• Dominique François
  • André Pineau
  • André Zaoui
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 191)


The main fatigue tests: rotating bar, axial force and strain controlled, torque controlled fatigue tests, as well as crack propagation fatigue tests are described. Gigacycle fatigue tests method is also explained. Fatigue crack nucleation results from strain irreversibility. Cyclic loading modifies the dislocations arrangements. Inclusions can be initiation sites in fatigue. The propagation of long cracks is linked with the cyclic plastic zone at the crack tip. Striations on the fracture surface result. Short cracks propagation is influenced essentially by the microstructure. Notches are preferential sites for fatigue cracks nucleation; the strain field at the notch root modifies the way they propagate. The Wöhler (or SN) curves can be described by empirical equations. Various formulations exist to account for the mean stress effect. Multiaxial loading is discussed. It is shown how cumulative damage can be represented. In low cycle fatigue, cyclic strain-hardening and the laws for the fatigue strength are described. There exist methods to account for the influence of notches. The Paris law and the way it is influenced by crack closure are described. Short cracks behave in a different manner from long ones. Over-loads slow down or even stop crack propagation. Testing under vacuum displays the intrinsic crack propagation behaviour. Surface treatments can improve the resistance to fatigue. Metallurgical factors influence fatigue behaviour. The case of titanium alloys is discussed in particular.


Fatigue Crack Fatigue Life Plastic Zone Stress Intensity Factor Test Piece 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Alexandre F, Deyber S, Pineau A (2004) Modelling the optimum grain size on the low-cycle fatigue life of a Ni-based superalloy in the presence of two possible crack initiation sites. Scrip Mater 50:25–30CrossRefGoogle Scholar
  2. ASTM (2011) ASTM standard E 1049-85 (2011) Standard practices for cycle counting in fatigue analysis. ASTM International, West Conshohocken, PAGoogle Scholar
  3. Bathias C (2010a) Gigacycle fatigue. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 179–226Google Scholar
  4. Bathias C (2010b) Plastic deformation mechanisms at the crack tip. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 311–343Google Scholar
  5. Bathias C, Pineau A (2010) Introduction to fatigue, fundamentals and methodology. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 1–19Google Scholar
  6. Baumel A, Seeger T (1990) Materials data for cyclic loading. Elsevier, OxfordGoogle Scholar
  7. Brown MW, Miller KJ (1973) A theory of fatigue failure under multiaxial stress-strain conditions. Proc Inst Mech Eng 187:745–755Google Scholar
  8. Brun G, Gauthier J-P, Pétrequin P (1976) Study of low cycle fatigue in a steel type 316L. Mém Sci Rev Met 73:461–483Google Scholar
  9. Buthod H, Lieurade H-P (1986) Influence des propriétés mécaniques sur les caractéristiques d’endurance en flexion d’une gamme étendue d’aciers. Rev de Met 83:485–491Google Scholar
  10. Calabrese C, Laird C (1974) Cyclic stress-strain response of two-phase alloys. 1. Microstructures containing particles penetrable by dislocations. Mater Sci Eng 13:141–149CrossRefGoogle Scholar
  11. Carpinteri A, Paggi M (2007) Are the Paris law parameters dependent on each other? Atti del Congresso, 19, Milano, pp 10–16Google Scholar
  12. Chaboche J-L (1974) Une loi différentielle d’endommagement de fatigue avec cumulation non-linéaire. Revue française de mécanique 50–51:71–82Google Scholar
  13. Chaboche J-L (2011) Cumulative damage. In: Bathias C, Pineau A (eds) Fatigue of materials and structures, application to design and damage. Wiley, Hoboken, pp 47–104Google Scholar
  14. Coffin LF Jr (1954) A study of the effect of cyclic thermal stresses on a ductile metal. Trans ASME 76:931–950Google Scholar
  15. Dang Van K (1973) Mémorial de l’artillerie française. Science et Technique de l’Armement 47:641–722Google Scholar
  16. Deyber S, Alexandre F, Vaissaud J, Pineau A (2006) Probabilistic life of DA718 for aircraft engine disks. In: Superalloys 718, 625, 706 and various derivatives (2005). TMS (The Minerals, Metals and Materials Society), Philadelphia, pp 97–110Google Scholar
