Skip to main content
Log in

Modeling and Prediction of Fatigue Properties of Additively Manufactured Metals

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Additive manufacturing (AM) has emerged as an advanced technique for the fabrication of complex near-net shaped and light-weight metallic parts with acceptable mechanical performance. The strength of AM metals has been confirmed comparable or even superior to that of metals manufactured by conventional processes, but the fatigue performance is still a knotty issue that may hinder the substitution of currently used metallic components by AM counterparts when the cyclic loading and thus fatigue failure dominates. As essential complements to high-cost and time-consuming experimental fatigue tests of AM metals, models for fatigue performance prediction are highly desirable. In this review, different models for predicting the fatigue properties of AM metals are summarized in terms of fatigue life, fatigue limit and fatigue crack growth, with a focus on the incorporation of AM characteristics such as AM defect and processing parameters into the models. For predicting the fatigue life of AM metals, empirical models and theoretical models (including local characteristic model, continuum damage mechanics model and probabilistic method) are presented. In terms of fatigue limit, the introduced models involve the Kitagawa–Takahashi model, the Murakami model, the El-Haddad model, etc. For modeling the fatigue crack growth of AM metals, the summarized methodologies include the Paris equation, the Hartman-Schijve equation, the NASGRO equation, the small-crack growth model, and numerical methods. Most of these models for AM metals are similar to those for conventionally processed materials, but are modified and pay more attention to the AM characteristics. Finally, an outlook for possible directions of the modeling and prediction of fatigue properties of AM metals is provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31

Similar content being viewed by others

References

  1. Wong KV, Hernandez A. A review of additive manufacturing. ISRN Mech Eng. 2012;2012:208760.

    Google Scholar 

  2. Beaman J, Bourell DL, Seepersad C, Kovar D. Additive manufacturing review: Early past to current practice. J Manuf Sci Eng. 2020;142(11):110812.

    Google Scholar 

  3. Li D, Qin R, Xu J, Zhou J, Chen B. Improving mechanical properties and energy absorption of additive manufacturing lattice structure by struts’node strengthening. Acta Mech Solida Sinica. 2022;35:1004–20.

    Google Scholar 

  4. Huang SH, Liu P, Mokasdar A, Hou L. Additive manufacturing and its societal impact: a literature review. Int J Adv Manufact Technol. 2013;67(5):1191–203.

    Google Scholar 

  5. Li N, Huang S, Zhang G, Qin R, Liu W, Xiong H, et al. Progress in additive manufacturing on new materials: a review. J Mater Sci Technol. 2019;35(2):242–69.

    Google Scholar 

  6. Schütz W. A history of fatigue. Eng Fract Mech. 1996;54(2):263–300.

    Google Scholar 

  7. Thompson SM, Bian L, Shamsaei N, Yadollahi A. An overview of direct laser deposition for additive manufacturing; part I: transport phenomena, modeling and diagnostics. Addit Manuf. 2015;8:36–62.

    Google Scholar 

  8. Yi M, Xu BX, Gutfleisch O. Computational study on microstructure evolution and magnetic property of laser additively manufactured magnetic materials. Comput Mech. 2019;64(4):917–35.

    MathSciNet  MATH  Google Scholar 

  9. Liu J, Pan X, Li Y, Chen X. A two-point method for multiaxial fatigue life prediction. Acta Mech Solida Sin. 2022;35:316–27.

    Google Scholar 

  10. Zhao T, Kang G. Fatigue life prediction for NiTi shape memory alloy microtubes under uniaxial stress-controlled one-way shape memory cyclic loading. Acta Mech Solida Sin. 2022;35:15–25.

    Google Scholar 

  11. Liu F, He C, Chen Y, Zhang H, Wang Q, Liu Y. Effects of defects on tensile and fatigue behaviors of selective laser melted titanium alloy in very high cycle regime. Int J Fatigue. 2020;140:105795.

    Google Scholar 

  12. Biswal R, Zhang X, Syed AK, Awd M, Ding J, Walther F, et al. Criticality of porosity defects on the fatigue performance of wire + arc additive manufactured titanium alloy. Int J Fatigue. 2019;122:208–17.

    Google Scholar 

  13. Wang S, Zhan L, Xi H, Xiao H. A unified approach toward simulating constant and varying amplitude fatigue failure effects of metals with east and effcient algorithms. Acta Mech Solida Sin. 2021;34:53–64.

    Google Scholar 

  14. Selcuk C. Laser metal deposition for powder metallurgy parts. Powder Metall. 2011;54(2):94–9.

    Google Scholar 

  15. Frazier WE. Metal additive manufacturing: a review. J Mater Eng Perform. 2014;23:1917–28.

    Google Scholar 

  16. Shamsaei N, Yadollahi A, Bian L, Thompson SM. An overview of direct laser deposition for additive manufacturing; part ii: mechanical behavior, process parameter optimization and control. Addit Manuf. 2015;8:12–35.

    Google Scholar 

  17. Townsend A, Senin N, Blunt L, Leach RK, Taylor JS. Surface texture metrology for metal additive manufacturing: a review. Precis Eng. 2016;46:34–47.

    Google Scholar 

  18. Yadollahi A, Shamsaei N. Additive manufacturing of fatigue resistant materials: challenges and opportunities. Int J Fatigue. 2017;98:14–31.

