MICROSTRUCTURE-BASED MODEL OF FATIGUE FRACTURE – A NEW APPROACH TO PREDICTING FATIGUE RESISTANCE OF STRUCTURAL ALLOYS

The present work is devoted to the development of a fatigue fracture model that makes it possible to calculate the number of loading cycles until initiation and during fatigue crack growth based on data on the monotonic strength and microstructure of the material. In Chapter 1, we review the current understanding of the mechanisms of fatigue crack initiation and growth and the current models for predicting fatigue life. Chapter 2 provides data on the materials used in the study, describes the methods and test results of the specimens. Chapter 3 is devoted to the development of a model for calculating the fatigue life of specimens under cyclic loading with constant and variable stress range. Chapter 4 provides examples of the model application for specimens made of various structural alloys.

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173. D. Halliday, J.Z. Zhang, P. Poole, P. Bowen, “In situ observation on the contrasting effects of an overload on small fatigue crack growth at two different load ratios in 2024-T351 aluminium alloy”, Int J Fatigue, 19(4), 273–282 (1997).
174. H. Noroozi, G. Glinka, S. Lambert, “A two parameter driving force for fatigue crack growth analysis”, Int J Fatigue, 27, 1277–1296 (2005).
175. Mikheevskiy, G. Glinka, “Elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra”, Int J Fatigue, 31, 1828–1836 (2009).
176. W. Landgraf, J. Morrow, T. Endo, “Determination of the cyclic stress–strain curve”, J Mater, 4(1), 176 (1969).
177. Technical report on low cycle fatigue properties: ferrous and nonferrous metals. SAE Standard No. J1099, Society of Automotive Engineers (SAE), Warrendale, Pennsylvania, (1998).
178. N. Smith, P. Watson, T.H. Topper, “A stress–strain function for the fatigue of metals”, J Mater, 5(4), 767–778 (1970).
179. K. Walker, “The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7076-T6 aluminum. Effect of environment and complex load history on fatigue life”, ASTM STP 462. Philadelphia: American Society for Testing and Materials, 1-14 (1970).
180. Neuber, “Theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress–strain law”, ASME J Appl Mech, 28, 544–551 (1961).
181. Moftakhar, A. Buczynski, G. Glinka, “Calculation of elastoplastic strains and Stresses in notched under multiaxial loading”, Int J Fract, 70(3), 357–373 (1995).
182. Glinka, G. Shen, “Universal features of weight functions for cracks in mode I.”, Eng Fract Mech, 40(6), 1135–1146 (1991).
183. E. Dowling, “Mechanical behavior of materials”, Prentice Hall Inc., New Jersy (2006).
184. Abdelkader Miloudi, Zemri Mokhtar, Mohamed Benguediab, M. Mazari, Abdelwaheb Amrouche, “Crack Propagation under Variable Amplitude Loading”, Materials Research, 16(5), 1161-1168 (2013).

References to Chapter 2 

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6. GOST 25.504-82 Raschetyi i ispyitaniya na prochnost. Metodyi rascheta harakteristik soprotivleniya ustalosti, Izdatelstvo standartov, M. (1982).
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9. B.A. Gryaznov, U.S. Nalimov, G.V. Tsyban’ov, O.M. Herasymchuk, O.M.Ivasishin, P.E. Markovskii, “Updating manufacture technology for critical parts of titanium alloy for increasing their fatigue characteristics”, Proceedings of the International Seminar on Manufacturing Technology Beyond 2000, India, Bangalore (1999).
10. M. Ivasishin, K.A. Bondareva, V.I. Bondarchuk, O.N. Gerasimchuk, D.G.Savvakin, B.A. Gryaznov, “Fatigue resistance of powder metallurgy Ti-6Al-4V alloy”, Strength Mater, 36, 225-230 (2004).
11. N. Gerasimchuk, G.A. Sergienko, V.I. Bondarchuk, A.V. Terukov, Yu.S.Nalimov, B.A. Gryaznov, “Fatigue strength of an () – type titanium alloy Ti-6Al-4V produced by the electron-beam physical vapor deposition method”, Strength Mater, 38, 651-658 (2006).
