International Journalof Fatigue

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1 Available online at International Journal of Fatigue 30 (2008) International Journalof Fatigue Estimation of the size of GBF area on fracture surface for high strength steels in very high cycle fatigue regime Z.G. Yang a, *, S.X. Li a, Y.B. Liu a, Y.D. Li a, G.Y. Li a, W.J. Hui b, Y.Q. Weng b a Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang , PR China b Central Iron and Steel Research Institute, Beijing , PR China Received 21 May 2007; received in revised form 14 August 2007; acceted 19 August 2007 Available online 1 Setember 2007 Abstract The sizes of the granular bright facet (GBF) areas on fracture surfaces of secimens subjected to very high cycle fatigue for two high strength sring steels were measured in a field emission scanning electron microscoe (FESEM) and comared with the estimated values, and a good agreement was found between the two sets of data. A criterion was roosed to estimate the sizes of GBF areas. It was assumed that when the increment of crack length in one alied stress cycle (numerically equal to crack growth rate, da/dn) is just equal to the lastic zone size in front of crack ti, r, the GBF stos develoing. It means that hydrogen accumulating in the lastic zone under alied stress influences mostly on the fatigue behaviors which results in the morhology of GBF area quite different from the conventional fatigue fracture surface. The estimated sizes of GBF areas were also in accordance with the sizes measured from fracture surfaces of other high strength steels rovided that the hydrogen concentration in those steels was not much higher than that in resent sring steels. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: High strength steel; Very high cycle fatigue; Granular bright facet (GBF); Hydrogen; The maximum size of the lastic zone; Fatigue crack growth rate 1. Introduction Hydrogen cannot be avoidably adsorbed in steels during different eriods such as in steelmaking, heat treating, machining, transorting, storing, and serving in various environments, etc. Hydrogen traed by nonmetallic inclusions can accumulate to a higher density in and around the inclusions [1]. The influence of hydrogen on fatigue behaviors becomes stronger with increase of steel strength. For a high strength steel, even if the alied stress amlitude is below the conventional fatigue limit, the secimens may fracture and fatigue cracks ossibly initiate at nonmetallic inclusions, and mostly interior inclusions. It is generally found a secial area in vicinity of the fractured * Corresonding author. address: zhgyang@imr.ac.cn (Z.G. Yang). inclusion which is quite different from the tyical fatigue fracture surface outside the area. In SEM, the morhology of the area aears quite bright and granular, so called granular bright facet (GBF) area [2]; however under otical microscoy, this area looks like darker, hence it is called otically dark area (ODA) [3]. It was reorted that the formation of the secial area was related to hydrogen in steels [1,3 6], as schematically shown in Fig. 1. In addition, the size of GBF area increases with increasing fatigue life [7 10]. The fatigue life is mostly sent in the formation of GBF area, esecially in the very high cycle fatigue regime (fatigue life N f >10 7 ), it can reach above 90% of the fatigue life N f [7,8]. Thus, investigation of the conditions to form the GBF area is necessary. This aer intends to investigate the relationshi between the size of GBF area and mechanical arameters and to examine the redictions with exerimental results /$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi: /j.ijfatigue

2 Z.G. Yang et al. / International Journal of Fatigue 30 (2008) Nomenclature area GBF the rojective area erendicular to stress axis, including the rojective area of inclusion and the GBF area around it, m 2 or lm 2 da/dn fatigue crack growth rate, m/cycle or lm/cycle H v Vichers hardness of steel, kgf/mm 2 K Imax the maximum stress intensity factor (SIF) of mode I crack ti, MPa ffiffiffiffi m (K Imax ) GBF the maximum SIF when crack grows to GBF boundary, MPa ffiffiffiffi m DK fatigue crack SIF range, MPa ffiffiffiffi m Dl the increment of crack growing in each cycle, numerically equal to da/dn, morlm N f fatigue life, cycle r alied fatigue stress amlitude, MPa r y yield strength of steel, MPa / diameter of a enny-crack, m / inc diameter of a sherical inclusion, m or lm / GBF equivalent diameter of a quasi-round GBF area measured from fracture surface, m or lm / GBF,E estimated diameter of GBF area, m or lm