Volume 48 Issue 1
Feb.  2018
Turn off MathJax
Article Contents
HONG Youshi, SUN Chengqi, LIU Xiaolong. A review on mechanisms and models for very-high-cycle fatigue of metallic materials[J]. Advances in Mechanics, 2018, 48(1): 1801. doi: 10.6052/1000-0992-17-002
Citation: HONG Youshi, SUN Chengqi, LIU Xiaolong. A review on mechanisms and models for very-high-cycle fatigue of metallic materials[J]. Advances in Mechanics, 2018, 48(1): 1801. doi: 10.6052/1000-0992-17-002

A review on mechanisms and models for very-high-cycle fatigue of metallic materials

doi: 10.6052/1000-0992-17-002
  • Received Date: 2017-01-16
  • Publish Date: 2018-02-08
  • The process of fatigue failure beyond 107 cycles for a metallic material subjected to cyclic load is called very-high-cycle fatigue (VHCF). This review will summarize the research progress of VHCF starting with its origination in early 1980s, until the cutting-edge development in recent years. After Introduction, this review contains following parts: Origination of VHCF research, Main characteristics of VHCF, Characteristic region of crack initiation and related parameters for VHCF, Formation mechanisms and models for characteristic region of crack initiation, and Prediction models of VHCF properties. The relevant descriptions attempt to answer the following questions: What is VHCF? Why VHCF should be investigated? What are the essential scientific issues for VHCF? Why the tendency of S-N curve for VHCF is changed? Why crack initiates from the interior of material (specimen) for VHCF? What are the process and the mechanism of interior crack initiation? Some of the questions will be clearly answered, but some of them be just addressed by newly results, which require further exploration.

     

  • loading
  • [1]
    洪友士, 赵爱国, 钱桂安. 2009. 合金材料超高周疲劳行为的基本特征和影响因素. 金属学报, 45: 769-780

    (Hong Y S, Zhao A G, Qian G A.2009. Essential characteristics and influential factors for very-high-cycle fatigue behavior of metallic materials. Acta Metallurgica Sinica, 45: 769-780).
    [2]
    钱桂安. 2009. 不同介质环境中低合金钢的高周和超高周疲劳实验研究. [博士论文]. 北京: 中国科学院力学研究所

    (Qian G A.2009. Experimental investigation on high cycle and very-high-cycle fatigue behavior of low alloy steel under different environmental media. [PhD Thesis]. Beijing: Institute of Mechanics, Chinese Academy of Sciences).
    [3]
    ASTM E468-90.2004. Annual book of ASTM standards 2006, Section 3, 03.01: 556-561.
    [4]
    Akiniwa Y, Miyamoto N, Tsuru H, Tanaka K.2006. Notch effect on fatigue strength reduction of bearing steel in the very high cycle regime. International Journal of Fatigue, 28: 1555-1565.
    [5]
    Asami K, Sugiyama Y.1985. Fatigue~strength~of~various~surface~hardened~steels. Journal of the Japan Society for Heat~Treatment, 25: 147-150.
    [6]
    Asami K, Emura H.1990. Fatigue strength characteristics of high-strength steel. JSME International Journal Series I-Solid Mechanics Strength of Materials, 33: 367-374.
    [7]
    Atrens A, Hoffelner W, Duerig T W, Allison J E.1983. Subsurface crack initiation in high cycle fatigue in Ti6Al4V and in a typical martensitic stainless steel. Scripta Metallurgica, 17: 601-606.
    [8]
    Bathias C, Paris P C.2005. Gigacycle Fatigue in Mechanical Practice. New York:Marcel Dekker.
    [9]
    Borrego L P, Costa J M, Silva S, Ferreira J M.2004. Microstructure dependent fatigue crack growth in aged hardened aluminium alloys. International Journal of Fatigue, 26: 1321-1331.
    [10]
    Chapetti M D, Tagawa T, Miyata T.2003. Ultra-long cycle fatigue of high-strength carbon steels part II: Estimation of fatigue limit for failure from internal inclusions. Materials Science & Engineering A, 356: 236-244.
    [11]
    Furuya Y.2011. Notable size effects on very high cycle fatigue properties of high-strength steel. Materials Science & Engineering A, 528: 5234-5240.
