briefly summarized by Li et al., several mechanisms have been proposed for facet formation including those associated with cleavage, dislocation slip, or twinning 12. However, Pilchak et al. conducted a fatigue test in which beach marks were placed on the surface-initiated facet surface and concluded that facets were gradually formed along with increasing numbers of cyclic loadings; the term cleavage or quasi-cleavage facet was used because of its smooth appearance 10. Furthermore, Joseph et al. stated that cyclic loadings are needed for facet formation 13. Everaerts et al. carefully investigated the facets at the internal crack initiation site in a Ti-6Al-4V drawn wire 14. They observed that most facets exhibited nano-roughness on the surface, whereas there was a facet with fan-shaped markings. They concluded that the former feature reflects prismatic slip and slip band formation, whereas the latter has a near-basal orientation and is formed by a cleavage mechanism. They also indicated that the wire-drawn texture led to a peculiar facet formation mechanism compared with that of forged or rolled alloys. Regarding VHCF, a cluster of multiple facets is known to be a common feature of internal fracture surfaces of titanium alloys 15-17. Fig. 1 shows a typical internal fracture surface of Ti-6Al-4V alloy where many facets were formed at the initiation site, as indicated by arrows.  Fig. 1 Internal fracture surface of the Ti-6Al-4V alloy (R = 0.1, σa = 650 MPa, Nf = 1.96 × 107). The arrows indicate multiple facets formed at the internal crack initiation site.The results mentioned above were mainly obtained from the analysis of the final fracture surface using scanning electron microscopy; hence, investigating the development of internal cracks over time is challenging. However, Furuya measured the growth rate of internal cracks in high tensile steels from the fracture surface using beach marks 18. Nevertheless, the direct observation of internal small cracks is strongly desired in the research on VHCF. In contrast, remarkable advances in the synchrotron radiation technology, including developments of third-generation synchrotron light sources, have enabled us to obtain excellent X-ray beams which have allowed for high-resolution non-destructive observations of the inside of metallic materials. The tomographic imaging technique using synchrotron radiation as an X-ray source is called synchrotron radiation X-ray computed tomography (SR-CT); the typical spatial resolution is on the order of ~1 µm. SR-CT has already been employed as a powerful method to characterize the fatigue fracture behavior of metallic materials 19-22. Recently, for example, Wu et al. visualized the distribution of defects and the cracking behavior in welded aluminum alloy, and the fatigue properties were evaluated using the Kitagawa–Takahashi diagram 23. Stannard et al. conducted in-situ observations of the corrosion fatigue process in an aluminum alloy, and corrosion products, corrosion pits, hydrogen bubbles, inclusions, and fatigue cracks were clearly visualized, allowing the examination of the corrosion fatigue crack behavior 24. Lopez-Crespo et al. established an estimation method of the stress intensity factor with a combination of X-ray diffraction analysis and the elastic analytical model 25. Recently, Messager et al. developed an ultrasonic fatigue testing system for in-situ SR-CT 26. In addition to experiments based on synchrotron radiation facilities, those utilizing the laboratory-based system should be noted. For example, Bachmann et al. reconstructed the crystallographic microstructure of aluminum using an X-ray diffraction contrast technique 27. In our previous work, we applied SR-CT to Ti-6Al-4V at SPring-8 to observe the internal fracture process 28-30. The experiment entailed fatigue tests and SR-CT repeatedly conducted at SPring-8. The obtained crack growth rate of internal cracks was extremely slow, less than 10-10 m/cycle, which was attributed to the effect of the vacuum environment inside the internal cracks 31. In our previous work 29,30, we studied internal crack growth. Regarding crack initiation, the relationship between the number of cracks and the number of cycles was investigated. In other words, we obtained the internal crack initiation life as the number of cycles when each crack was first detected. However, internal crack initiation behaviors have not yet been fully characterized; for example, the relationship between the crack initiation life and spatial distributions of internal cracks or initial crack lengths has not been investigated. In addition, the mechanism of multiple facet regions at the site of internal fracture origin is yet to be elucidated.In the present study, we investigated the internal crack initiation in Ti-6Al-4V alloys based on the CT images