Table 2 Heat treatment rocedures and mechanical roerties of investigated steels Steel Heat treatment rocedure Mechanical roerties Fig. 1. Scheme of the mechanism for suer-long fatigue failure from internal inclusion with an initial hydrogen assisted fatigue crack initiation and early roagation [6]. r b (MPa) r y (MPa) H v (kgf/ mm 2 ) 50CrV4 860 C (30 min, in vacuum) + oil quenched (in vacuum) C (30 min) 54SiCrV Materials and exeriments Two clean and high strength 50CrV4 and 54SiCrV6 sring steels were used in this study. Their chemical comositions, heat treatment rocedures and mechanical roerties are shown in Tables 1 and 2, resectively. The microstructures of these two steels are tyical temered martensite. Tension comression fatigue (TCF) tests were conducted on a Shimadzu USF-2000 ultrasonic fatigue testing machine at a resonance frequency of 20 khz, resonance interval of 150 ms and the stress ratio of R = 1, at room temerature in air. Comressive air was used during fatigue testing to avoid the self-heating of secimens at such high frequency. The secimen configuration is shown in Fig. 2. The tests terminated until the fatigue cycles reached u to 10 9 for non-fractured secimens. All fracture surfaces Table 1 Chemical comositions of investigated steels Steel Chemical comositions (wt%) C Mn Si Cr V S P Al 50CrV SiCrV were observed and the arameters of crack origin (sizes of inclusions and GBF areas around the inclusions) were measured in a field emission scanning electron microscoe (FESEM). 3. Exerimental results When the fatigue lives of two grous of secimens exceeded 10 7 cycles, all of the fatigue cracks initiated at internal VC inclusion clusters excet one crack that started from a large single VC inclusion. The diameter of a single inclusion and the equivalent diameter of an inclusion cluster are less than 10 lm as shown in Figs. 3 and 4, resectively. However, the diameters of these inclusions and inclusion clusters are greater than the critical size of about 3 lm for these steels as estimated in Ref. [11]. Each crack origin is surrounded by a quasi-round GBF area. Observed in FESEM, the GBF areas showed the aearance of fracture surfaces quite different from other areas. There were many small black articles in GBF area shown in backscattered electron image (Fig. 4b), and the electron robe microelement analysis (EPMA) revealed that they are carbide articles. The fatigue testing data of these secimens as well as the diameters of the inclusions or equivalent diameters of inclusion clusters, / Inc, and corresonding diameters of GBF areas, / GBF, are listed in Table 3.

3 1018 Z.G. Yang et al. / International Journal of Fatigue 30 (2008) K Imax ¼ 2 rffiffiffiffiffiffiffi r / 2 ð2þ Therefore combining Eqs. (1) and (2), we get: r ¼ r / ð3þ r y Fig. 2. Configuration of secimen for ultrasonic fatigue testing. 2. Small crack growth rate, da/dn. A GBF-crack is considered as a small crack for the diameter of the GBF area observed is generally not greater than about tens of microns, however it may be much greater than r. As an examle, for a GBF area with diameter of 40 lm and when alied stress amlitude r = 0.5r y, r 0.7lm. Therefore, both the conditions of lane strain and liner elastic fracture mechanics (LEFM) are satisfied and they can be used for describing the crack growing behavior of such crack. In the case of small crack growth, Fig. 3. Aearance of fracture surface, crack initiating at a single VC inclusion, observed by FESEM (50CrV4). 4. Measured and estimated sizes of GBF area 4.1. The exressions used for describing small crack behavior of high strength steel 1. The maximum size of the lastic zone in front of crack ti, r. It is well known that there is a lastic zone in front of crack ti. Irwin [12] indicated that this was the zone where Von Mises equivalent stress, r Von ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ½ðr 6 1 r 2 Þ 2 þðr 2 r 3 Þ 2 þðr 3 r 1 Þ 2 Š(r 1, r 2 and r 3 are rincial stresses), exceeded the yield stress of steel, r y (MPa). Under the condition of lane strain and mode-i crack, the maximum size of the lastic zone was obtained: r ¼ K Imax ; ð1þ r y where K Imax ðmpa ffiffiffiffi m Þ is the maximum stress intensity factor (SIF) of the crack ti. Considering an mode-i internal enny-crack with a diameter of / (m) in an infinite solid under a uniform remote tensile stress r (MPa), the maximum SIF, K Imax, can also be exressed by [13]: Fig. 4. Aearance of fracture surface, crack initiating at a VC inclusion cluster (54SiCrV6). (Secimen no. 10: the maximum inclusion in the cluster is about 2.2 lm in diameter).