    Google Scholar 

  19. Chern AH, Nandwana P, Yuan T, Kirka MM, Dehoff RR, Liaw PK, et al. A review on the fatigue behavior of Ti-6Al-4V fabricated by electron beam melting additive manufacturing. Int J Fatigue. 2019;119:173–84.

    Google Scholar 

  20. Shao S, Khonsari MM, Guo S, Meng WJ, Li N. Overview: additive manufacturing enabled accelerated design of Ni-based alloys for improved fatigue life. Addit Manuf. 2019;29:100779.

    Google Scholar 

  21. du Plessis A, Yadroitsava I, Yadroitsev I. Effects of defects on mechanical properties in metal additive manufacturing: a review focusing on X-ray tomography insights. Mater Des. 2020;187:108385.

    Google Scholar 

  22. Sanaei N, Fatemi A. Defects in additive manufactured metals and their effect on fatigue performance: a state-of-the-art review. Prog Mater Sci. 2021;117:100724.

    Google Scholar 

  23. Suraratchai M, Limido J, Mabru C, Chieragatti R. Modelling the influence of machined surface roughness on the fatigue life of aluminium alloy. Int J Fatigue. 2008;30(12):2119–26.

    Google Scholar 

  24. Beretta S, Romano S. A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes. Int J Fatigue. 2017;94:178–91.

    Google Scholar 

  25. Li P, Warner DH, Fatemi A, Phan N. Critical assessment of the fatigue performance of additively manufactured Ti-6Al-4V and perspective for future research. Int J Fatigue. 2016;85:130–43.

    Google Scholar 

  26. Li C, Hu Z, Sun C, Song Q, Zhang W. Probabilistic control volume method for evaluating the effects of notch size and loading type on fatigue life. Acta Mech Solida Sinica. 2020;33(2):141–9.

    Google Scholar 

  27. Yang Y, Ragnvaldsen O, Bai Y, Yi M, Xu BX. 3D non-isothermal phase-field simulation of microstructure evolution during selective laser sintering. Npj Comput Mater. 2019;5:81.

    Google Scholar 

  28. Zerbst U, Bruno G, Buffiere JY, Wegener T, et al. Damage tolerant design of additively manufactured metallic components subjected to cyclic loading: State of the art and challenges. Progress Mater Sci. 2021;121:100786.

    Google Scholar 

  29. Basquin O. (1910) The exponential law of endurance tests. In: Proc Am Soc Test Mater; p. 625–630

  30. Burr A, Persenot T, Doutre PT, Buffere JY, Lhuissier P, Martin G, et al. A numerical framework to predict the fatigue life of lattice structures built by additive manufacturing. Int J Fatigue. 2020;139:105769.

    Google Scholar 

  31. Le VD, Pessard E, Morel F, Edy F. Interpretation of the fatigue anisotropy of additively manufactured TA6V alloys via a fracture mechanics approach. Eng Fract Mech. 2019;214:410–26.

    Google Scholar 

  32. Caton MJ, Jones JW, Boileau JM, Allison JE. The effect of solidification rate on the growth of small fatigue cracks in a cast 319-type aluminum alloy. Metall Mater Trans A. 1999;30(12):3055–68.

    Google Scholar 

  33. Goodman J. Mechanics applied to engineering. London: Longmans, Green and Co; 1919.

    MATH  Google Scholar 

  34. Zargarian A, Esfahanian M, Kadkhodapour J, Ziaei-Rad S, Zamani D. On the fatigue behavior of additive manufactured lattice structures. Theoret Appl Fract Mech. 2019;100:225–32.

    Google Scholar 

  35. Lipinski P, Barbas A, Bonnet AS. Fatigue behavior of thin-walled grade 2 titanium samples processed by selective laser melting. Application to life prediction of porous titanium implants. J Mech Behav Biomed Mater. 2013;28:274–90.

    Google Scholar 

  36. Zhou J, Barrett RA, Leen SB. Three-dimensional finite element modelling for additive manufacturing of Ti-6Al-4V components: Effect of scanning strategies on temperature history and residual stress. J Adv Join Processes. 2022;5:100106.

    Google Scholar 

  37. Merot P, Morel F, Gallegos Mayorga L, Pessard E, Buttin P, Baffe T. Observations on the influence of process and corrosion related defects on the fatigue strength of 316L stainless steel manufactured by Laser Powder Bed Fusion (LPBF). Int J Fatigue. 2022;155:106552.

    Google Scholar 

  38. Coffn LF Jr. A study of the effects of cyclic thermal stresses on a ductile metal. Trans Am Soc Mech Eng. 1954;76:931–50.

    Google Scholar 

  39. Manson SS. (1953) Behavior of materials under conditions of thermal stress. National Advisory Committee for Aeronautics

  40. Muhammad M, Nezhadfar PD, Thompson S, Saharan A, Phan N, Shamsaei N. A comparative investigation on the microstructure and mechanical properties of additively manufactured aluminum alloys. Int J Fatigue. 2021;146:106165.