12. A. Gryaznov, Yu.S. Nalimov, V.E. Ryabtsev, O.N. Gerasimchuk, “Influence of surface defects and corrosive medium on the fatigue resistance of ST17G1S steel”, Strength Mater, 39, 408-414 (2007).
13. O.M. Herasymchuk, “Nonlinear relationship between the fatigue limit and quantitative parameters of material microstructure”, Int J Fatigue, 33, 649–659 (2011).
14. P.E. Markovsky, V.I. Bondarchuk, O. Herasymchuk, “Influence of grain size, aging conditions and tension rate on the mechanical behavior of titanium low-cost metastable beta-alloy in thermally hardened condition”, Mater Sci Eng A, 645(1), 150–162 (2015).
15. M. Herasymchuk, Yu.S. Nalimov, P.E. Markovs’kyi, A.V. Terukov, V.I. Bondarchuk, “Effect of the microstructure of titanium alloys on the fatigue strength characteristics”, Strength Mater, 43, 282-293 (2011).
16. M. Herasymchuk, O.V. Kononuchenko, “Vpliv tehnologIchnih defektIv ta mIkrostrukturi na opIr vtomI kondensatIv Iz titanovogo splavu TI-6Al-4V, otrimanih metodom EV RVD”, V kn.: Prochnost materialov i elementov konstruktsiy: Trudyi Mezhdunarodnoy nauchno-tehnicheskoy konferentsii. In-t problem prochnosti im. G.S.Pisarenko NAN Ukrainyi, Kyiv (2011).
17. M. Herasymchuk, O.V. Kononuchenko, “Effect of surface stress concentrators and microstructure on the fatigue limit of the material”, Strength Mater, 43, 374-383 (2011).
18. Oleg M. Herasymchuk, O.V. Kononuchenko, Olena M. Herasymchuk, V.I. Bondarchuk, “Fatigue life prediction of titanium alloys effected by process factors”, Strength Mater, 47, 579-585 (2015).
19. M. Herasymchuk, O.V. Kononuchenko, V.I. Bondarchuk, “Fatigue life calculation for titanium alloys considering the influence of microstructure and manufacturing defects”, Int J Fatigue, 81, 257–264 (2015).
20. M. Herasymchuk, P.E. Markovsky, V.I. Bondarchuk, “Calculating the fatigue life of smooth specimens of two-phase titanium alloys subject to symmetric uniaxial cyclic load of constant amplitude, Int J Fatigue, 83. 313–322 (2016).
21. M. Herasymchuk, O.V. Kononuchenko, “Peculiarities of short fatigue cracks growth from a blind hole in specimens made of steel 45. Part 1. Experimental results”, Strength Mater, 53, 213–221 (2021).
22. M. Herasymchuk, O.V. Kononuchenko, “Theoretical estimation of fatigue life before crack initiation in metal materials”, Strength Mater, 55, 457-468 (2023).
23. Tsvikker, Titan i ego splavyi, Metallurgiya, M. (1979).
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27. M. Ivasishin, P.E. Markovsky, “Enhancing the Mechanical Properties of Titanium Alloys with Rapid Heat Treatment (Overview)”, JOM, 7, 48–56 (1996).
28. M. Ivasishin, S.P. Oshkaderov, P.E. Markovskiy, “Issledovaniya skorostnogo nagreva pod zakalku titanovyih splavov”, Metallovedenie i termicheskaya obrabotka metallov, No 1, 32–35 (1990).
29. O. Peters, G. Luetjering, O.M. Ivasishin, P.E. Markovsky, “Mechanical Properties of Fine- Grained Beta-Titanium Alloys”, Proc. Of 3^rd ASM Conf. On Synthesis, Processing and Modelling of Advanced Materials, 269–274 (1997).