    [12]
    Furuya Y, Takeuchi E.2014. Gigacycle fatigue properties of Ti-6Al-4V alloy under tensile mean stress. Materials Science & Engineering A, 598: 135-140.
    [13]
    Grad P, Reuscher B, Brodyanski A, Kopnarski M, Kerscher E.2012. Mechanism of fatigue crack initiation and propagation in the very high cycle fatigue regime of high-strength steels. Scripta Materialia, 67: 838-641.
    [14]
    Harlow D G, Wei R P, Sakai T, Oguma N.2006. Crack growth based probability modeling of S-N response for high strength steel. International Journal of Fatigue, 28: 1479-85.
    [15]
    Heinz S, Balle F, Wagner G, Eifler D.2013. Analysis of fatigue properties and failure mechanisms of Ti6Al4V in the very high cycle fatigue regime using ultrasonic technology and 3D laser scanning vibrometry. Ultrasonics, 53: 1433-1440.
    [16]
    Heinz S, Eifler D.2016. Crack initiation mechanisms of Ti6A14V in the very high cycle fatigue regime. International Journal of Fatigue, 93: 301-308.
    [17]
    Hertzberg R W, Vinci R P, Hertzberg J L.2012. Deformation and Fracture Mechanics of Engineering Materials. 5th ed. New York: Wiley.
    [18]
    Holper B, Mayer H, Vasudevan A K, Stanzl-Tschegg S E.2004. Near threshold fatigue crack growth at positive load ratio in aluminium alloys at low and ultrasonic frequency: influences of strain rate, slip behaviour and air humidity. International Journal of Fatigue, 26: 27-38.
    [19]
    Hong Y, Qian G, Zhou C.2009. Experiment and simulation of very-high-cycle fatigue behavior for low alloy steels//Proceedings of the 12th International Conference on Fracture, July 12-17, 2009, Ottawa, Canada, ICF12 CD-ROM, T26.003.
    [20]
    Hong Y, Zhao A, Qian G, Zhou C.2012. Fatigue strength and crack initiation mechanism of very-high-cycle fatigue for low alloy steels. Metallurgical and Materials Transactions A, 43: 2753-2762.
    [21]
    Hong Y, Lei Z, Sun C, Zhao A.2014. Propensities of crack interior initiation and early growth for very-high-cycle fatigue of high strength steels. International Journal of Fatigue, 58: 144-151.
    [22]
    Hong Y, Liu X, Lei Z, Sun C.2016. The formation mechanism of characteristic region at crack initiation for very-high-cycle fatigue of high-strength steels. International Journal of Fatigue, 89: 108-118.
    [23]
    Huang X, Moan T.2007. Improved modeling of the effect of R-ratio on crack growth rate. International Journal of Fatigue, 29: 591-602.
    [24]
    Huang Z Y, Wang C, Wagner D, Bathias C.2014. A very high cycle fatigue thermal dissipation investigation for titanium alloy TC4. Materials Science & Engineering A, 600: 153-158
    [25]
    Huang Z Y, Liu H Q, Wang C, Wang Q Y.2015. Fatigue life dispersion and thermal dissipation investigations for titanium alloy TC17 in very high cycle regime. Fatigue & Fracture of Engineering Materials & Structures, 38: 1285-1293.
    [26]
    Ishida W, Yamamoto T, Kaneda S, Ogawa T.2012. Fatigue strength and internal crack growth behavior of high strength steel under variable amplitude stressing in very high cycle regime. Transaction of Japan Society of Mechanical Engineers A, 78: 23-33.
    [27]
    Jha S K, Ravi Chandran K S.2003. An unusual fatigue phenomenon: duality of the S-N fatigue curve in the β-titanium alloy Ti-10V-2Fe-3Al. Scripta Materialia, 48: 1207-1212.
    [28]
    Jiang Q, Sun C, Liu X, Hong Y.2016. Very-high-cycle fatigue behavior of a structural steel with and without induced surface defects. International Journal of Fatigue, 2016, 93: 352-362.
    [29]
    Kikukawa M, Ohji K, Ogura K.1965. Push-pull fatigue strength of mild steel at very high frequencies of stress up to 100 kc/s. Journal of Basic Engineering, Transactions of the ASME, 87: 857-864.