obtained at SPring-8. The spatial distributions and initiation lives of the internal cracks were measured using wide field of view (FOV) CT. The nature of internal facet formation was investigated by measuring the initial crack length and estimating the facet formation rate considering facet formation as the crack growth process from the crack length corresponding to the detection limit of the CT system. Based on the results of a high spatial resolution CT that can visualize the α+β microstructure around the internal crack, the plausible mechanism for the formation of the cluster of multiple facets at the internal crack initiation site was proposed.2. Experimental procedureTi-6Al-4V was prepared using the following procedure: a Ф20 × L1000 mm forged bar was heat treated by solution heating for 1 h at 1203 K followed by air cooling and over aging for 2 h at 978 K followed by air cooling. The resultant microstructure comprised the primary equiaxial α phase and an α/β colony, as shown in Fig. 2. The average grain size of the α phase and α/β colony was 9.8 μm and 9.3 μm, respectively.  Fig. 2 Microstructure of the Ti-6Al-4V alloy.SR-CT was performed at BL20XU at SPring-8. We utilized two setups with different FOVs and spatial resolutions: wide FOV (micro-CT) and high-res (nano-CT) setups. The micro-CT setup, which was used to measure the spatial distribution and initiation lives of internal cracks, had an FOV of 3 × 2.5 mm with a pixel size of 1.45 μm. The nano-CT setup, which was used to visualize the α+β microstructure around the internal crack, had an FOV of 56.8 × 50.2 μm with a pixel size of 32.7 nm. Only in the nano-CT, a Fresnel zone plate was used as the objective lens. A reduced size specimen was required for SR-CT imaging. The specimen configurations for the micro- and nano-CT are shown in Fig.3. A specimen with a parallel part of Ф1.8 × L3 mm and an hourglass shaped specimen with a minimum diameter of Ф0.4 mm were used for micro- and nano-CT imaging, respectively. The specimen used for the micro-CT investigation in the present study was the same as that used in our previous research 30. The specimens were machined from the bar, and the work hardening layer was removed by mechanical polishing using emery papers from #120 to #1500 for 100 μm diameter. A conventional back projection method was used for 3D reconstruction 32, and the obtained CT images were analyzed using Image J software 33.Fatigue tests were performed with stress control. Uni-axial, sinusoidal loadings with a stress ratio R of 0.1 and a frequency f of 400 Hz were applied at room temperature. Regarding the specimen used for micro-CT, the maximum stress σmax was 650 MPa, where the internal fatigue fractures occurred with the average number of cycles to failure Nf of 2–3 × 107 cycles 29. In contrast, probably owing to size reduction, the fatigue fracture did not occur at 650 MPa for the specimen with a diameter of Ф0.4 mm used for nano-CT; therefore, a σmax of 800 MPa, where the surface fracture is the dominant fracture mode but internal fractures also occur around Nf = 106 cycles in the Ф1.8 mm specimen, was used instead.  Fig. 3 Specimen configurations for (a) micro-CT and (b) nano-CT (unit: mm).3. Experimental results3.1 Internal crack initiation lifeMicro-CT was first performed at 0 and 5.0 × 105 cycles, and at every 2.0 × 106 cycles after that. The time for which the beamline was available ran out at N =1.8 × 107, roughly corresponding to 70% of the average fatigue life, and the specimen was not fractured. In the present study, we defined the crack initiation life Ni of each crack as the number of cycles when each crack was first detected. Therefore, Ni in this work does not refer to the number of cycles at the very moment of crack initiation because conducting CT imaging at every cycle is difficult.As shown in our previous study, 28 cracks were detected in total up to 1.8 × 107 with the shortest crack initiation life of Ni = 5.0 × 106, corresponding to roughly 20% of the average fatigue life under the current testing condition 30. Whereas some internal cracks are initiated in the early stage of fatigue life, internal crack initiation occurred even after 107 cycles, including 1.8 × 107 cycles when the final scan was conducted in the present work. Fig. 4 shows the CT images of internal cracks initiated with different Ni values on the sections parallel to the loading direction (the longitudinal sections). Some cracks have also been reported in the literature 30 to investigate their growth behaviors. In the present study, we labeled the cracks with numbers such as C-1 based on the following rules of labeling: cracks were numbered in ascending order of initiation life. When multiple cracks had the same initiation life, these cracks were numbered in descending order of crack length 2a at the final imaging at N = 1.8 × 107. The definition of 2a was the same as that given in the previous paper 29: the distance between each of the two crack tips projected to the plane perpendicular to the loading direction.   