30. M. Ivasishin, S.L. Semiatin, “Rapid heat treatment of titanium alloys, In: Processing and Mechanical Properties of Titanium Alloys with Ultra-Fine Equiaxed Microstructure, «THERMEC»2000”, Proceedings International Conference on Processing and Manufacturing of аdvanced Materials las Vegas, USA. – CDROM. “Special Issue: Journal of Materials Processing Technology, Elsevier Science, UK, Section A1, 117/3 (2000).
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32. Zarkades, F.R. Larson, “Effect of textures on the charpy impact energy of some Ti alloy plate”, The Science, Technology and Application of Titanium, Pergamon Press, Oxford, UK (1970).
33. P. Jones, W.B. Hutchinson, “Stress-state dependence of slip in titanium-6Al-4V and other HCP metals”, Acta Met, 29, 951–968 (1981).
34. Bantounas, D. Dye, T.C. Lindley, “The effect of grain orientation on fracture morphology during high-cycle fatigue of Ti-6Al-4V”, Acta Mater, 57, 3584–3595 (2009).
35. Venkatraman, S. Ghosh, V. Mills, “A size dependent crystal plasticity finite–element model for creep and load shedding in polycrystalline titanium alloys”, Acta Mater, 55, 3971–3986 (2007).
36. S. Ravichandran, “Near threshold fatigue crack growth behavior of a titanium alloy: Ti-6A1-4V”, Acta Metall Mater, 39(3), 401–410 (1991).
37. N. Gerasimchuk, Vyinoslivost i tsiklicheskaya treschinostoykost titanovogo splava VT3-1 v razlichnyih strukturnyih sostoyaniyah. Dissertatsiya na soisk. uch.st. kand.tehn.nauk, Kiev (1995).
38. F. Savage, J. Tatalovich, M. Zupan, K.J. Hemker, M.J. Mills, “Deformation mechanisms and microtensile behavior of single colony Ti-6242Si”, Mater Sci Eng, A319–A321, 398–403 (2001).
39. Sansoz, H. Ghonem, “Fatigue Crack Growth Mechanisms in Ti6242 Lamellar Microstructures: Influence of Loading Frequency and Temperatur”, Metallurgical and Materials Transactions A, 34a, 2565–2578 (2003).
40. Lin Xiao, “Twinning behavior in the Ti–5 at.% Al single crystals during cyclic loading along [0 0 0 1]”, Materials Science and Engineering A, 394, 168–175 (2005).
41. Mechanical Properties of a Titanium Blading Alloy, EPRI CS-2933. Res. Proj. 1266-1, Final Report (1983).
42. A Movchan, “Neorganicheskie materialyi, osazhdaemyie iz parovoy fazyi v vakuume”, Suchasne materIaloznavstvo HHI StorIchchya, Nauk. dumka, Kiev, 318–332 (1998).
43. R. Smith, K. Kennedy, F.S. Boericke, “Metallurgical Charactenstics of Titanium – Alloy Foil Prepared by Electron Beam Evaporation”, J Vac Sci Technology, 6, 48–51 (1970).
44. H. Froes, D. Eylon, Powder metallurgy of titanium alloys – a review. Titanium. Technology: Present Status and Future Trends, Warrendale, 49–59 (1985).
45. M. Hagivara, Y. Kaieda, Y. Kawade, Miura, “Property enhancement of titanium alloys by blended elemental P/M method”, Titanium 92, Science and Technology: Proc 7 World Conf on Titanium, Warrendale, 1, 887–894 (1993).
46. H. Fujii, K. Takahashi, K. Fujisawa, “Low cost process of blended elemental powder metallurgy”, Titanium 95, Science and Technology: Proc 8 World Conf on Titanium, London, 1, 2547–2554 (1996).
47. Abkowits, D. Rowell, “Superior fatigue properties for blended elemental P/M Ti–6Al–4V”, J. Met., 8, 36–39. 1986.
48. A. Saltyikov, Stereometricheskaya metallografiya, Metallurgiya, M. (1976).
49. H. Zuo, Z.G. Wang, E.H. Han, “Effect of microstructure on ultra-high cycle fatigue behavior of Ti–6Al–4V”, Materials Science and Engineering A, 473, (2008).