  17. Doquet V (2009) Plasticité cyclique et amorçage de fissures en fatigue. In: Clavel M, Bompard P (eds) Endommagement et rupture des matériaux, vol 1. Hermes-Lavoisier, Paris, pp 135–172Google Scholar
  18. Dowling NE (1977) Crack growth during low cycle fatigue of smooth axial specimens. In: Cyclic stress-strain and plastic deformation aspects of fatigue crack growth. ASTM STP 637. ASTM, West Conshohocken, PA, pp 97–121Google Scholar
  19. El Haddad MH, Smith KN, Topper TH (1979) A stress based intensity factor solution for short fatigue cracks initiating from notches. In: Fracture Mechanics. Proceedings of the Eleventh National Symposium on Fracture Mechanics: Part I. ASTM STP 677. ASTM, West Conshohocken, PA, pp 274–289Google Scholar
  20. Elber W (1971) The significance of crack closure. In: Damage tolerance in aircraft structures. ASTM STP 486. ASTM, West Conshohocken, PA, pp 230–242Google Scholar
  21. Espinosa G (1995) La propagation des fissures courtes à partir d’entailles. Ph.D. thesis, École Polytechnique de Montréal, CanadaGoogle Scholar
  22. Fatemi A, Yang L (1998) Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. Int J Fatigue 20:9–34CrossRefGoogle Scholar
  23. Fournier D, Pineau A (1977) Low-cycle fatigue behavior of inconel 718 at 298 K and 823 K. Metall Trans 8A:1095–1105Google Scholar
  24. Frost NE (1959) A relation between the critical alternating propagation stress and crack length for mild steel. Proc Inst Mech Eng 173:811–827CrossRefGoogle Scholar
  25. Gallet G, Lieurade H-P (1974) Influence de la structure métallographique d’un acier au Ni-Cr-Mo sur son comportement en fatigue plastique. Rapport IRSID, Nov 1974Google Scholar
  26. Grosskreutz JC (1971) Mechanisms of metal fatigue. Phys Stat Sol B 47:11–31CrossRefGoogle Scholar
  27. Hahn GT, Hoagland RG, Rosenfield AR (1972) Local yielding attending fatigue crack growth. Met Trans 3:1189–1202CrossRefGoogle Scholar
  28. Hamam R, Pommier S, Bumieler F (2007) Variable amplitude fatigue crack growth, experimental results and modelling. Int J Fatigue 29:1634–1646zbMATHCrossRefGoogle Scholar
  29. Hobson PD, Brown MW, de los Rios ER (1986) Two phases of short crack growth in a medium carbon steel. In: Miller KJ, de los Rios ER (eds) The behaviour of short fatigue cracks. Mechanical Engineering Publications, London, pp 441–459Google Scholar
  30. ISO 1099:2006 Metallic materials – fatigue testing – axial force-controlled methodGoogle Scholar
  31. ISO 1143:2010 Metallic materials – fatigue testing – rotating bar bending fatigue testingGoogle Scholar
  32. ISO 1352:2011 Metallic materials – fatigue testing – torque controlled fatigue testingGoogle Scholar
  33. ISO 12106:2003 Metallic materials – fatigue testing – axial strain controlled methodGoogle Scholar
  34. ISO 12107:2003 Metallic materials – fatigue testing –statistical planning and analysis of dataGoogle Scholar
  35. ISO 12108:2002 Metallic materials – fatigue testing – fatigue crack growth methodGoogle Scholar
  36. James MN, Sharpe WN Jr (1989) Closure development and crack opening displacement in the short crack regime for fine and coarse grained A533b steel. Fatigue Fract Eng Mater Struct 12:347–361CrossRefGoogle Scholar
  37. Journet B-G, Lefrançois A, Pineau A (1989) A crack closure study to predict the threshold behaviour of small cracks. Fatigue Fract Eng Mater Struct 12:237–246CrossRefGoogle Scholar
  38. Kitagawa H, Takahashi S (1976) Applicability of fracture mechanics to very small cracks or cracks at an early stage. In: Proceedings of the 2nd international conference on mechanical behaviour of materials, Boston, pp 627–631Google Scholar
  39. Klesnil M, Lukas P (1965) Dislocation arrangements in surface layer of alpha-iron grains during cyclic loading. J Iron Steel Inst 203:1043–1048Google Scholar
  40. Lankford J (1985) Influence of microstructure on the growth of short fatigue cracks. Fatigue Fract Eng Mater Struct 8:161–175CrossRefGoogle Scholar
  41. Laue S, Baumas H (2006) Spectrum fatigue life assessment of notched specimens based on the initiation and propagation of short fatigue cracks. Int J Fatigue 28–29:1011–1021CrossRefGoogle Scholar