Fig. 4 Micro-CT images of the internal cracks at the scan when each crack was first detected on the section parallel to the loading direction (R = 0.1, σa = 650 MPa): (a) C-1 (Ni = 5.0 × 106, the crack length at Ni 2aini = 21.6 µm), (b) C-2 (Ni = 5.0 × 106, 2aini = 9.5 µm), (c) C-3 (Ni = 5.0 × 106, 2aini = 8.0 µm), (d) C-9 (Ni = 8.0 × 106, 2aini = 15.9 µm), and (e) C-23 (Ni = 1.4 × 107, 2aini = 29.4 µm). The white arrows indicate internal cracks.The fracture origin size has been reported to affect fatigue life 34,35. Therefore, the relationship between crack origin size and crack initiation life must be investigated. As mentioned in Section 1, fatigue cracks are generally initiated by forming facets at the α phase in Ti-6Al-4V. Compared with materials in which fatigue cracks originate from defects such as nonmetallic inclusions, the meaning of “crack origin size” might be different in the case of faceted crack initiation in titanium alloys; however, the present work regards the size of the α phase where the crack initiates (or the size of the crack initiation facet) as the crack origin size. Thus, the relationship between the size of the crack initiation facet and the crack initiation life is important in the present work. However, the CT image in which the crack was first detected does not indicate the crack image immediately after facet formation was completed. Thus, the present work assumes that the size of the crack initiation facet is almost the same as the crack length when it was first detected (the initial crack length 2aini); we investigated the relationship between the initial crack length and initiation life. Notably, there can be a large spread on the data because the crack might have propagated for a while before it is first detected by the scan. The spread can even be 2 × 106 cycles if the crack initiation (more accurately, when the crack size reaches the detection limit of micro-CT) occurred immediately after the former scan. Fig. 5 shows the relationship between initial crack length 2aini and crack initiation life Ni for all detected cracks. We found some variability in 2aini, ranging from 8.0 to 31.5 μm with an average value of 16.4 μm. The size of the primary α phase was distributed between 4.0 and 22.8 μm, as indicated by the measurement results based on the scanning electron microscopy (SEM) image of the etched sample, which was prepared for microstructure observation. The internal cracks with large 2aini (≈ 30 μm) were therefore considered to have had propagated for some time before these cracks were first detected. Most of the 2aini values were in the range of α grain size; therefore, the 2aini shown in Fig. 5 would be comparable to the initiation facet sizes. No correlation between 2aini and the crack initiation life implies that the size of the crack initiation α grain has little influence on the crack initiation life defined in this study.However, this tendency should be carefully interpreted because the crack initiation life is defined as the number of cycles when the crack is first detected; it does not express the actual crack-initiation life. Chandran proposed a constitutive equation for the S-N fatigue behavior of metal single crystals based on the physical definition of the endurance limit, corresponding to the critical resolved shear stress for dislocation slip initiation, and succeeded in describing a wide range of S-N behaviors of nickel-based superalloy single crystals as well as Fe and Zn single crystals 36. This concept implies that the real crack initiation begins at the first fatigue cycle, which triggers slip; therefore, the first crack size can be equal to Burger’s vector. According to his theory, the crack initiation life defined in this study consists of two regimes: the consumed fatigue cycles in which the crack propagates until it reaches the detection limit of the SR-CT system, and those in which the crack forms a facet(s) to be detected as the value of 2aini. The material used in the present study was not a single crystal; however, the aforementioned concept regarding crack initiation is meaningful and will be discussed in detail in Section 3.3.  Fig. 5 Relationship between the initial crack length 2aini and crack initiation life Ni.3.2 Spatial distribution of crack initiation sitesFig. 