    [30]
    Kovacs S, Beck T, Singheiser L.2013. Influence of mean stresses on fatigue life and damage of a turbine blade steel in the VHCF-regime. International Journal of Fatigue, 49: 90-99.
    [31]
    Lei Z, Hong Y, Xie J, Sun C, Zhao A.2012. Effects of inclusion size and location on very-high-cycle fatigue behavior for high strength steels. Materials Science & Engineering A, 558: 234-241.
    [32]
    Lei Z, Xie J, Sun C, Hong Y.2014. Effect of loading condition on very-high-cycle fatigue behavior and dominant variable analysis. Science China-Physics Mechanics & Astronomy, 57: 74-82.
    [33]
    Li S X.2012. Effects of inclusions on very high cycle fatigue properties of high strength steels. International Materials Reviews, 57: 92-114.
    [34]
    Li W, Sakai T, Li Q, Lu L T, Wang P.2010. Reliability evaluation on very high cycle fatigue property of GCr15 bearing steel. International Journal of Fatigue, 32: 1096-1107.
    [35]
    Li Y D, Yang Z G, Li S X, Liu Y B, Chen S M.2008. Correlations between very high cycle fatigue properties and inclusions of GCr15 bearing steel. Acta Metallurgica Sinica, 44: 968-972.
    [36]
    Liu X, Sun C, Hong Y.2015. Effects of stress ratio on high-cycle and very-high-cycle fatigue behavior of a Ti-6Al-4V alloy. Materials Science & Engineering A, 622: 228-235.
    [37]
    Liu X, Sun C, Zhou Y, Hong Y.2016a. Effects of microstructure and stress ratio on high-cycle and very-high-cycle fatigue of Ti-6Al-4V alloy. Acta Metallurgica Sinica, 52: 923-930.
    [38]
    Liu X, Sun C, Hong Y.2016b. Faceted crack initiation characteristics for high-cycle and very-high-cycle fatigue of a titanium alloy under different stress ratios. International Journal of Fatigue,92: 434-441.
    [39]
    Liu Y B, Li Y D, Li S X, Yang Z G, Chen S M, Hui W J, Weng Y Q.2010. Prediction of the S-N curves of high-strength steels in the very high cycle fatigue regime. International Journal of Fatigue, 32: 1351-1357.
    [40]
    Marines-Garcia I, Paris P C, Tada H, Bathias C.2007. Fatigue crack growth from small to long cracks in very-high-cycle fatigue with surface and internal "fish-eye" failures for ferrite-perlitic low carbon steel SAE 8620. Materials Science & Engineering A, 468-470: 120-128.
    [41]
    Marines-Garcia I, Paris P C, Tada H, Bathias C, Lados D.2008. Fatigue crack growth from small to large cracks on very high cycle fatigue with fish-eye failures. Engineering Fracture Mechanics, 75: 1657-1665.
    [42]
    Mason W P.1956. Internal friction and fatigue in metals at large strain amplitudes. Journal of the Acoustical Society of America, 28: 1207-1218.
    [43]
    Mayer H.1999. Fatigue crack growth and threshold measurements at very high frequencies. International Materials Reviews, 44: 1-36.
    [44]
    Mayer H, Haydn W, Schuller R, Issler S, Furtner B, Bacher-H"{o}chst M.2009. Very high cycle fatigue properties of bainitic high carbon-chromium steel. International Journal of Fatigue, 31: 242-249.
    [45]
    Mayer H.2016. Recent developments in ultrasonic fatigue. Fatigue & Fracture of Engineering Materials & Structures, 39: 3-29.
    [46]
    Mughrabi H.1999. On the life-controlling microstructural fatigue mechanisms in ductile metals and alloys in the gigacycle regime. Fatigue & Fracture of Engineering Materials & Structures, 22: 633-641.
    [47]
    Mughrabi H.2002. On "multi-stage" fatigue life diagrams and the relevant life-controlling mechanisms in ultrahigh-cycle fatigue. Fatigue & Fracture of Engineering Materials & Structures, 25: 755-764.
    [48]
    Mughrabi H.2009. Cyclic slip irreversibilities and the evolution of fatigue damage. Metallurgical and Materials Transactions A, 40A: 1257-1279.
    [49]
    Mughrabi H.2010. Fatigue, an everlasting materials problem-still en vogue. Procedia Engineering, 2: 3-26.