  42. Lee TK, Morris JW, Lee S, Clarke J (2006) Detection of fatigue damage prior to crack initiation with scanning SQUID microscopy. AIP Conf Proc 820:1378–1385CrossRefGoogle Scholar
  43. Leis BN (1982) Fatigue crack propagation through inelastic gradient fields. Int J Press Vessel Pip 10:141–158CrossRefGoogle Scholar
  44. Levaillant C, Pineau A (1983) Assessment of high temperature low-cycle fatigue life of austenitic stainless steels by using intergranular damage as a correlating parameter. In low-cycle fatigue and life prediction ASTM STP770:169–193Google Scholar
  45. Lieurade H-P, Degallaix S, Degallaix G, Gauthier J-P (2008) Fatigue tests. In: François D (ed) Structural components. Wiley, Hoboken, pp 125–192CrossRefGoogle Scholar
  46. Lieurade H-P, Bastenaire F, Régnier L (2010) Modeling of fatigue strength and endurance curve. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 23–66Google Scholar
  47. Lukas P, Klesnil M (1973) Cyclic stress strain response and fatigue life of metals in low amplitude region. Mater Sci Eng 11:345–356CrossRefGoogle Scholar
  48. Manson SS (1952) Behavior of materials under conditions of thermal stress. Heat transfer symposium. University of Michigan Press, Lansing, pp 27–28, 9–76Google Scholar
  49. Manson SS (1972) Pressure vessels and piping, analysis and design. ASME, New YorkGoogle Scholar
  50. Manson SS, Halford GR (2006) Fatigue and durability of structural materials. ASM International, Materials ParkGoogle Scholar
  51. Masounave J, Baïlon J-P, Dickson JI (2010) Fatigue crack growth laws. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 231–261Google Scholar
  52. McEvily AJ, Minakawa K, Nakamura H (1984) Fracture mechanics, microstructure and the growth of short and long cracks. In: Wells J, Stolz T, Landes J (eds) Fracture: interactions of microstructures, mechanisms and mechanics. Proceedings of the AIME symposium, Warrendale, PA, pp 215–233Google Scholar
  53. Miller KJ (1993) The two thresholds of fatigue behaviour. Fatigue Fract Eng Mater Struct 11:931–939Google Scholar
  54. Minakawa K, Nakamura M, McEvily AJ (1984) On the development of crack closure with crack advance in a ferritic steel. Scrip Metall 18:1371–1374CrossRefGoogle Scholar
  55. Miner MA (1945) Cumulative damage in fatigue. J Appl Mech 12:A159–A164Google Scholar
  56. Mughrabi H (1988) Dislocations clustering and long range internal stresses in monotonically and cyclically deformed metal crystals. Revue Phys Appl 23:367–379CrossRefGoogle Scholar
  57. Murakami Y (2002) Metal fatigue – effects of small defects and nonmetallic inclusions. Elsevier Science Ltd, OxfordGoogle Scholar
  58. Murakami Y, Endo M (1983) Quantitative evaluation of fatigue strength of metals containing various small defects or cracks. Eng Fract Mech 17:1–15CrossRefGoogle Scholar
  59. Murakami Y, Endo M (1986) Effects of hardness and crack geometries on ΔK th of small cracks emanating from small defects. In: The behaviour of short fatigue cracks. Mechanical Engineering Publications, London, pp 275–293Google Scholar
  60. Murakami Y, Usukuki H (1989) Quantitative evaluation of effects of non-metallic inclusions on fatigue strength of high strength steels. II. Fatigue limit evaluation based on statistics of extreme values of inclusion size. Int J Fatigue 11:299–307CrossRefGoogle Scholar
  61. Murakami Y, Kodama S, Komina S (1989) Quantitative evaluation of effects of non-metallic inclusions on fatigue strength of high strength steels. I. Basic fatigue mechanisms and evaluation of the correlation between the fatigue stress and the size and location of non-metallic inclusions. Int J Fatigue 11:291–298CrossRefGoogle Scholar
  62. Murakami Y, Uemura Y, Natsume Y, Miyakawa S (1990) Effect of mean stress on the fatigue strength of high strength steels containing small defects or non-metallic inclusions. Trans J SME 56:1074–1081Google Scholar
  63. Muralidharan U, Manson SS (1988) A modified universal slopes equation for estimation of fatigue characteristics of metals. Trans ASME 110:55–58Google Scholar
  64. Navarro A, de Los Rios ER (1988) A micro-structurally-short crack growth equation. Fatigue Fract Eng Mater Struc 11:383–396CrossRefGoogle Scholar
  65. Palin-Luc T (2010) Fatigue under variable amplitude loadings. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 457–502Google Scholar