6 shows the spatial distribution of the cracks in the examined volume of the specimen. Figs. 6 (a) and (b) show the projection view in the direction parallel (cross-sectional view) and perpendicular (longitudinal view) to the loading axis, respectively. In the figures, the cracks are indicated by numbered circles based on the abovementioned labeling rule in Section 3.1. As shown in Fig. 6, crack initiation sites were distributed across the examined volume, and no tendency for cracks to be concentrated in a certain place was observed. The distance between some cracks appears small in the figure; however, all cracks initiated at locations different from those of other cracks. The minimum value of the distance between two cracks was 123 µm for C-16 and C-17, which are indicated by dashed rectangles labeled with A. Additionally, no meaningful relationship was observed between the initiation position and initiation life; for example, the initiation positions of C-4 and C-25, which are indicated by dashed rectangles labeled with B, were relatively close (203 µm) but their initiation lives were largely different: Ni = 6.0 × 106 (C-4) and 1.4 × 107 (C-25). In the present work, we visualized the spatial distribution of the crack initiation sites and showed that most cracks initiated from their internal initiation sites with the exception of one crack (C-12), which initiated from the specimen surface. C-12 is indicated in Fig. 6 with an asterisk (*). Note that the initiation life of the surface-initiated crack C-12 was 1.2 × 107 cycles and was comparable to those of internal cracks. The difference in the number between surface and internal cracks is discussed in Section 4.  Fig. 6 Spatial distribution of cracks detected in the examined volume of Ф1.8 × L2.5 mm: (a) Cross-sectional view, and (b) longitudinal view. Circles indicate the place where the crack initiated, and their gray value corresponds to the crack initiation life as shown in the scale bar.3.3 Facet formation processIn this section, the facet formation process is examined based on SR-CT images. As mentioned in Section 1, facets in titanium alloys seem to be formed by cyclic loading 13,37. Therefore, this study considers the facet formation process as the crack growth process from the crack length corresponding to the detection limit of the CT system. Thus, the crack growth rate in the facet formation process, da/dN|f can be approximated using Eq. 1. In the equation, aini is half the initial crack length, and a0 is half the detection limit. The pixel size was 1.45 μm in the present setup; therefore, the detection limit was regarded as 2 μm, and a0 was considered equal to 1 μm. Ni is the number of cycles when the crack is first detected (crack initiation life defined in this study), and Ni-1 is the number of cycles one step before Ni when SR-CT is conducted.  (1)Additionally, to compare the crack growth rate between facet formation and the following growth, the crack growth rate immediately after initiation da/dN|ini was calculated using Eq. 2. In the equation, Ni+1 is the number of cycles when SR-CT was conducted just after Ni, and ai+1 indicates half of the crack length measured at Ni+1.  (2)Fig. 7 shows the calculated da/dN|f for all cracks. Regarding the cracks that did not show apparent growth immediately after initiation (between Ni and Ni+1), C-2, C-3, C-6, C-12, and C-21 are shown as cross marks on the horizontal axis in Fig. 7. The fact that some cracks with a short initiation life, such as C-2 and C-3, hardly propagated after initiation indicates that early initiation does not necessarily imply subsequent rapid growth. 63% of internal cracks (C1–C9, C12, C13, C15, C16, C20 ~ C22, C24) showed larger da/dN|f than da/dN|ini. In these cracks, facet formation was considered smooth compared to the following crack growth. Especially, for C-1, da/dN|f was 20 times larger than da/dN|ini. In contrast, 22% of internal cracks (C17, C19, C23, C25 ~ C27) exhibited higher da/dN|ini than da/dN|f.The fact that many initiated cracks had lower da/dN|ini than da/dN|f suggests difficulties in propagating into adjacent gains. In intermittent CT observations, the retardation of the smooth crack growth after its initiation (facet formation) can increase the possibility of recognizing the initial crack length 2aini as comparable to the α grain. In contrast, the fact that some cracks had higher da/dN|ini than da/dN|f suggests the ease of breaking the barrier to propagate into the surrounding matrix. These cracks may continue to grow.   