50. T. Troschenko, G.V. Tsyibanev, A.A. Gryaznov, S.S. Nalimov, Prochnost materialov i konstruktsiy. T.2: Ustalost metallov. Vliyanie sostoyaniya poverhnosti i kontaktnogo vzaimodeystviya, Institut problem prochnosti, Kiev (2009).
51. M. Babakov, Teoriya kolebaniy, Nauka, M. (1965).
52. V. Prokopenko, M.V. Baumshtein, “Theoretical estimate of the life of gas-turbine-engine compressor blades”, Strength Mater, 13, 575–579 (1981).
53. Irvin, Osnovyi teorii rosta treschin i razruscheniya, v kn: Razrushenie. – pod red. G. Libovitsa, T. 3., Mir, M. (1976).
54. Microstructure and Texture Effects on Titanium Alloys, CS–472. Project 1266–33, Interim. Report (1986).
55. M. Ivasishin, V.M. Anokhin, A.N. Demidik, D.G. Savvakin, “Cost-effective blended elemental powder metallurgy of titanium alloys for transport application”, Key Eng Materials, 188, 55–62 (2000).
56. M. Ivasishin, D.G. Savvakin, K.A. Bondareva, “Sintez splava Ti–6Al–4V s nizkoy ostatochnoy poristostyu metodom poroshkovoy metallurgii”, Poroshkovaya metallurgiya, No. 7–8, 54–64 (2002).
57. M. Ivasishin, D.G. Savvakin, V.S. Moxson, “Titanium powder metallurgy for automotive components”, Materials Techn Adv Perform Materials, 17(1), 20–25 (2002).
58. Standard Test Methods for Determining Average Grain Size, ASTM, E-112 (1996).
59. O.M. Herasymchuk, “Nonlinear relationship between the fatigue limit and quantitative parameters of material microstructure”, Int J Fatigue, 33, 649–659 (2011).

References to Chapter 3 

1. E. Stromeyer, “The determination of fatigue limits under alternating stress conditions”. Proc of the Royal Society of London. Series A, containing papers of a mathematical and physical character, 90(620), 411–25 (1914).
2. К. Tanaka, T. Mura, “A dislocation model for fatigue crack initiation”, ASME J Appl Mech, 48, 97–103 (1981).
3. S Chan, “A microstructure – based fatigue – crack – initiation model”, Metall Mater Trans A, 34A, 43–58 (2003).
4. Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials, ASTM E466-15 (2015).
5. O. Herasymchuk, “Nonlinear relationship between the fatigue limit and quantitative parameters of material microstructure”, Int J Fatigue, 33, 649–659 (2011).
6. D. Chapetti, “Fatigue propagation threshold of short cracks under constant amplitude loading”, Int J Fatigue, 25, 1319–1326 (2003).
7. M.H. El Haddad, T.H. Topper, K.N. Smith, “Prediction of non propagating cracks”, Eng Fract Mech, 11(3), 573–584 (1979).
8. J. McEvily, M. Endo, Y. Murakami, “On the relationship and the short fatigue threshold”, Fatigue Fract Eng Mater Struct, 26, 269–278 (2003).
9. Kitagawa, S. Takahashi, “Applicability of fracture mechanics to very small cracks or the cracks in the early stage”, in: Proc. of the Second Int. Conf. of Mechanical Behavior of Materials. Metals Park (OH): ASM, 627–631 (1976).
10. U. Krupp, Fatigue Crack Propagation in Metals and Alloys: Microstructural Aspects and Modeling Concepts, Wiley–VCH, Weinheim (2007).
11. W. Hertzberg, “A simple calculation of da/dN data in the near threshold regime and above”, Int J Fract, 64, 53–58 (1993).