4 Z.G. Yang et al. / International Journal of Fatigue 30 (2008) Table 3 Results of fatigue testing and the data of fracture origins measured from fracture surfaces of investigated steels 50CrV4 54SiCrV6 Secimen no. r (MPa) N f (cycle) / inc (lm) / GBF (lm) Secimen no. r (MPa) N f (cycle) / inc (lm) / GBF (lm) there were evidences that crack growth rate increased sinuately with SIF range [14]. More recently, Paris et al. [15] and Marines et al. [16] still suggested that Paris-tye equation, da/dn = C(DK eff ) n, could be used to redict the growth rate of small internal crack at extremely low rate stage. In this exression, C and n are materials constants deending on stress ratio R, and the exonent n may be a larger number, say of the order of 100 in some cases; the effective SIF range DK eff generally defined as DK eff = (K Imax K Imin )or(k Imax K oen ) that K oen deends on crack closure. And they ointed out further that small cracks such as those growing from small inclusions do not exhibit crack closure, i.e. DK eff K Imax. However, unlike low strength steels, high strength steels ossess of higher strength and higher brittleness so that it is assumed that their fatigue behaviors are rather close to brittle materials, articularly, it is reasonable to assume that material around an inclusion is rather brittle due to hydrogen traed there, in other words, the fatigue crack can also grow in the half-cycle of comressive stress as well as that of tensile stress [17], and when the stress ratio is R = 1, the SIF range can be written as DK ¼ K Imax K Imin ¼ 2K Imax ¼ 4 rffiffiffiffiffiffiffi r / ð4þ 2 As the first order aroximation, the exression about surface crack growth rate is used for describing the internal crack growth, because the latter is very difficult to be measured exerimentally. And since the tensile strength and fatigue strength of steels investigated are quite close to that of a Cr Si sring steel [8], its Paris-tye exression about fatigue crack growth rate at low rate stage is adoted, that is da dn ¼ ðdkþ 9:5 ; ð5þ where the unit of da/dn (equal to d(//2)/dn) is m/cycle. After combining with Eq. (4), the Eq. (5) becomes da dn ¼ 1: r 9:5 / 9:5=2 ð6þ Fig. 5 shows the relation between r and da/dn, vs. the crack size (data from secimen no. 4, 50CrV4 steel). It is obvious that both r and da/dn increase with crack growing. In the earlier stage of crack growth, r is numerically greater than da/dn. However the sloe of the latter is larger than that of the former, therefore when the crack exands to a certain value the two curves intersect at a oint, say, Q. This means that when the crack grows u to the length corresonding to the abscissa of Q, the increment that the crack growing in one stress cycle (defined as Dl, numerically equal to da/dn) is just equal to the size of lastic zone in front of crack ti. After that, the increment of the crack length at each cycle, Dl, is greater than r The size of GBF area estimated from the resent exerimental data Assuming the fatigue crack in GBF area to be a ennycrack, the size of lastic zone in front of crack ti, r, and the increment of the crack growing in each cycle, Dl (numerically equal to da/dn), were calculated according size of lastic zone, r, and crack growth rate, da/dn (or Δl), μm r da/dn (or Δl) Diameter of inclusion Crack length (in diameter), φ, μm Fig. 5. The size of lastic zone and crack growth rate altering with crack size. Q

5 1020 Z.G. Yang et al. / International Journal of Fatigue 30 (2008) to Eqs. (3) and (6), resectively. When the crack reached to the measured size of GBF area, / GBF, as listed in Table 3, the calculation results of r and Dl are listed in Table 4. From Table 4, one can see that the values r and Dl for every secimen at the boundary of GBF area are aroximately equal to each other. In other words, the condition, r = Dl, could be used to determine the size of GBF area. If this is the case, the size of GBF area can be determined by combining Eqs. (3) and (6) / GBF;E ¼ r 0:533 y r ; ð7þ 2 where / GBF,E is the estimated diameter of GBF area, unit in m. This exression illustrates that the size of GBF area on fracture surface is determined by alied stress, along with the yield stress which is affected by microstructure and hydrogen (via influencing on the crack growth rate), etc. The sizes of GBF areas estimated by Eq. (7) for 50CrV4 and 54SiCrV6 steels are listed in Table 5. The estimated sizes of the GBF