  66. Papadopoulos IV (1999) Multiaxial fatigue limit criterion for metals: a mesoscopic scale approach. In: Dang Van K, Papadopoulos IV (eds) High-cycle metal fatigue: from theory to applications. CISM courses and lectures, 392. Springer, Wien/New York, pp 89–143Google Scholar
  67. Paris PC, Erdogan F (1963) A critical analysis of crack propagation laws. Trans ASME 85D:528–534Google Scholar
  68. Pelloux RM (1969) Mechanism of formation of ductile fatigue striations. Trans ASM 62:281–285Google Scholar
  69. Petit J, Sarrazin-Baudoux C (2010) Effect of environment. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 401–444Google Scholar
  70. Petit J, Henaff G, Sarrazin-Baudoux C (2003) Environmentally assisted fatigue in gaseous atmosphere. In: Petit J, Scott P (eds) Comprehensive structural integrity, vol 6. Elsevier, Amsterdam, pp 211–280CrossRefGoogle Scholar
  71. Pineau A (2010) Low-cycle fatigue. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 113–173Google Scholar
  72. Pineau A, Antolovich S (2011) Intergranular fatigue. Chapter 5. In: Priester L (ed) Grain boundaries and crystalline plasticity. ISTE/Wiley, London/Hoboken, pp 217–280Google Scholar
  73. Plumtree A, Abdel-Raouf HA (2001) Cyclic stress-strain response and substructure. Int J Fatigue 23:799–805CrossRefGoogle Scholar
  74. Polak J (1991) Cyclic plasticity and low cycle fatigue life of metals. Academia, PragueGoogle Scholar
  75. Pommier S (2010) Local approach to crack growth. In: Bathias C and Pineau A (eds) In Fatigue of materials and structures; fundamentals. Wiley Hoboken:347–373Google Scholar
  76. Ritchie RO (1999) Mechanisms of fatigue crack propagation in ductile and brittle solids. Int J Fract 100:55–83CrossRefGoogle Scholar
  77. Skelton RP (1975) High strain fatigue of 20Cr25NiNb at 1025 K part III crack propagation. Mat Sci Eng 19:193–200CrossRefGoogle Scholar
  78. Smith RA (1990) The Versailles railway accident of 1842 and the first research into metal fatigue. In Fatigue 90 EMAS Birmingham:2033–2041Google Scholar
  79. Suresh S (1998) Fatigue of materials, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  80. Tanaka K, Mura T (1981) A dislocation model for fatigue crack initiation. J Appl Mech 48:97–103zbMATHCrossRefGoogle Scholar
  81. Taylor D (1989) Fatigue thresholds. Butterworths, LondonGoogle Scholar
  82. Thielen PN, Fine ME, Fournelle RA (1976) Cyclic stress-strain relations and strain-controlled fatigue in 4140 steel. Acta Metall 24:1–10CrossRefGoogle Scholar
  83. Tokaji K, Ogawa T, Ohya K (1994) The effect of grain size on small fatigue crack growth in pure titanium. Int J Fatigue 16:571–578CrossRefGoogle Scholar
  84. Tomkins B (1968) Fatigue crack propagation – an analysis. Philos Mag 18:1041–1066CrossRefGoogle Scholar
  85. van Swam LF, Pelloux RM, Grant NJ (1975) Fatigue behavior of maraging-steel 300. Metall Trans 6A:45–54Google Scholar
  86. Verreman Y (2010) Short crack propagation. In: Bathias C, Pineau A (eds) Fatigue of materials and structures; fundamentals. Wiley, Hoboken, pp 269–303Google Scholar
  87. Verreman Y, Espinosa G (1997) Mechanically short crack growth from notches in a mild steel. Fatigue Fract Eng Mater Struct 20:129–142CrossRefGoogle Scholar
  88. Wagner L, Bigoney JK (2003) Fatigue of titanium alloys. Fundamental and applications. Chapter 5. In: Leyens C, Peters M (eds) Titanium and titanium alloys. Wiley VCH Verlag GmbH and Co, Weinheim, pp 153–185Google Scholar
  89. Weibull W (1961) Fatigue testing and analysis of results. Pergamon, OxfordGoogle Scholar
  90. Wheeler OE (1972) Spectrum loading and crack growth. J Basic Eng 4:181–186CrossRefGoogle Scholar
  91. Willenborg J, Engle RM, Wood HA (1971) Crack retardation model using an effective stress concept. AFFDL-TM 71-1Google Scholar
  92. Wöhler A (1870) Über die Festigkeitsversuche mit Eisen und Stahl. Zeitschrift für Bauwesen 20:73–106Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Dominique François
    • 1
  • André Pineau
    • 2
    • 3
  • André Zaoui
    • 3
    • 4
  1. 1.École Centrale de ParisParisFrance
  2. 2.École des Mines de Paris Paris Tech Centre des Matériaux UMR CNRSÉvry CedexFrance
  3. 3.Academy of EngineeringParisFrance
  4. 4.French Académie des SciencesParisFrance

Personalised recommendations