    [50]
    Murakami Y, Kodama S, Konuma S.1988. Quantitative evaluation of effects of nonmetallic inclusions on fatigue strength of high strength steel. Transactions of the Japan Society of Mechanical Engineers, 54A: 688-695.
    [51]
    Murakami Y, Kodama S, Konuma S.1989. Quantitative evaluation of effects of non-metallic inclusions on fatigue strength of high strength steels. I: Basic fatigue mechanism and evaluation of correlation between the fatigue fracture stress and the size and location of non-metallic inclusions. International Journal of Fatigue, 11: 291-298.
    [52]
    Murakami Y, Usuki H.1989. Quantitative evaluation of effects of non-metallic inclusions on fatigue strength of high strength steels. II: Fatigue limit evaluation based on statistics for extreme values of inclusion size. International Journal of Fatigue, 11: 299-307.
    [53]
    Murakami Y, Nomoto T, Ueda T.1999. Factors influencing the mechanism of superlong fatigue failure in steels. Fatigue & Fracture of Engineering Materials & Structures, 22: 581-590.
    [54]
    Murakami Y, Nomoto T, Ueda T, Murakami Y.2000a. On the mechanism of fatigue failure in the superlong life regime ((N > 10^{7}) cycles), Part I: influence of hydrogen trapped by inclusions. Fatigue & Fracture of Engineering Materials & Structures, 23: 893-902.
    [55]
    Murakami Yu, Nomoto T, Ueda T, Murakami Ya.2000b. On the mechanism of fatigue failure in the superlong life regime ((N > 10 ^{7}) cycles), Part II: a fractographic investigation. Fatigue & Fracture of Engineering Materials & Structures, 23: 903-910.
    [56]
    Murakami Y.2002. Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions. London:Elservier.
    [57]
    Murakami Y, Yokoyama N N, Nagata J.2002b. Mechanism of fatigue failure in ultralong life regime. Fatigue & Fracture of Engineering Materials & Structures, 25: 735-746.
    [58]
    Naito T, Ueda H, Kikuchi M.1983. Observation of fatigue fracture surface of carburized steel. Journal of the Society of Materials Science, Japan, 32: 1162-1166.
    [59]
    Naito T, Ueda H, Kikuchi M.1984. Fatigue behavior of carburized steel with internal oxides and nonmartensitic microstructure near the surface. Metallurgical Transactions A, 15A: 1431-1436.
    [60]
    Nakajima M, Tokaji K, Itoga H, Shimizu T.2010. Effect of loading condition on very high cycle fatigue behavior in a high strength steel. International Journal of Fatigue, 32: 475-480.
    [61]
    Neal D F, Blenkinsop P A.1976. Internal fatigue origins in (alpha -eta ) titanium alloys. Acta Metallurgica, 24: 59-63.
    [62]
    Nishijima S, Kanazawa K.1999. Stepwise S-N curve and fish-eye failure in gigacycle fatigue. Fatigue & Fracture of Engineering Materials & Structures, 22: 601-607.
    [63]
    Nix W D, Gao H J.1998. Indentation size effects in crystalline materials: A law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 46: 411-425.
    [64]
    Ochi Y, Matsumura T, Masaki K, Yoshida S.2002. High-cycle rotating bending fatigue property in very long-life regime of high-strength steels. Fatigue & Fracture of Engineering Materials & Structures, 25: 823-830.
    [65]
    Ogawa T, Stanzl-Tschegg S, Schonbauer B.2014. A fracture mechanics approach to interior fatigue crack growth in the very high cycle regime. Engineering Fracture Mechanics, 115: 241-254.
    [66]
    Oguma N, Harada H, Sakai T.2003. Mechanism of long life fatigue fracture induced by interior inclusion for bearing steel in rotating bending. Journal of the Society of Materials Science,Japan, 52: 1292-1297.
    [67]
    Oguma H, Nakamura T.2010. The effect of microstructure on very high cycle fatigue properties in Ti-6Al-4V. Scripta Materialia, 63: 32-34.
    [68]
    Oguma H, Nakamura T.2013. Fatigue crack propagation properties of Ti-6Al-4V in vacuum environments. International Journal of Fatigue, 50: 89-93.
    [69]
    Pang J C, Li S X, Wang Z G, Zhang Z F.2014. Relations between fatigue strength and other mechanical properties of metallic materials. Fatigue & Fracture of Engineering Materials & Structures, 37: 958-976.