    Google Scholar 

  41. Shao CW, Zhang P, Liu R, Zhang ZJ, Pang JC, Duan QQ, et al. A remarkable improvement of low-cycle fatigue resistance of high-Mn austenitic TWIP alloys with similar tensile properties: Importance of slip mode. Acta Mater. 2016;118:196–212.

    Google Scholar 

  42. Zhang P, He AN, Liu F, Zhang K, Jiang J. Evaluation of low cycle fatigue performance of selective laser melted Titanium Alloy Ti-6Al-4V. Metals. 2019;9(10):1041.

    Google Scholar 

  43. Xin H, Correia JAFO, Veljkovic M, Zhang Y, Berto F, de Jesus AMP. Probabilistic strain-fatigue life performance based on stochastic analysis of structural and WAAM-stainless steels. Eng Fail Anal. 2021;127:105495.

    Google Scholar 

  44. Ren D, Li S, Wang H, Hou W, Hao Y, Jin W, et al. Fatigue behavior of Ti-6Al-4V cellular structures fabricated by additive manufacturing technique. J Mater Sci Technol. 2019;35(2):285–94.

    Google Scholar 

  45. Cui W. A state-of-the-art review on fatigue life prediction methods for metal structures. J Mar Sci Technol. 2002;7(1):43–56.

    MathSciNet  Google Scholar 

  46. Ou CY, Voothaluru R, Liu CR. Fatigue crack initiation of metals fabricated by additive manufacturing-a crystal plasticity energy-based approach to IN718 life prediction. Crystals. 2020;10(10):1–10.

    Google Scholar 

  47. Bhat SP, Fine ME. Fatigue crack nucleation in iron and a high strength low alloy steel. Mater Sci Eng, A. 2001;314(1):90–6.

    Google Scholar 

  48. Yang C, Zhu K, Liu Y, Cai Y, Liu W, Zhang K, et al. A comparative study of fatigue energy dissipation of additive manufactured and cast AlSi10Mg alloy. Metals. 2021;11(8):1–14.

    Google Scholar 

  49. Huang J, Pastor ML, Garnier C, Gong X. Rapid evaluation of fatigue limit on thermographic data analysis. Int J Fatigue. 2017;104:293–301.

    Google Scholar 

  50. Guo Q, Guo X, Fan J, Syed R, Wu C. An energy method for rapid evaluation of high-cycle fatigue parameters based on intrinsic dissipation. Int J Fatigue. 2015;80:136–44.

    Google Scholar 

  51. Zhan Z, Li H, Lam KY. Development of a novel fatigue damage model with AM effects for life prediction of commonly-used alloys in aerospace. Int J Mech Sci. 2019;155:110–24.

    Google Scholar 

  52. Beretta S, Gargourimotlagh M, Foletti S, du Plessis A, Riccio M. Fatigue strength assessment of “as built” AlSi10Mg manufactured by SLM with different build orientations. Int J Fatigue. 2020;139:105737.

    Google Scholar 

  53. Sheridan L, Gockel JE, Scott-Emuakpor OE. Stress-defect-life interactions of fatigued additively manufactured alloy 718. Int J Fatigue. 2021;143:106033.

    Google Scholar 

  54. Yadollahi A, Mahtabi MJ, Khalili A, Doude HR, Newman JC. Fatigue life prediction of additively manufactured material: Effects of surface roughness, defect size, and shape. Fatigue Fract Eng Mater Struct. 2018;41(7):1602–14.

    Google Scholar 

  55. Romano S, Nezhadfar PD, Shamsaei N, Seifi M, Beretta S. High cycle fatigue behavior and life prediction for additively manufactured 17–4 PH stainless steel: effect of sub-surface porosity and surface roughness. Theoret Appl Fract Mech. 2020;106:102477.

    Google Scholar 

  56. Hu YN, Wu SC, Wu ZK, Zhong XL, Ahmed S, Karabal S, et al. A new approach to correlate the defect population with the fatigue life of selective laser melted Ti-6Al-4V alloy. Int J Fatigue. 2020;136:105584.

    Google Scholar 

  57. Biswal R, Zhang X, Shamir M, Al Mamun A, Awd M, Walther F, et al. Interrupted fatigue testing with periodic tomography to monitor porosity defects in wire + arc additive manufactured Ti-6Al-4V. Addit Manuf. 2019;28:517–27.

    Google Scholar 

  58. Molaei R, Fatemi A, Sanaei N, Pegues J, Shamsaei N, Shao S, et al. Fatigue of additive manufactured Ti-6Al-4V, Part II: The relationship between microstructure, material cyclic properties, and component performance. Int J Fatigue. 2019;132:105363.

    Google Scholar 

  59. Torries B, Sterling AJ, Shamsaei N, Thompson SM, Daniewicz SR. Utilization of a microstructure sensitive fatigue model for additively manufactured Ti-6Al-4V. Rapid Prototyping Journal. 2016;22(5):817–25.

    Google Scholar 

  60. Xue Y, Pascu A, Horstemeyer MF, Wang L, Wang PT. Microporosity effects on cyclic plasticity and fatigue of LENS™-processed steel. Acta Mater. 2010;58(11):4029–38.

    Google Scholar 

  61. Xue Y, Li T. Micromechanical simulations for fatigue damage incubation mechanisms of LENSTM processed steel. Procedia Eng. 2010;2(1):1165–72.