12. M. Herasymchuk, O.V. Kononuchenko, P.E. Markovsky, V.I. Bondarchuk, “Calculating the fatigue life of smooth specimens of two-phase titanium alloys subject to symmetric uniaxial cyclic load of constant amplitude”, Int J Fatigue, 83, 313–322 (2016).
13. M. Herasymchuk, “Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth”, Int J Fatigue, 81, 148–161 (2015).
14. P. Lukas, W.W. Gerberich, “A proposed criterion for fatigue threshold: dislocation substructure approach”, Fatigue Fract Eng Mater Struct, 6, 271–80 (1983).
15. Hanlon, E.D. Tabachnikova, S. Suresh, “Fatigue behavior of nanocrystalline metals and alloys”, Int J Fatigue, 27, 1147–1158 (2005).
16. O. Peters, B.L. Boyce, X. Chen, et.al., “On the application of the Kitagawa–Takahashi diagram to foreign-object damage and high-cycle fatigue”, Eng Fract Mech, 69, 1425–1446 (2002).
17. M. Herasymchuk, O.V. Kononuchenko, “Peculiarities of short fatigue cracks growth from a blind hole in specimens made of steel 45. Part 1. Experimental results”, Strength Mater, 53, 213–221 (2021).
18. Tanaka, Y. Nakai, Y. Yamashita, “Fatigue growth threshold of small cracks”, Int J Fract, 17(5), 519–33 (1981).
19. S. Park, S.J. Kim, K. H. Kim, et.al.,“A microstructural model for predicting high cycle fatigue life of steels”, Int J Fatigue, 27, 1115–1123 (2005).
20. N. Hanlon, W.M. Rainforth, “Some observations on cyclic deformation structures in the high-strength commercial aluminum alloy AA 7150”, Metall Mater Trans A, 29A, 2727–2736 (1998).
21. Akiniwa, K. Tanaka, “Statistical characteristics of propagation of small fatigue crack in smoth specimens of aluminium alloy 2024-T3”, Mater Sci Eng, A104, 105–115 (1988).
22. Tokaji, M. Kamakura, Y. Ishiizumi, N. Hasegawa, “Fatigue behaviour and fracture mechanism of a rolled AZ31 magnesium alloy”, Int J Fatigue, 26, 1217–1224 (2004).
23. J. McEvily, M. Endo, K. Yamashita, et al., “Fatigue notch sensitivity and the notch size effect”, Int J Fatigue, 30, 2087–2093 (2008).
24. S. Chan, “Variability of large-crack fatigue-crack-growth thresholds in structural alloys”, Metall Mater Trans A, 35A, 3721–3735 (2004).
25. Sun, Z. Lei, Y. Hong, “Effects of stress ratio on crack growth rate and fatigue strength for high cycle and very-high-cycle fatigue of metallic materials”, Mech Mater, 69, 227–236 (2014).
26. “Standard Test Method for Measurements of Fatigue Crack Growth Rates”, ASTM STP, E647–00 (2000).
27. Lukas, M. Klesnil, “Fatigue limit of notched bodies”, Mater Sci Eng, 34, 61–66 (1978).
28. M. Herasymchuk, O.V. Kononuchenko, “Peculiarities of short fatigue crack growth from a blind hole in specimens made of steel 45. Part 2. Model of short fatigue crack growth from a notch”, Strength Mater, 53, 405–416 (2021).
29. Tanaka, Y. Akiniwa, “Resistance curve method for predicting propagation threshold of short fatigue cracks at notches”, Eng Fract Mech, 30, 863–876 (1988).
30. Atzori, P. Lazzarin, G. Meneghetti, “Fracture mechanics and notch sensitivity”, Fatigue Fract Eng Mater Struct, 26, 257–267 (2003) .
31. M. Ciavarella, G. Meneghetti, “On fatigue limit in the presence of notches: classical vs. recent unified formulations”, Int J Fatigue, 26, 289–298 (2004).
32. C. Ting, F.V. Lawrence, “A crack closure model for predicting the threshold stresses of notches”, Fatigue Fract Eng Mater Struct, 16, 93–114 (1993).