    [70]
    Papakyriacou M, Mayer H, Fuchs U, Stanzl-Tschegg S E, Wei R P.2002. Influence of atmospheric moisture on slow fatigue crack growth at ultrasonic frequency in aluminium and magnesium alloys. Fatigue & Fracture of Engineering Materials & Structures, 25: 795-804.
    [71]
    Paris P C, Tada H, Donald J K.1999. Service load fatigue damage-a historical perspective. International Journal of Fatigue, 21: S35-S46.
    [72]
    Petit J, Sarrazin-Baudoux C.2006. An overview on the influence of the atmosphere environment on ultra-high-cycle fatigue and ultra-slow fatigue crack propagation. International Journal of Fatigue, 28: 1471-1478.
    [73]
    Qian G, Zhou C, Hong Y.2011. Experimental and theoretical investigation of environmental media on very-high-cycle fatigue behavior for a structural steel. Acta Materialia, 59: 1321-1327.
    [74]
    Qian G, Zhou C, Hong Y.2015. A model to predict S-N curves for surface and subsurface crack initiations in different environmental media. International {it Journal of Fatigue}, 71: 35-44.
    [75]
    Ravi Chandran K S, 2005. Duality of fatigue failures of materials caused by Poisson defect statistics of competing failure modes. Nature Materials, 4: 303-308.
    [76]
    Ravi Chandran K S, Jha S K.2005. Duality of the S-N fatigue curve caused by competing failure modes in a titanium alloy and the role of Poisson defect statistics. Acta Materialia, 53: 1867-1881.
    [77]
    Ritchie R O, Davidson D L, Boyce B L, Campbell J P, Roder O.1999. High-cycle fatigue of Ti-6Al-4V. Fatigue & Fracture of Engineering Materials & Structures, 22: 621-631.
    [78]
    Sakai T. Takeda M, Shiozawa K, Ochi Y, Nakajima M, Nakamura T, Oguma N.2000. Experimental reconfirmation of characteristic S-N property for high carbon chromium bearing steel in wide life region in rotating bending. Journal of the Society of Materials Science, Japan, 49: 779-785.
    [79]
    Sakai T, Takeda M, Tanaka N, Kanemitsu M, Oguma N, Shiozawa K.2001. S-N property and fractography of high carbon chromium bearing steel over ultra wide life region under rotating bending. Transactions of the Japan Society of Mechanical Engineers, 67A: 1805-1812.
    [80]
    Sakai T, Sato Y, Oguma N.2002. Characteristic S-N properties of high-carbon-chromium-bearing steel under axial loading in long-life fatigue. Fatigue & Fracture of Engineering Materials & Structures, 25: 765-773.
    [81]
    Sakai T, Sato Y, Nagano Y, Takeda M, Oguma N.2006. Effect of stress ratio on long life fatigue behavior of high carbon chromium bearing steel under axial loading. International Journal of Fatigue, 28: 1547-1554.
    [82]
    Sakai T.2009. Review and prospects for current studies on very high cycle fatigue of metallic materials for machine structural use. Journal of Solid Mechanics and Materials Engineering, 3: 425-39.
    [83]
    Sakai T, Oguma N, Morikawa A.2015. Microscopic and nanoscopic observations of metallurgical structures around inclusions at interior crack initiation site for a bearing steel in very high-cycle fatigue. Fatigue & Fracture of Engineering Materials & Structures, 38: 1305-1314.
    [84]
    Sander M, M"{u}ller T, Lebahn J.2014. Influence of mean stress and variable amplitude loading on the fatigue behaviour of a high-strength steel in VHCF regime. International Journal of Fatigue, 62: 10-20.
    [85]
    Sander M, M"{u}ller T, St"{a}cker C.2016. Very high cycle fatigue behavior under constant and variable amplitude loading. Procedia Structural Integrity, 2: 34-41.
    [86]
    Shanyavskiy A A.2013. Mechanisms and modeling of subsurface fatigue cracking in metals. Engineering Fracture Mechanics, 110: 350-363.
    [87]
    Shiozawa K, Lu L, Ishihara S.2001. S-N curve characteristics and subsurface crack initiation behaviour in ultra-long life fatigue of a high carbon-chromium bearing steel. Fatigue & Fracture of Engineering Materials & Structures, 24: 781-790.