    Google Scholar 

  62. McDowell DL, Gall K, Horstemeyer MF, Fan J. Microstructure-based fatigue modeling of cast A356–T6 alloy. Eng Fract Mech. 2003;70(1):49–80.

    Google Scholar 

  63. Torries B, Shrestha R, Imandoust A, Shamsaei N. (2018) Fatigue life prediction of additively manufactured metallic materials using a fracture mechanics approach. In: 2018 International solid freeform fabrication symposium

  64. Zhang Q, Xie J, London T, Griffths D, Bhamji I, Oancea V. Estimates of the mechanical properties of laser powder bed fusion Ti-6Al-4V parts using finite element models. Mater Des. 2019;169:107678.

    Google Scholar 

  65. Papa E, Taliercio A. Anisotropic damage model for the multiaxial static and fatigue behaviour of plain concrete. Eng Fract Mech. 1996;55(2):163–79.

    Google Scholar 

  66. Zhan Z, Hu W, Meng Q. Data-driven fatigue life prediction in additive manufactured titanium alloy: a damage mechanics based machine learning framework. Eng Fract Mech. 2021;252:107850.

    Google Scholar 

  67. Liu S, Shi W, Zhan Z, Hu W, Meng Q. On the development of error-trained BP-ANN technique with CDM model for the HCF life prediction of aluminum alloy. Int J Fatigue. 2022;160:106836.

    Google Scholar 

  68. Zhan Z, Ao N, Hu Y, Liu C. Defect-induced fatigue scattering and assessment of additively manufactured 300M-AerMet100 steel: an investigation based on experiments and machine learning. Eng Fract Mech. 2022;264:108352.

    Google Scholar 

  69. Wan H, Wang Q, Jia C, Zhang Z. Multi-scale damage mechanics method for fatigue life prediction of additive manufacture structures of Ti-6Al-4V. Mater Sci Eng, A. 2016;669:269–78.

    Google Scholar 

  70. Pei C, Zeng W, Yuan H. A damage evolution model based on micro-structural characteristics for an additive manufactured superalloy under monotonic and cyclic loading conditions. Int J Fatigue. 2020;131:105279.

    Google Scholar 

  71. Pei C, Yuan H, Li B, Ma S. Anisotropic damage evolution and modeling for a nickel-based superalloy built by additive manufacturing. Eng Fract Mech. 2022;268:108450.

    Google Scholar 

  72. Deng K, Wei H, Liu W, Zhang M, Zhao P, Zhang Y. Probabilistic-based random maximum defect estimation and defect-related fatigue life prediction for laser direct deposited 316L parts. J Mater Process Technol. 2022;299:117389.

    Google Scholar 

  73. Ming Tang P. Oxides, porosity and fatigue performance of AlSi10Mg parts produced by selective laser melting. Int J Fatigue. 2017;94:192–201.

    Article  Google Scholar 

  74. Tiryakioǧlu M. Relationship between defect size and fatigue life distributions in Al-7 Pct Si-Mg alloy castings. Metall Mater Trans A. 2009;40(7):1623–30.

    Google Scholar 

  75. Wang T, He X, Wang J, Li Y. Detail fatigue rating method based on bimodal Weibull distribution for DED Ti-6.5Al-2Zr-1Mo-1V titanium alloy. Chin J Aeronautics. 2022;35(4):281–91.

    Google Scholar 

  76. Siddique S, Awd M, Tenkamp J, Walther F. Development of a stochastic approach for fatigue life prediction of AlSi12 alloy processed by selective laser melting. Eng Fail Anal. 2017;79:34–50.

    Google Scholar 

  77. Doh J, Raju N, Raghavan N, Rosen DW, Kim S. Bayesian inference-based decision of fatigue life model for metal additive manufacturing considering effects of build orientation and post-processing. Int J Fatigue. 2022;155:106535.

    Google Scholar 

  78. Mu PG, Wan XP, Zhao MY. A new SN curve model of fiber reinforced plastic composite. Key Eng Mater. 2011;462:484–8.

    Google Scholar 

  79. Zhurkov SN. Kinetic concept of the strength of solids. Int J Fract. 1984;26:295–307.

    Google Scholar 

  80. Liu B, Wang K, Bao R, Sui F. The effects of α/β phase interfaces on fatigue crack deflections in additively manufactured titanium alloy: a peridynamic study. Int J Fatigue. 2020;137:105622.

    Google Scholar 

  81. Prithivirajan V, Sangid MD. Examining metrics for fatigue life predictions of additively manufactured IN718 via crystal plasticity modeling including the role of simulation volume and microstructural constraints. Mater Sci Eng, A. 2020;783:139312.

    Google Scholar 

  82. Yan W, Lian Y, Yu C, Kafka OL, Liu Z, Liu WK, et al. An integrated processstructure-property modeling framework for additive manufacturing. Comput Methods Appl Mech Eng. 2018;339:184–204.

    MATH  Google Scholar 

  83. Molaei R, Fatemi A, Phan N. Significance of hot isostatic pressing (HIP) on multiaxial deformation and fatigue behaviors of additive manufactured Ti-6Al-4V including build orientation and surface roughness effects. Int J Fatigue. 2018;117:352–70.