Fig. 7 Facet formation rate da/dN|f and initial growth rate da/dN|ini.3.4 Nano-CT imaging of the microstructure around the internal crackThe α+β microstructure around the internal crack was visualized using the nano-CT technique. Here, the FOV of nano-CT was narrow. Micro-CT with a wider FOV was therefore conducted first on the Ф0.4 mm specimen to find the internal crack. Fatigue tests and micro-CT tests were repeated, and an internal crack was found after N = 4.7 × 105 cycles. Then, the crack initiation site was observed using nano-CT. Fig. 8 shows the nano-CT image. Fig. 8 (a) shows the longitudinal section around the internal crack. The several grain-sized internal crack, primary α phases (bright grains), and α/β colonies (lamellar region with brightly observed α and darkly observed β phases) were clearly visualized. The center of the crack was in the primary α phase and might be the crack initiation facet. The loading axis of the facet was inclined at ~50°. The deflected shape of the internal crack indicates microstructure sensitive propagation. Fig. 8 (b) shows the crack surface observed from the direction parallel to the loading axis, i.e., the same observation direction as general fracture surface observation. At the initiation site of the crack, the crack initiation facet was nondestructively observed. In the FOV, many primary α phases were detected; however, no other cracks were observed.  Fig. 8 Nano-CT image of the internal crack and microstructure (R = 0.1, σa = 800 MPa): (a) the longitudinal section, and (b) the crack surface observed from the direction parallel to the loading axis.4. DiscussionAs shown in Fig. 6, numerous cracks initiated inside the specimen while only one did on the surface. The number of α phases that can form facets is a crucial factor to discuss the crack initiation process. Such potential crack initiation sites differ with the loading condition; under a low stress condition where VHCF becomes a problem, the number of α phases that can form crack initiation facets might be limited. The fact that the number of internal cracks was significantly larger than that of surface cracks could be key to understanding why the internal fracture is the dominant fracture mode in the VHCF regime in this alloy. One possibility is that the residual compressive stress on the specimen surface could suppress crack initiation. In the present study, the specimen surface was mechanically polished using emery paper for 100 μm after machining; however, thin hardening layer due to polishing may have affected the surface crack initiation. To carefully discuss the difference in the number of cracks initiated between the surface and the internal cracks, the specimen finished by electro-polishing, for example, might be appropriate. The other more likely possibility is a difference in the risk volumes. Here, the risk volume for surface cracks is significantly smaller than that for internal cracks. Thus, the number of α phases that can form surface crack initiation facets is considered to be very limited. Based on this idea, the difference in the number of initiations between the surface cracks and internal cracks can be attributed to the difference in the size of their risk volumes. The fact that the fracture hardly occurred in the Ф0.4 specimen used for nano-CT at 650 MPa and that the internal fracture easily occurred in the Ф1.8 specimen used for micro-CT might be due to the small risk volume. Chandran showed that the probabilities of surface and interior fractures in β-titanium alloys could be explained by the Poisson spatial patterns of microstructural defects. In the alloy with sparsely distributed crack-initiating defects, the fracture mode depends on specimen size 38. Although this result was for the fracture modes of individual specimens, the multiple crack initiations in a single specimen observed in the present study may similarly depend on the spatial distribution of the α-phase that can initiate cracks under the current loading conditions. Additionally, some researchers focused not only on the α grain at which a crack finally initiated but also on its adjacent grains 13. Thus, the probability of existence of a region that meets such conditions must be less than the probability of existence of a single α phase, which is favorably oriented for basal slip.It has been reported that facet formation tends to occur at the α phase, which is favorably oriented for basal slip 39. The da/dN|f values shown in Fig. 7 are the roughly estimated ones to examine the facet formation behavior, and the observation should be conducted with smaller ΔN to measure da/dN|f accurately. However, facet formation rapidly occurred even for cracks that did not show apparent propagation for a while after their initiation. In contrast, some cracks showed higher da/dN|ini values than da/dN|f. Jha et al. proposed a hypothesis for the hierarchy of local deformation heterogeneity in titanium alloys to discuss the variability in fatigue life 39. In their hypothesis, the most frequent microstructural arrangement of the fracture origin site is an isolated primary α phase oriented for basal slip. The cracks that showed no apparent propagation after being detected in the present study could have been initiated under this microstructural arrangement, where the neighboring grains of the crack-initiating grain might not have been favorably oriented for further propagation. The more complex