33. Sadananda, S. Sarkar, D. Kujawski, A.K. Vasudevan, “A two-parameter analysis of S–N fatigue life using and ”, Int J Fatigue, 31, 1648–1659 (2009).
34. M. Herasymchuk, O.V. Kononuchenko, “The range of use of the critical distance concept to predict the endurance limit in the presence of stress raisers”, Strength Mater, 52, 722-730 (2020).
35. Maierhofer, H.P. Ganser, R. Pippan, “Modified Kitagawa–Takahashi diagram accounting for finite notch depths”, Int J Fatigue, 70, 503–509 (2015).

References to Chapter 4

1. Depres, C.F. Robertson, M.C. Fivel, “Crack initiation in fatigue: experiments and three-dimensional dislocation simulations”, Mater Sci Eng, 387, 288–291 (2004).
2. P. Hirth, J.Lothe, Theory of dislocations (2 ed.), USA, Wiley (1982).
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4. J. Caton, R. John, W.J. Porter, M.E. Burba, “Stress ratio effects on small fatigue crack growth in Ti–6Al–4V”, Int J Fatigue, 38, 36–45 (2012).
5. Akiniwa, K. Tanaka, “Statistical characteristics of propagation of small fatigue crack in smooth specimens of aluminium alloy 2024-T3”, Mater Sci Eng, 104, 105–115 (1988).
6. T. Lee, M. Peters, G. Wirth, “Effects of thermomechanical treatment on microstructure and mechanical properties of blended elemental Ti-6Al-4V compacts”, Mater Sci Eng, A102, 105–114 (1988).
7. T. Lee, M. Peters. G. Welsch, “Elastic moduli and tensile and physical properties of heat-treated and quenched powder metallurgical Ti-6Al-4V alloy”, Metall Trans A, 22A, 709–713 (1991).
8. W. Hertzberg, “A simple calculation of da/dN data in the near threshold regime and above”, Int J Fract, 64, R53–R58 (1993).
9. S. Chan, “Variability of large-crack fatigue-crack-growth thresholds in structural alloys”, Metall Mater Trans A, 35A, 3721–3735 (2004).
10. Tanaka, Y. Akiniwa, “Resistance curve method for predicting propagation threshold of short fatigue cracks at notches,” Eng Fract Mech, 30, 863–876 (1988).
11. Maierhofer, H.P. Ganser, R. Pippan, “Modified Kitagawa–Takahashi diagram accounting for finite notch depths,” Int J Fatigue, 70, 503–509 (2015).
12. M. Herasymchuk, “Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth,” Int J Fatigue, 81, 148–161 (2015).
13. Leopold, Y. Nadot, T. Billaudeau, J. Mendez, “Influence of artificial and casting defects on fatigue strength of moulded components in Ti-6Al-4V alloy”, Fatigue Fract Eng Mater Struct, 38, 1026–1041 (2015).
14. British Standard: Guide to methods for assessing the acceptability of flaws in metallic structures. BS 7910 (2005).
15. Bantounas, D. Dye, T.C. Lindley, “The effect of grain orientation on fracture morphology during high-cycle fatigue of Ti-6Al-4V”, Acta Materialia, 57, 3584–3595 (2009).
16. Polák, J. Man, “Experimental evidence and physical models of fatigue crack initiation”, Int J Fatigue, 91, 294–303 (2016).
17. C. Newman, Jr. and I. S. Raju, “Stress-intensity factor equations for cracks in three-dimensional finite bodies”, NASA Technical Memorandum 83200, (1981).
18. Schijve, “Fatigue of structures and materials in the 20th century and the state of the art”, Int J Fatigue, 25, 679–702 (2003).
19. Rege, D.G. Pavlou, “A one-parameter nonlinear fatigue damage accumulation model”, Int J Fatigue, 98, 234–246 (2017).
20. Santecchia, A.M.S. Hamouda, F. Musharavati et al., “A Review on fatigue life prediction methods for metals”, Adv Mater Sci Eng, 1–26 (2016).