    Google Scholar 

  84. Wang J, Zhang M, Wang B, Tan X, Wu WJ, Liu Y, et al. Influence of surface porosity on fatigue life of additively manufactured ASTM A131 EH36 steel. Int J Fatigue. 2021;142:105894.

    Google Scholar 

  85. Murakami Y. Effect of size and geometry of small defects on the fatigue limit. Oxford: Elsevier Science Ltd; 2002.

    Google Scholar 

  86. Wu Z, Wu S, Bao J, Qian W, Karabal S, Sun W, et al. The effect of defect population on the anisotropic fatigue resistance of AlSi10Mg alloy fabricated by laser powder bed fusion. Int J Fatigue. 2021;151:106317.

    Google Scholar 

  87. Lian Y, Wang P, Gao J, Liu J, Li Q, Liu C, et al. Fundamental mechanics problems in metal additive manufacturing: a state-of-art review. Adv Mech. 2021;51(3):648–701.

    Google Scholar 

  88. Masuo H, Tanaka Y, Morokoshi S, Yagura H, Uchida T, Yamamoto Y, et al. Effects of defects, surface roughness and HIP on fatigue strength of Ti-6Al-4V manufactured by Additive Manufacturing. Procedia Structural Integrity. 2017;7:19–26.

    Google Scholar 

  89. Kitagawa H. (1976) Applicability of fracture mechanics to very small cracks or the cracks in the early stage. In: Proc of 2nd ICM, Cleveland. p. 627–631

  90. Pessard E, Lavialle M, Laheurte P, Didier P, Brochu M. High-cycle fatigue behavior of a laser powder bed fusion additive manufactured Ti-6Al-4V titanium: effect of pores and tested volume size. Int J Fatigue. 2021;149:106206.

    Google Scholar 

  91. Wei LW, James MN. Fatigue crack closure for inclined and kinked cracks. Int J Fract. 2002;116(1):25–50.

    Google Scholar 

  92. Murakami Y, Usuki H. 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. Int J Fatigue. 1989;11(5):299–3074.

    Google Scholar 

  93. Dowling NE, Calhoun CA, Arcari A. Mean stress effects in stress-life fatigue and the Walker equation. Fatigue Fract Eng Mater Struct. 2009;32(3):163–79.

    Google Scholar 

  94. Rigon D, Meneghetti G. An engineering estimation of fatigue thresholds from a microstructural size and Vickers hardness: application to wrought and additively manufactured metals. Int J Fatigue. 2020;139:105796.

    Google Scholar 

  95. Qian G, Jian Z, Qian Y, Pan X, Ma X, Hong Y. Very-high-cycle fatigue behavior of AlSi10Mg manufactured by selective laser melting: effect of build orientation and mean stress. Int J Fatigue. 2020;138:105696.

    Google Scholar 

  96. El Haddad M, Topper T, Smith K. Prediction of non propagating cracks. Eng Fract Mech. 1979;11(3):573–84.

    Google Scholar 

  97. Yang K, Huang Q, Wang Q, Chen Q. Competing crack initiation behaviors of a laser additively manufactured nickel-based superalloy in high and very high cycle fatigue regimes. Int J Fatigue. 2020;136:105580.

    Google Scholar 

  98. Masuo H, Tanaka Y, Morokoshi S, Yagura H, Uchida T, Yamamoto Y, et al. Influence of defects, surface roughness and HIP on the fatigue strength of Ti-6Al-4V manufactured by additive manufacturing. Int J Fatigue. 2018;117:163–79.

    Google Scholar 

  99. Leuders S, Vollmer M, Brenne F, Tröster T, Niendorf T. Fatigue strength prediction for Titanium Alloy TiAl6V4 manufactured by selective laser melting. Metall Mater Trans A. 2015;46(9):3816–23.

    Google Scholar 

  100. Danninger H, Weiss B. The influence of defects on high cycle fatigue of metallic materials. J Mater Process Technol. 2003;143:179–84.

    Google Scholar 

  101. Chapetti MD. Fatigue propagation threshold of short cracks under constant amplitude loading. Int J Fatigue. 2003;25(12):1319–26.

    Google Scholar 

  102. Aigner R, Pusterhofer S, Pomberger S, Leitner M, Stoschka M. A probabilistic Kitagawa-Takahashi diagram for fatigue strength assessment of cast aluminium alloys. Mater Sci Eng, A. 2019;745:326–34.

    Google Scholar 

  103. Zhai Y, Galarraga H, Lados DA. Microstructure, static properties, and fatigue crack growth mechanisms in Ti-6Al-4V fabricated by additive manufacturing: LENS and EBM. Eng Fail Anal. 2016;69:3–14.

    Google Scholar 

  104. Konečná R, Kunz L, Bača A, Nicoletto G. Long fatigue crack growth in Ti6Al4V produced by direct metal laser sintering. Procedia Eng. 2016;160:69–76.

    Google Scholar 

  105. Xu Z, Liu A, Wang X, Liu B, Guo M. Fatigue limit prediction model and fatigue crack growth mechanism for selective laser melting Ti6Al4V samples with inherent defects. Int J Fatigue. 2021;143:106008.