arrangements with low probability of occurrence consisted of the primary α phase and its neighbors both oriented for basal slip is given as an example for the case of short fatigue life. Oja et al. investigated the nucleation of fatigue cracks in Waspaloy, a nickel-base superalloy 40. They clarified that the grains at the crack initiation site had similar Schmidt factors close to 0.5 and explained that the effective crack initiation site size was larger than the grain size. These discussions are regarding the fatigue life and cannot be directly compared with the crack initiation life obtained in the present work. However, the relationship between da/dN|f and da/dN|ini shown in Fig. 7 can be explained based on their hypothesis. That is, many cracks that had a low da/dN|ini correspond to the isolated primary α type. In contrast, a limited number of cracks that had a relatively high da/dN|ini might correspond to the primary α phase and its neighbors both oriented for basal slip type. In the present work, no cracks with a high da/dN|ini were observed among the ones with a short initiation life. However, considering the large variability in the fatigue life in the VHCF of titanium alloys, the primary α phase that can form facets with a short initiation life surrounded by grains with poor crack growth resistance might be the worst-case scenario. The data acquisition of the internal crack initiation life and initial growth rate is necessary to evaluate the variability in VHCF life, and the micro-CT is almost the only means to obtain such information.As shown in Fig. 1, the cluster of multiple facets (hereinafter referred to as simply “cluster”) is frequently observed at the origin site of the internal fracture in titanium alloys. Jha et al. measured the spatial angle of facets to the loading axis and conducted crystallographic analysis of the faceted grains 15. They concluded that some of the facets were formed during small-crack growth. However, they did not mention whether only one facet was first formed or some facets were formed at almost the same number of cycles. In contrast, Liu et al. suggested that the coalescence of isolatedly initiated facets is the mechanism underlying the formation of clusters in internal fracture based on the observation of cracks beneath the fracture surface 16. Li et al. also suggested that subsurface fracture was caused by the nucleation of multiple micro-cracks and their coalescence 41. The present study discusses the formation of clusters based on SR-CT results. As shown in Fig. 6, numerous internal cracks or facets were initiated in the specimen; however, there were no groups of internal cracks the distances between which were in the order of the grain size (~10 µm). Additionally, only one isolated internal crack was observed, and no other cracks were detected even using nano-CT, which can visualize the facet with a resolution comparable to that of the fracture surface observation using SEM, as shown in Fig. 8. These results suggest that cluster formation by concurrently initiated facets is unlikely. Thus, the cluster is considered to be formed during small crack growth. If so, there is a possibility that the accumulation of microscopic damage during cyclic loadings and the presence of cracks might promote the formation of facets during crack growth. Judging from the CT images obtained in our previous study, the internal crack seemed to propagate spatially successively 30. However, our observations were obtained with a relatively large ΔN; therefore, it could not be determined whether the facets in the crack growth region are continuously formed at the tip of the crack originating from the first facet or are formed at a distance from the crack. An important future research topic is to clarify the formation process of internal small cracks within multiple facet clusters through SR-CT images with a smaller ΔN, i.e., a fine time-resolution.5. ConclusionWe investigated the process of internal crack initiation of Ti-6Al-4V alloys in the VHCF regime using SR-CT at SPring-8. The just-initiated internal cracks were successfully detected using micro-CT. Up to 1.8 × 107 cycles, where the beam time ran out, 28 cracks consisting of 27 internal cracks and a surface crack were detected in total; the difference in the number of initiations between the surface and internal cracks can be attributed to the difference in the size of their risk volumes. The initiation lives varied widely from 5.0 × 106 (20% of the average fatigue life) to 1.8 × 107 cycles (70%). In particular, certain internal cracks initiated at the later stage of fatigue life, including after 1.8 × 107 cycles, when the final scan was conducted, whereas other cracks initiated in the early stage. The lengths of cracks when they were first detected were distributed from 8.0 to 31.5 μm