areas are in well agreement with the measured ones The size of GBF area estimated from other exerimental data To confirm further the availability of Eq. (7), exerimental data from Murakami and co-workers are examined [18 22]. The material used in their work was a Cr Mo martensite steel SCM435. Here, three series of secimens are cited, the first called QT1, the second QT2 and the third VQ. Furthermore, rotating bending fatigue (RBF) tests were carried out for QT1 and VQ secimens and tension comression fatigue (TCF) tests for QT2 secimens. The heat treatment rocedure of QT1 secimens was quenched at 850 C and temered at 170 C. The hardness of this steel was H v = 560 kg f/mm 2 [18]. The sizes of GBF areas are calculated from Fig. 6 (denoted by ODA in original Fig [19]) and their corresonding data (shown in original Fig [20], data of ten secimens offered). The hydrogen concentration was m in these secimens. Eleven QT2 secimens were heat-treated with hardness H v = 562 kgf/mm 2. There were three hydrogen concentration levels in secimens as following: 0.3 m for secimen Table 4 Calculated values of r and Dl (numerically equals da/dn) at the boundary of GBF for secimens of two investigated steels 50CrV4 54SiCrV6 Secimen no. r (lm) Dl (lm) Relative error a (%) Secimen no. r (lm) Dl (lm) Relative error a (%) a Relative error is defined as (D l r )/r 100%. Table 5 The sizes of GBF areas, / GBF and / GBF,E, measured from fracture surface of investigated steels and estimated by Eq. (7), resectively 50CrV4 54SiCrV6 Secimen no. / GBF (lm) / GBF,E (lm) Error a (%) Secimen no. / GBF (lm) / GBF,E (lm) Error a (%) a Error is defined as (/ GBF,E / GBF )// GBF 100%.

6 Z.G. Yang et al. / International Journal of Fatigue 30 (2008) However, because the yield stress of these three series of secimens was not reorted in the references, it has to be estimated by a comarative method using the yield stress and hardness of two steels in our study, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðh v Þ ðh v Þ r y ¼ ðr y Þ ðh v Þ 50CrV4 ðr y Þ 50CrV4 ðh v Þ 54SiCrV6 54SiCrV6 Fig. 6. Relationshi between fatigue life and the ratio of the size of GBF area to that of inclusion for QT1 steel [19]. (This figure has been re-drawn according to the data oints in the original figure in the reference). no. QT2-1 5 (fatigue tests started directly after heat-treated for QT2-1 3, 4300 h after hydrogen charging for QT2-4 and 5), 0.8 m for QT2-8 (fatigue tests started 100 h after hydrogen charging) and 10 m for QT2-11 (fatigue tests started 1.5 h after hydrogen charging) [21]. The VQ secimens (three secimens offered) were heated in a vacuum and quenched and temered under the same condition as QT1 secimens, and the hardness was also 560 kgf/mm 2. This grou of secimens had a hydrogen concentration of 0.01 m [22]. The sizes of inclusions and GBF areas of QT1 and VQ secimens can be gained directly from Refs. [21,22], resectively. therefore the estimated values, r y = 1745 MPa for QT1 and VQ secimens and 1751 MPa for QT2 secimens, are obtained. ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Finally, all the sizes of GBF areas area GBF quoted from the references are converted into diameter by / GBF ¼ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi area GBF = ffiffiffi, and the data of twenty-four secimens are gained. Table 6 shows the sizes of GBF areas, / GBF, obtained by exeriments, and / GBF,E, estimated by Eq. (7). As regards these data, some cautions have to be ointed out: 1. For QT1 and VQ secimens under RBF test condition (13 secimens in all). It can be seen that most of the estimated / GBF,E agree well with the measured / GBF, excet three ones belonging to secimens QT1 1, 8 and 9. The reasons of greater errors may be: (i) different materials studied, including different microstructure and different density of hydrogen in steels, which cause the constants in Eq. (7) deduced from two resent steels not comletely suitable for SCM435 steel; (ii) inaccurate estimation of yield strength for SCM435 steel and (iii) the different testing methods, RBF test for Table 6 The / GBF,E estimated by Eq. (7) with exerimental data in other researchers study Secimen grou Hydrogen concentration Secimen no. r (MPa) N f (cycle) / Inc (lm) / GBF (lm) / GBF,E (lm) Error ** (%) QT m (no GBF area) QT2 0.3 m (no GBF area) m (no GBF area) m (no GBF area) (no GBF area) VQ 0.01 m ** Error is defined as (/ GBF,E / GBF )// GBF 100%.