    Google Scholar 

  106. Zhai Y, Lados DA, Brown EJ, Vigilante GN. Fatigue crack growth behavior and microstructural mechanisms in Ti-6Al-4V manufactured by laser engineered net shaping. Int J Fatigue. 2016;93:51–63.

    Google Scholar 

  107. Paris P, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng. 1963;85(4):528–33.

    Google Scholar 

  108. Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. J Basic Eng. 1957;24(3):361–4.

    Google Scholar 

  109. Gordon J, Haden C, Nied H, Vinci R, Harlow D. Fatigue crack growth anisotropy, texture and residual stress in austenitic steel made by wire and arc additive manufacturing. Mater Sci Eng, A. 2018;724:431–8.

    Google Scholar 

  110. Wu Y, Bao R. Fatigue crack tip strain evolution and crack growth prediction under single overload in laser melting deposited Ti-6.5Al-3.5Mo-1.5Zr-0.3Si titanium alloy. Int J Fatigue. 2018;116:462–72.

    Google Scholar 

  111. Harter JA. Comparison of contemporary FCG life prediction tools. Int J Fatigue. 1999;21:S181–5.

    Google Scholar 

  112. Wang X. Predicting fatigue crack growth life in additive manufactured titanium alloy. UK: Coventry University; 2016.

    Google Scholar 

  113. Griffth AA. The phenomena of rupture and flow in solids. Philosophical Trans Royal Soci London Series A, Containing Papers of a Math Phys Character. 1921;221:163–98.

    Google Scholar 

  114. Li FZ, Shih CF, Needleman A. A comparison of methods for calculating energy release rates. Eng Fract Mech. 1985;21(2):405–21.

    Google Scholar 

  115. Kahlin M, Ansell H, Moverare J. Fatigue crack growth for through and partthrough cracks in additively manufactured Ti6Al4V. Int J Fatigue. 2022;155:106608.

    Google Scholar 

  116. Parks DM. A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Fract. 1974;10(4):487–502.

    Google Scholar 

  117. Walsh RM Jr, Pipes RB. Strain energy release rate determination of stress intensity factors by finite element methods. Eng Fract Mech. 1985;22(1):17–33.

    Google Scholar 

  118. El Haddad M, Smith K, Topper TH. Fatigue crack propagation of short cracks. J Eng Mater Technol. 1979;101(1):42–6.

    Google Scholar 

  119. Fomin F, Horstmann M, Huber N, Kashaev N. Probabilistic fatigue-life assessment model for laser-welded Ti-6Al-4V butt joints in the high-cycle fatigue regime. Int J Fatigue. 2018;116:22–35.

    Google Scholar 

  120. Arola D, Williams C. Estimating the fatigue stress concentration factor of machined surfaces. Int J Fatigue. 2002;24(9):923–30.

    Google Scholar 

  121. Samadian K, de Waele W. Fatigue crack growth model incorporating surface waviness for wire + arc additively manufactured components. Procedia Struct Integrity. 2020;28:1846–55.

    Google Scholar 

  122. Zargarian A, Esfahanian M, Kadkhodapour J, Ziaei-Rad S. Numerical simulation of the fatigue behavior of additive manufactured titanium porous lattice structures. Mater Sci Eng, C. 2016;60:339–47.

    Google Scholar 

  123. Huang JS, Lin JY. Fatigue of cellular materials. Acta Mater. 1996;44(1):289–96.

    MathSciNet  Google Scholar 

  124. Wu MW, Chen JK, Lin BH, Chiang PH, Tsai MK. Compressive fatigue properties of additive-manufactured Ti-6Al-4V cellular material with different porosities. Mater Sci Eng, A. 2020;790:139695.

    Google Scholar 

  125. Dallago M, Fontanari V, Torresani E, Leoni M, Pederzolli C, Potrich C, et al. Fatigue and biological properties of Ti-6Al-4V ELI cellular structures with variously arranged cubic cells made by selective laser melting. J Mech Behav Biomed Mater. 2018;78:381–94.

    Google Scholar 

  126. Jones R, Michopoulos J, Iliopoulos A, Raman RS, Phan N, Nguyen T. Representing crack growth in additively manufactured Ti-6Al-4V. Int J Fatigue. 2018;116:610–22.

    Google Scholar 

  127. Forman RG, Kearney V, Engle R. Numerical analysis of crack propagation in cyclic-loaded structures. J Basic Eng. 1967;89(3):459–63.

    Google Scholar 

  128. Hartman A, Schijve J. The effects of environment and load frequency on the crack propagation law for macro fatigue crack growth in aluminium alloys. Eng Fract Mech. 1970;1(4):615–31.

    Google Scholar 

  129. Zhang X, Martina F, Ding J, Wang X, Williams SW. Fracture toughness and fatigue crack growth rate properties in wire + arc additive manufactured Ti-6Al-4V. Fatigue Fract Eng Mater Struct. 2017;40(5):790–803.

    Google Scholar 

  130. Jones R. Fatigue crack growth and damage tolerance. Fatigue Fract Eng Mater Struct. 2014;37(5):463–83.

    Google Scholar 

  131. Caton M, John R, Porter W, Burba M. Stress ratio effects on small fatigue crack growth in Ti-6Al-4V. Int J Fatigue. 2012;38:36–45.