and were not correlated with the crack initiation life. Crack initiation sites were distributed across the examined volume, and no tendencies for crack initiation to be concentrated in a certain place were observed. Based on the idea that the faceted crack initiation is crack growth from the length corresponding to the detection limit of the CT system, the crack growth rate at facet formation was roughly estimated. Thus, facet formation occurred rapidly compared to the following crack growth for many cracks. Using nano-CT, the several-grain-sized internal crack and the surrounding microstructure were clearly visualized; however, no other cracks were detected in the FOV. Regarding the cluster of multiple facets reported for the origin site of titanium alloys, a plausible formation process was proposed based on the obtained CT images. Considering the fact that there were no groups of internal cracks with distances among them in the order of grain size, it is unlikely that clusters are formed by concurrently initiated facets, but multiple facet formations occur during small crack growth.AcknowledgementsThe synchrotron radiation experiments were performed at the BL20XU in SPring-8 with the approval of JASRI (Proposal No. 2014A1020, 2014A1459, 2016B1701, 2017B1421, 2020A0172 and 2021B1245). The authors acknowledge the support of a Grant-in-Aid for Early-Career Scientists (19K14853) and for Scientific Research (18H03748 and 21H04529) from the Japan Society for the Promotion of Science, Japan.References1. Marines I, Bin X, Bathias C. An understanding of very high cycle fatigue of metals. Int. J. Fatigue. 2003;25(9):1101-1107.2. Sakai T. Review and Prospects for Current Studies on Very High Cycle Fatigue of Metallic Materials for Machine Structural Use. J. Solid Mech. Mater. Eng. 2009;3(3):425-439.3. Shiozawa K, Morii Y, Nishino S, Lu L. Subsurface crack initiation and propagation mechanism in high-strength steel in a very high cycle fatigue regime. Int. J. Fatigue. 2006;28(11):1521-1532.4. Stanzl-Tschegg S. Very high cycle fatigue measuring techniques. Int. J. Fatigue. 2014;60:2-17.5. Chai G. The formation of subsurface non-defect fatigue crack origins. Int. J. Fatigue. 2006;28(11):1533-1539.6. Le Biavant K, Pommier S, Prioul C. Local texture and fatigue crack initiation in a Ti‐6Al‐4V titanium alloy. Fat. Fract. Eng. Mater. Struct. 2002;25(6):527-545.7. Liu X, Sun C, Hong Y. Effects of stress ratio on high-cycle and very-high-cycle fatigue behavior of a Ti–6Al–4V alloy. Mater. Sci. Eng. A. 2015;622:228-235.8. Neal DF, Blenkinsop PA. Internal fatigue origins in α-β titanium allols. Acta Metall. 1976;24(1):59-63.9. Pan X, Su H, Sun C, Hong Y. The behavior of crack initiation and early growth in high-cycle and very-high-cycle fatigue regimes for a titanium alloy. Int. J. Fatigue. 2018;115:67-78.10. Pilchak AL, Bhattacharjee A, Rosenberger AH, Williams JC. Low ΔK faceted crack growth in titanium alloys. Int. J. Fatigue. 2009;31(5):989-994.11. Sackett EE, Germain L, Bache MR. Crystal plasticity, fatigue crack initiation and fatigue performance of advanced titanium alloys. Int. J. Fatigue. 2007;29(9):2015-2021.12. Li W, Zhao H, Nehila A, Zhang Z, Sakai T. Very high cycle fatigue of TC4 titanium alloy under variable stress ratio: Failure mechanism and life prediction. Int. J. Fatigue. 2017;104:342-354.13. Joseph S, Bantounas I, Lindley TC, Dye D. Slip transfer and deformation structures resulting from the low cycle fatigue of near-alpha titanium alloy Ti-6242Si. Int. J. Plast. 2018;100:90-103.14. Everaerts J, Verlinden B, Wevers M. Investigation of fatigue crack initiation facets in Ti‐6Al‐4V using focused ion beam milling and electron backscatter diffraction. J. Microsc. 2017;267(1):57-69.15. Jha SK, Szczepanski CJ, Golden PJ, Porter WJ, John R. Characterization of fatigue crack-initiation facets in relation to lifetime variability in Ti–6Al–4V. Int. J. Fatigue. 2012;42:248-257.16. Liu X, Sun C, Hong Y. Faceted crack initiation characteristics for high-cycle and very-high-cycle fatigue of a titanium alloy under different stress ratios. Int. J. Fatigue. 2016;92:434-441.17. Yue Y, Dai LY, Zhong H, et al. Effect of microstructure on high cycle fatigue behavior of Ti-20Zr-6.5Al-4V alloy. J. Alloys Compd. 2017;696:663-669.18. Furuya Y. Small internal fatigue crack growth rate measured by beach marks. Mater. Sci. Eng. A. 2016;678:260-266.19. Buffiere J-Y, Ferrie E, Proudhon H, Ludwig W. Three-dimensional visualisation of fatigue cracks in metals using high resolution synchrotron X-ray micro-tomography. Mater. Sci. Technol. 2006;22(9):1019-1024.20. Hassanipour M, Watanabe S, Hirayama K, Toda H, Uesugi K, Takeuchi A. Short crack growth behavior and its transitional interaction with 3D microstructure in Ti-6Al-4V. Mater. Sci. Eng. A. 2018;738:229-237.21. Lorenzino P, Buffiere J-Y, Verdu C. 3D characterization of the propagation of small fatigue cracks in steels with different forging conditions. Int. J. Fatigue. 