    [88]
    Shiozawa K, Lu L.2002. Very high-cycle fatigue behaviour of shot-peened high-carbon-chromium bearing steel. Fatigue & Fracture of Engineering Materials & Structures, 25: 813-822.
    [89]
    Shiozawa K, Morii Y, Nishino S.2006a. Subsurface crack initiation and propagation mechanism under the super-long fatigue regime for high speed tool steel (JIS SKH51) by fracture surface topographic analysis. JSME International Journal Series A-Solid Mechanics and Material Engineering, 49: 1-10.
    [90]
    Shiozawa K, Morii Y, Nishino S, Lu L.2006b. Subsurface crack initiation and propagation mechanism in high strength steel in a very high cycle fatigue regime. International Journal of Fatigue, 28: 1521-1532.
    [91]
    Shiozawa K, Hasegawa T, Kashiwagi Y, Lu L.2009. Very high cycle fatigue properties of bearing steel under axial loading condition. International Journal of Fatigue, 31: 880-888.
    [92]
    Stanzl S E, Tschegg E K, Mayer H.1986. Lifetime measurements for random loading in the very high cycle fatigue range. International Journal of Fatigue, 8: 195-200.
    [93]
    Stanzl-Tschegg S, Schonbauer B.2010. Near-threshold crack propagation and internal cracks in steel. Procedia Engineering, 2: 1547-1555.
    [94]
    Stanzl-Tschegg S.2014. Very high cycle fatigue measuring techniques. International Journal of Fatigue, 60: 2-17.
    [95]
    Stepanskiy L G.2012. Cumulative model of very high cycle fatigue. Fatigue & Fracture of Engineering Materials & Structures, 35: 513-522.
    [96]
    Su H, Liu X, Sun C, Hong Y.2017. Nanograin layer formation at crack initiation region for very-high-cycle fatigue of a Ti-6Al-4V alloy. Fatigue & Fracture of Engineering Materials & Structures, 40: 979-993.
    [97]
    Sun C, Xie J, Zhao A, Hong Y.2012. A cumulative damage model for fatigue life estimation of high-strength steels in high-cycle and very-high-cycle fatigue regimes. Fatigue & Fracture of Engineering Materials & Structures, 35: 638-647.
    [98]
    Sun C, Lei Z, Xie J, Hong Y.2013. Effects of inclusion size and stress ratio on fatigue strength for high-strength steels with fish-eye mode failure. International Journal of Fatigue, 48: 19-27.
    [99]
    Sun C, Lei Z, Hong Y.2014. Effects of stress ratio on crack growth rate and fatigue strength for high cycle and very-high-cycle fatigue of metallic materials. Mechanics of Materials, 69: 227-236.
    [100]
    Sun C, Liu X, Hong Y.2015. A two-parameter model to predict fatigue life of high-strength steels in a very high cycle fatigue regime. Acta Mechanica Sinica, 31: 383-391.
    [101]
    Sun C, Zhang X, Liu X, Hong Y.2016. Effects of specimen size on fatigue life of metallic materials in high-cycle and very-high-cycle fatigue regimes. Fatigue & Fracture of Engineering Materials & Structures, 39: 770-779.
    [102]
    Szczepanski C J, Jha S K, Larsen J M, Jones J W.2008. Microstructural influences on very high cycle fatigue crack initiation in Ti-6246. Metallurgical and Materials Transactions A, 39: 2841-2851.
    [103]
    Takai K, Seki J, Seki J, Honma Y.1995. Observation of trapping sites of hydrogen and deuterium in high-strength steels by using secondary ion mass spectrometry. Materials Transactions,JIM, 36: 1134-1139.
    [104]
    Takai K, Honma Y, Izutsu K, Nagumo M.1996. Identification of trapping sites in high-strength steels by secondary ion mass spectrometry for thermally desorbed hydrogen. The Journal of the Japan Institute of Metals, 60: 1155-1162.
    [105]
    Takeuchi E, Furuya Y, Nagashima N, Matsuoka S.2008. The effect of frequency on the giga-cycle fatigue properties of a Ti-6Al-4V alloy. Fatigue & Fracture of Engineering Materials & Structures, 31: 599-605.