    Google Scholar 

  132. Iliopoulos A, Jones R, Michopoulos J, Phan N, Singh RR. Crack growth in a range of additively manufactured aerospace structural materials. Aerospace. 2018;5(4):118.

    Google Scholar 

  133. Iliopoulos AP, Jones R, Michopoulos JG, Phan N, Rans C. Further studies into crack growth in additively manufactured materials. Materials. 2020;13(10):2223.

    Google Scholar 

  134. Jones R, Molaei R, Fatemi A, Peng D, Phan N. A note on computing the growth of small cracks in AM Ti-6Al-4V. Procedia Structural Integrity. 2020;28:364–9.

    Google Scholar 

  135. Main B, Jones M, Barter S. The practical need for short fatigue crack growth rate models. Int J Fatigue. 2021;142:105980.

    Google Scholar 

  136. Shamir M, Zhang X, Syed AK. Characterising and representing small crack growth in an additive manufactured titanium alloy. Eng Fract Mech. 2021;253:107876.

    Google Scholar 

  137. Gupta A, Sun W, Bennett C. Simulation of fatigue small crack growth in additive manufactured Ti-6Al-4V material. Continuum Mech Thermodyn. 2020;32(6):1745–61.

    Google Scholar 

  138. Jones R, Raman RS, Iliopoulos A, Michopoulos J, Phan N, Peng D. Additively manufactured Ti-6Al-4V replacement parts for military aircraft. Int J Fatigue. 2019;124:227–35.

    Google Scholar 

  139. Poulin JR, Brailovski V, Terriault P. Long fatigue crack propagation behavior of Inconel 625 processed by laser powder bed fusion: influence of build orientation and post-processing conditions. Int J Fatigue. 2018;116:634–47.

    Google Scholar 

  140. Sanaei N, Fatemi A. Defect-based fatigue life prediction of L-PBF additive manufactured metals. Eng Fract Mech. 2021;244:107541.

    Google Scholar 

  141. Ritchie R, Yu W, Blom A, Holm D. An analysis of crack tip shielding in aluminum alloy 2124: a comparison of large, small, through-thickness and surface fatigue cracks. Fatigue Fract Eng Mater Struct. 1987;10(5):343–62.

    Google Scholar 

  142. Rettenmeier P, Roos E, Weihe S, Schuler X. Assessment of mixed mode crack propagation of crane runway girders subjected to cyclic loading. Eng Fract Mech. 2016;153:11–24.

    Google Scholar 

  143. Stephens RI, Fatemi A, Stephens RR, Fuchs HO. Metal fatigue in engineering. UK: John Wiley & Sons; 2000.

    Google Scholar 

  144. Sanaei N, Fatemi A. Defect-based multiaxial fatigue life prediction of L-PBF additive manufactured metals. Fatigue Fract Eng Mater Struct. 2021;44(7):1897–915.

    Google Scholar 

  145. Elber W, et al. The significance of fatigue crack closure. USA: ASTM International West Conshohocken; 1971.

    Google Scholar 

  146. Zhang W, Wang Q, Li X, He J. A simple fatigue life prediction algorithm using the modified NASGRO equation. Math Problems Eng. 2016;2016:1–8.

    Google Scholar 

  147. Wang X, Zhao Y, Wang L, Wei L, He J, Guan X. In-situ SEM investigation and modeling of small crack growth behavior of additively manufactured titanium alloy. Int J Fatigue. 2021;149:106303.

    Google Scholar 

  148. Shyam A, Allison J, Jones J. A small fatigue crack growth relationship and its application to cast aluminum. Acta Mater. 2005;53(5):1499–509.

    Google Scholar 

  149. Shyam A, Allison JE, Szczepanski CJ, Pollock TM, Jones JW. Small fatigue crack growth in metallic materials: a model and its application to engineering alloys. Acta Mater. 2007;55(19):6606–16.

    Google Scholar 

  150. Bilby BA, Cottrell AH, Swinden KH. The spread of plastic yield from a notch. Proc R Soc Lond A. 1963;272(1350):304–14.

    Google Scholar 

  151. Garcia C, Lotz T, Martinez M, Artemev A, Alderliesten R, Benedictus R. Fatigue crack growth in residual stress fields. Int J Fatigue. 2016;87:326–38.

    Google Scholar 

  152. Dinh TD, Han S, Yaghoubi V, Xiang H, Erdelyi H, Craeghs T, et al. Modeling detrimental effects of high surface roughness on the fatigue behavior of additively manufactured Ti-6Al-4V alloys. Int J Fatigue. 2021;144:106034.

    Google Scholar 

  153. Zhang J, Wang X, Paddea S, Zhang X. Fatigue crack propagation behaviour in wire + arc additive manufactured Ti-6Al-4V: effects of microstructure and residual stress. Mater Des. 2016;90:551–61.

    Google Scholar 

  154. Alshoaibi AM, Fageehi YA. Simulation of Quasi-Static crack propagation by adaptive finite element method. Metals. 2021;11(1):98.

    Google Scholar 

  155. Syed AK, Ahmad B, Guo H, Machry T, Eatock D, Meyer J, et al. An experimental study of residual stress and direction-dependence of fatigue crack growth behaviour in as-built and stress-relieved selective-laser-melted Ti6Al4V. Mater Sci Eng, A. 2019;755:246–57.