2018;115:2-10.22. Nakayama T, Yuse F, Tsubokawa Y, Matsui J. Direct observations of cracks and voids in structural materials by X-ray imaging using ultra-bright synchrotron radiation. ISIJ Int. 2003;43(4):589-596.23. Wu SC, Song Z, Kang GZ, Hu YN, Fu YN. The Kitagawa-Takahashi fatigue diagram to hybrid welded AA7050 joints via synchrotron X-ray tomography. Int. J. Fatigue. 2019;125:210-221.24. Stannard TJ, Williams JJ, Singh SS, Sundaram Singaravelu AS, Xiao X, Chawla N. 3D time-resolved observations of corrosion and corrosion-fatigue crack initiation and growth in peak-aged Al 7075 using synchrotron X-ray tomography. Corros. Sci. 2018;138:340-352.25. Lopez-Crespo P, Peralta JV, Kelleher JF, Withers PJ. In situ through-thickness analysis of crack tip fields with synchrotron X-ray diffraction. Int. J. Fatigue. 2019;127:500-508.26. Messager A, Junet A, Palin‐Luc T, et al. In situ synchrotron ultrasonic fatigue testing device for 3D characterisation of internal crack initiation and growth. Fat. Fract. Eng. Mater. Struct. 2020;43(3):558-567.27. Bachmann F, Bale H, Gueninchault N, Holzner C, Lauridsen EM. 3D grain reconstruction from laboratory diffraction contrast tomography. J. Appl. Crystallogr. 2019;52(3):643-651.28. Nakamura T, Yoshinaka F, Nakayama S, et al. Detection of small internal fatigue cracks in Ti-6Al-4V by using synchrotron radiation μCT imaging. Mech. Eng. Lett. 2016;2:16-00233-00216-00233.29. Yoshinaka F, Nakamura T, Nakayama S, Shiozawa D, Nakai Y, Uesugi K. Non-destructive observation of internal fatigue crack growth in Ti–6Al–4V by using synchrotron radiation μCT imaging. Int. J. Fatigue. 2016;93:397-405.30. Yoshinaka F, Nakamura T, Takeuchi A, Uesugi M, Uesugi K. Initiation and growth behaviour of small internal fatigue cracks in Ti‐6Al‐4V via synchrotron radiation microcomputed tomography. Fat. Fract. Eng. Mater. Struct. 2019;42:2093-2105.31. Yoshinaka F, Xue G, Fujimura N, Nakamura T. Effect of vacuum pressure on small crack propagation in Ti-6Al-4V. Int. J. Fatigue. 2021;142:105961.32. Uesugi K, Hoshino M, Takeuchi A, Suzuki Y, Yagi N, Nakano T. Development of fast (sub‐minute) micro‐tomography. AIP Conf. Proc. 2010;1266:47-50.33. Schneider CA, Rasband WS, Eliceiri KW. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods. 2012;9(7):671.34. Cao F, Ravi Chandran KS. The role of crack origin size and early stage crack growth on high cycle fatigue of powder metallurgy Ti-6Al-4V alloy. Int. J. Fatigue. 2017;102:48-58.35. Lei Z, Hong Y, Xie J, Sun C, Zhao A. Effects of inclusion size and location on very-high-cycle fatigue behavior for high strength steels. Mater. Sci. Eng. A. 2012;558:234-241.36. Ravi Chandran KS. A constitutive equation for the S–N fatigue behavior of metal single crystals and validation by the physical definition of fatigue endurance limit. Int. J. Fatigue. 2016;91:21-28.37. Pilchak AL. Fatigue crack growth rates in alpha titanium: Faceted vs. striation growth. Script. Mater. 2013;68(5):277-280.38. Chandran K. Duality of fatigue failures of materials caused by Poisson defect statistics of competing failure modes. Nat. materials. 2005;4(4):303-308.39. Jha SK, Szczepanski CJ, John R, Larsen JM. Deformation heterogeneities and their role in life-limiting fatigue failures in a two-phase titanium alloy. Acta Mater. 2015;82:378-395.40. Oja M, Chandran KR, Tryon R. Orientation imaging microscopy of fatigue crack formation in Waspaloy: crystallographic conditions for crack nucleation. Int. J. Fatigue. 2010;32(3):551-556.41. Li W, Xing X, Gao N, et al. Subsurface facets-induced crack nucleation behavior and microstructure-based strength evaluation of titanium alloys in ultra-long life regime. Mater. Sci. Eng. A. 2019;761:138055.Highlights· Initiation of internal cracks in Ti-6Al-4V was observed using SR-CT.· No relationship was found among distribution, initial length, and initiation life.· Crack initiation facet formation was often rapid compared to the following crack growth.· Fracture origin site with multiple facets is due to small crack growth forming facets.image3.pngimage4.emf(e)40 µm(d)40 µm(c)40 µm(b)40 µm(a)40 µmLoading directionimage5.emf0.5 1.0 1.5 (× 107)Crack initiation life Ni [cycles]Initial crack length 2aini [µm]010203040image6.emf3(3)5(8)1(9)6(15)7(22)4(26)1(27)1(28)123456789101112131516171819202122232425262728146*123456781011121314151618192021222324252627289173*0 1.8 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6(× 107) Number of cycles N [cycles]**(**)Number of crack initiations during ΔNCumulative number of cracks up to Nxyz // LD z // LDxy(a) (b)ϕ1.8 mm 2.5 mm ABABimage7.jpegimage8.emf(b)(a)Facet10 µmFacetα/β α(a)5 µmLoading directionLoading directionimage1.pngimage2.png