7 1022 Z.G. Yang et al. / International Journal of Fatigue 30 (2008) Crack Δl Crack Δl Crack Δl GBF area r H GBF area r H GBF area r H Fig. 7. Schematic diagram illustrating the relation between GBF area range and Dl and r. (a) When Dl < r, formation of GBF area continues; (b) when Dl = r, GBF area reaches to its outer boundary; (c) when Dl > r, GBF area disaears. SCM435 steel and TCF test for ours. There is certainly a stress gradient in the cross section of secimen for the RBF test so that the nominal stress is not always consistent with the real stress emloyed at the boundary of GBF area. Besides, there was no GBF area for secimen QT1 2 due to the fact that the exected size of the GBF area was smaller than that of the original inclusion. 2. For QT2 secimens under tension comression fatigue test condition (11 secimens in all). For secimens QT2-2 5 with a hydrogen concentration of 0.3 m, almost all of the relative errors between the estimated and measured sizes of GBF areas are very small. The absence of GBF area on fracture surface of secimen QT2-1 may be attributed to the difficult measurement since the exected size of GBF area is close to that of the original inclusion. However, excet for secimen QT2-6 that exected size of GBF area is smaller than the original inclusion size, the errors of the rest (secimens QT2-7 11) are very large, esecially GBF areas of some secimens disaeared. It is not surrising to notice that these secimens are of higher hydrogen concentrations that result in crack growing faster and the growth rate numerically reaching to the size of the lastic zone quickly. In this case, the size of GBF area should turn out to be a smaller value, and if this value is smaller than the original inclusion size, the GBF area cannot nucleate. Therefore Eq. (7) can only be used reasonably to estimate the sizes of GBF areas for lower hydrogen concentrations in the steels. How the constants in Eq. (7) vary with hydrogen concentrations in steels is an oen question that will be discussed in coming aer. 5. Discussion 5.1. On the criterion to determine the size of GBF area According to Eq. (7), the size of GBF area decreases with increasing alied stress amlitude. This argument agrees well with the exerimental data from all researchers studies elsewhere [6]. It should be noted, if an excessively large stress amlitude r is emloyed so that the size of inclusion that acts as cracking origin in steel exceeds the estimated size of GBF area, GBF will not occur on fracture surface. This is why GBF does not occur at higher stress or low cycle fatigue. Hydrogen has imortant influence on fatigue crack growth in GBF area for high strength steels [3 6,21]. For a fatigue crack initiating from internal inclusions, its environment is almost vacuum, however under tension stress condition, some of the hydrogen dissolved in steel matrix as well as traed in and near the carbide articles and inclusions can diffuse together into the region where the stress is higher [23], and assemble to a larger enough value of density to influence the crack growth behaviors, for examles, crack growth rate, crack growth route, etc. An earlier fatigue crack grew very slowly and the size of lastic zone r was much greater than the increment of crack Dl in each cycle, so the crack extended always in the lastic zone where higher density of hydrogen existed (Fig. 7a). This could cause the secial aearance of fracture surface different from that controlled by ure mechanical factors. If the crack grew fast and the increment Dl was larger than the size r, this is to say, most art of the growing increment was achieved in low-density hydrogen area, hydrogen in the lastic zone would influence infirmly crack growth (Fig. 7c). The boundary of GBF area was just the distinction between the two different areas (Fig. 7b). All in a word, r = Dl is the criterion to determine the size of GBF area. Besides, it