    Google Scholar 

  156. Parker AP. Linear elastic fracture mechanics and fatigue crack growth-residual stress effects. Residual Stress Stress Relaxation. 1982;28:249–71.

    Google Scholar 

  157. Zhang X, Martina F, Syed AK. (2017) Fatigue Crack Growth in Additive Manufactured Titanium: Residual stress control and life evaluation method development. In: 2017 Aeronautical Fatigue and Structural Integrity; 2017. p. 7–9

  158. Hedayati R, Hosseini-Toudeshky H, Sadighi M, Mohammadi-Aghdam M, Zadpoor AA. Multiscale modeling of fatigue crack propagation in additively manufactured porous biomaterials. Int J Fatigue. 2018;113:416–27.

    Google Scholar 

  159. Gong H, Rafi K, Starr T, Stucker B. (2012) Effect of defects on fatigue tests of AsBuild Ti-6Al-4V parts fabricated by selective laser melting. In: 2012 International solid freeform fabrication symposium. University of Texas at Austin

  160. Ferreira FF, Neto DM, Jesus JS, Prates PA, Antunes FV. Numerical prediction of the fatigue crack growth rate in SLM Ti-6Al-4V based on crack tip plastic strain. Metals. 2020;10(9):1133.

    Google Scholar 

  161. Antunes F, Santos L, Capela C, Ferreira J, Costa J, Jesus J, et al. Fatigue crack growth in maraging steel obtained by selective laser melting. Appl Sci. 2019;9(20):4412.

    Google Scholar 

  162. Verma R, Kumar P, Jayaganthan R, Pathak H. Extended finite element simulation on tensile, fracture toughness and fatigue crack growth behaviour of additively manufactured Ti6Al4V alloy. Theoret Appl Fract Mech. 2022;117:103163.

    Google Scholar 

  163. Solob A, Grbović A, Božić Ž, Sedmak S. XFEM based analysis of fatigue crack growth in damaged wing-fuselage attachment lug. Eng Fail Anal. 2020;112:104516.

    Google Scholar 

  164. Xin H, Correia JA, Veljkovic M. Three-dimensional fatigue crack propagation simulation using extended finite element methods for steel grades S355 and S690 considering mean stress effects. Eng Struct. 2021;227:111414.

    Google Scholar 

  165. Ghandriz R, Hart K, Li J. Extended finite element method (XFEM) modeling of fracture in additively manufactured polymers. Addit Manuf. 2020;31:100945.

    Google Scholar 

  166. Duan CH, Weng ZW, Luo XP, Han XX, Zhao MH. Study on fatigue crack growth of laser melting deposited 12CrNi2 alloy steel based on XFEM. Key Eng Mater. 2021;871:46–52.

    Google Scholar 

  167. Yi M, Chang K, Liang C, Liucheng Z, Yangyiwei Y, Yi X, et al. Computational study of evolution and fatigue dispersity of microstructures by additive manufacturing. Chin J Theoret Appl Mech. 2021;53(12):3263–73.

    Google Scholar 

  168. Ohmer D, Yi M, Gutfleisch O, Xu B. Phase-field modeling of paramagnetic austenite-ferromagnetic martensite transformation coupled with mechanics and micromagnetics. Int J Solids Struct. 2022;238:111365.

    Google Scholar 

  169. Stinville JC, Charpagne MA, Cervellon A, Hemery S, Wang F, Callahan PG, et al. On the origins of fatigue strength in crystalline metallic materials. Science. 2022;377(6610):1065–71.

    MathSciNet  Google Scholar 

  170. Omar MM, El-Awady JA. Foreseeing metal failure from its inception. Science. 2022;377(6610):1047–8.

    MathSciNet  Google Scholar 

  171. Wang C, Tan XP, Tor SB, Lim CS. Machine learning in additive manufacturing: state-of-the-art and perspectives. Addit Manuf. 2020;36:101538.

    Google Scholar 

  172. Bao H, Wu S, Wu Z, Kang G, Peng X, Withers PJ. A machine-learning fatigue life prediction approach of additively manufactured metals. Eng Fract Mech. 2021;242:107508.

    Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support from National Science and Technology Major Project (J2019-IV-0014-0082), National Key Research and Development Program of China (2022YFB4600700), 15th Thousand Youth Talents Program of China, the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-I-0419G01), the Fundamental Research Funds for the Central Universities (1001-XAC21021), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Author information

Authors and Affiliations

Authors

Contributions

WT: Conceptualization, Investigation, Data curation, Writing–original draft. ZT: Conceptualization, Investigation, Data curation, Writing–original draft. WL: Investigation, Writing–review & editing. SW: Investigation, Writing–review & editing. MY: Conceptualization, Resources, Supervision, Project administration, Funding acquisition, Writing–original draft & review & editing.

Corresponding author

Correspondence to Min Yi.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, W., Tang, Z., Lu, W. et al. Modeling and Prediction of Fatigue Properties of Additively Manufactured Metals. Acta Mech. Solida Sin. 36, 181–213 (2023). https://doi.org/10.1007/s10338-023-00380-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10338-023-00380-5

Keywords

Navigation