    [106]
    Takeuchi E, Furuya Y, Nagashima N, Matsuoka S.2010. Effect of stressratio on giga-cycle fatigue properties for Ti-6Al-4V Alloy. Tetsu-to-Hagan'{e}, 96: 36-41.
    [107]
    Tanaka K, Mura T.1982. A theory of fatigue crack initiation at inclusions. Metallurgical Transactions A, 13A: 117-123.
    [108]
    Tanaka K, Akiniwa Y.2002. Fatigue crack propagation behaviour derived from S-N data in very high cycle regime. Fatigue & Fracture of Engineering Materials & Structures, 25: 775-784.
    [109]
    Tien J K.1982. The state of ultrasonic fatigue (keynote address). Ultrasonic Fatigue//Proceedings of the First International Conference on Fatigue and Corrosion Fatigue up to Ultrasonic Frequencies, The Metallurgical Society of AIME, New York: 1-14.
    [110]
    Wang Q Y, Berard J Y, Rathery S, Bathias C.1999. High-cycle fatigue crack initiation and propagation gehaviour of high-strength spring steel wires. Fatigue & Fracture of Engineering Materials & Structures, 22: 673-677.
    [111]
    Wang Q Y, Bathias C, Kawagoishi N, Chen Q.2002. Effect of inclusion on subsurface crack initiation and gigacycle fatigue strength. International Journal of Fatigue, 24: 1269-1274.
    [112]
    Willertz L E.1980. Ultrasonic fatigue. International Metals Reviews, 25: 65-78.
    [113]
    Wells J M, Buck O, Roth L D,Tien J K.1982. Ultrasonic fatigue//Proceedings of the First International Conference on Fatigue and Corrosion Fatigue up to Ultrasonic Frequencies, The Metallurgical Society of AIME. New York.
    [114]
    W"{o}hler A.1867. W"{o}hler's experiments on the strength of metals. Engineering, 4: 160-161.
    [115]
    Yang Z G, Li S X, Liu Y B, Li Y D, Li G Y, Hui W J, Weng Y Q.2008. Estimation of the size of GBF area on fracture surface for high strength steels in very high cycle fatigue regime. International Journal of Fatigue, 30: 1016-1023.
    [116]
    Yu Y, Gu J L, Shou F L, Xu L, Bai B Z, Liu Y B.2011. Competition mechanism between microstructure type and inclusion level in determining VHCF behavior of bainite/martensite dual phase steels. International Journal of Fatigue, 33: 500-506.
    [117]
    Zerbst U, Beretta S, Koehler G, Lawton A, Vormwald M, Beier H Th, Klinger C, Cerny I, Rudlin J, Heckel T, Klingbeil D.2013. Safe life and damage tolerance aspects of railway axles---A review. Engineering Fracture Mechanics, 98: 214-271.
    [118]
    Zhang M, Wang W, Wang P, Liu Y, Li J.2016. The fatigue behavior and mechanism of FV520B-I with large surface roughness in a very high cycle regime. Engineering Failure Analysis, 66: 432-444.
    [119]
    Zhao A, Xie J, Sun C, Lei Z, Hong Y.2011. Prediction of threshold value for FGA formation. Materials Science & Engineering A, 528: 6872-6877.
    [120]
    Zhao A, Xie J, Sun C, Lei Z, Hong Y.2012. Effects of strength level and loading frequency on very-high-cycle fatigue behavior for a bearing steel. International Journal of Fatigue, 38: 46-56.
    [121]
    Zhao S, Xie J, Zhao A, Wu X.2014. An energy-equilibrium model for complex stress effect on fatigue crack initiation. Science China Physics, Mechanics & Astronomy, 57: 916-926.
    [122]
    Zhao Y X, Yang B, Feng M F, Wang H.2009. Probabilistic fatigue S-N curves including the super-long life regime of a railway axle steel. International Journal of Fatigue, 31: 1550-1558.
    [123]
    Zimmermann M.2012. Diversity of damage evolution during cyclic loading at very high numbers of cycles. International Materials Reviews, 57: 73-91.
    [124]
    Zuo J H, Wang Z G, Han E H.2008. Effect of microstructure on ultra-high cycle fatigue behavior of Ti-6Al-4V. Materials Science & Engineering A, 473: 147-152.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (4096) PDF downloads(2313) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return