has to be emhasized that the small carbide articles in steel may lay the indisensable role in GBF area or earlier crack growing, because hydrogen traed in and near the articles can also weaken the binding force between the articles and steel matrix The maximum SIF at the front of GBF, (K Imax ) GBF When the crack grows to GBF boundary, its maximum SIF can be obtained from combining Eqs. (2) and (7) sffiffiffiffiffiffiffiffiffiffi 1 ðk Imax Þ GBF ¼ 27:87 ðmpa ffiffiffiffi m Þ r 0:533 y This means that (K Imax ) GBF is a constant for a given steel, not deendent on the alied stress amlitude and inclusion size. A similar result had been reorted by Sakai et al. [24] and they considered that constant equal to the threshold SIF for long crack. For 50CrV4 and 54SiCrV6 steels with similar microstructures and aroximate strength, ðk Imax Þ GBF 3:9MPa ffiffiffiffiffiffi m. 6. Conclusions The boundary of GBF area is the lace where the size of lastic zone is equal to the increment of crack growing in one stress cycle. This viewoint is well confirmed by the

8 Z.G. Yang et al. / International Journal of Fatigue 30 (2008) GBF area measured from fracture surfaces of secimens with lower or normal hydrogen concentrations in high strength steels. However, some modifications are needed to redict the size of GBF area for steels with high hydrogen concentration. Acknowledgement This work was financially suorted by key roject of basic research of China (2004CB619100). The authors wish to thank Dr. L. Zhou for her advice and exerimental suorts. References [1] Takai K, Honma Y, Izutsu K, Nagumo M. J Jn Inst Met 1996;60(12): [2] Shiozawa K, Lu L, Ishihara S. Fatigue Fract Engng Mater Struct 2001;24: [3] Murakami Y, Nomoto T, Ueta T. Fatigue Fract Engng Mater Struct 1999;22(7): [4] Murakami Y, Nomoto T, Ueda T, Murakami Y. Fatigue Fract Engng Mater Struct 2000;23(11): [5] Murakami Y, Nomoto T, Ueda T, Murakami Y. Fatigue Fract Engng Mater Struct 2000;23(11): [6] Chaetti MD, Tagawa T, Miyata T. Mater Sci Engng A 2003;A356: [7] Shiozawa K, Morii Y, Nishino S, Lu L. Int J fatigue 2006;28: [8] Wang QY, Berard JY, Rathery S, Bathias C. Fatigue Fract Engng Mater Struct 1999;22: [9] Murakami Y. Metal fatigue: effects of small defects and nonmetallic inclusions. Amsterdam & Boston ed.: Elsevier; [10] Furuya Y, Matsuoka S. Metallur Mater Trans A 2002;33A(11): [11] Yang ZG, Zhang JM, Li SX, Li GY, Wang QY, Hui WJ, et al. Mater Sci Eng A 2006;427: [12] Irwin GR. Proceedings of the seventh Sagamore Ordnance materials conference, vol. 4. New York: Syracuse University; [13] Suresh S. Fatigue of materials [Z G Wang, Trans. in Chinese]. Beijing: National Defense Industry Press; [14] Kinefuchi M., Yokomaku T. In: Bailon JP, Dickson JI, editors. Proceedings of the 5th international conference on fatigue and fatigue thresholds (Fatigue 1993), vol. 1. Montreal, Quebec, Canada: May [15] Paris PC, Marines I, Hertzberg RW, Donald JK. In: Proceeding of VHCF III, Set 16 19, Kusatsu, Jaan: [16] Marines I, Paris PC, Tada H, Bathias C. Int J Fatigue 2007;29: [17] Suresh S. Fatigue of materials [Z G Wang, Trans. in Chinese]. Beijing: National Defense Industry Press; [18] Murakami Y. Metal fatigue: effects of small defects and nonmetallic inclusions. Amsterdam & Boston ed.: Elsevier; [19] Murakami Y. Metal fatigue: effects of small defects and nonmetallic inclusions. Amsterdam & Boston ed.: Elsevier; [20] Murakami Y. Metal fatigue: effects of small defects and nonmetallic inclusions. Amsterdam & Boston ed.: Elsevier; [21] Murakami Y, Matsunaga H. Int J Fatigue 2006;28: [22] Murakami Y. In: Blom AF, and Emas, editors. Proceedings of the 8th international fatigue congress (Fatigue 2002), vol. 5. Stockholm, Sweden, UK: June [23] Chu WY, Qiao LJ, Chen QZ, Gao KW, editors. Fracture and environmental fracture. Beijing: Science Press; [24] Sakai T, Sato Y, Oguma N. Fatigue Fract Engng Mater Struct 2002;25: