{"id":6328,"date":"2025-09-16T22:17:48","date_gmt":"2025-09-16T22:17:48","guid":{"rendered":"https:\/\/akademperiodyka.org.ua\/uk\/?p=6328"},"modified":"2026-01-12T05:36:28","modified_gmt":"2026-01-12T05:36:28","slug":"%d0%bc%d1%96%d0%ba%d1%80%d0%be%d1%81%d1%82%d1%80%d1%83%d0%ba%d1%82%d1%83%d1%80%d0%be%d0%b7%d0%b0%d0%bb%d0%b5%d0%b6%d0%bd%d0%b0-%d0%bc%d0%be%d0%b4%d0%b5%d0%bb%d1%8c-%d0%b2%d1%82%d0%be%d0%bc%d0%bd%d0%be","status":"publish","type":"post","link":"https:\/\/akademperiodyka.org.ua\/en\/books\/microstructure-based-model\/","title":{"rendered":"MICROSTRUCTURE-BASED MODEL OF FATIGUE FRACTURE – A NEW APPROACH TO PREDICTING FATIGUE RESISTANCE OF STRUCTURAL ALLOYS"},"content":{"rendered":"

Authors: \"\"<\/strong><\/p>\n

Herasymchuk Oleh Mykolaiovych<\/p>\n

Head of department of Fatigue and crack resistance of structural materials, G.S.Pisarenko Institute for problems of strength of the National Academy of Sciences of Ukraine, Kyiv, Ukraine;<\/p>\n

Doctor of technical sciences;<\/p>\n

Senior researcher;<\/p>\n

https:\/\/www.scopus.com\/authid\/detail.uri?authorId=57197739466<\/a><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

\"\"<\/p>\n

Kononuchenko Oleh Vasyliovych<\/p>\n

Senior researcher of department of Fatigue and crack resistance of structural materials G.S.Pisarenko Institute for problems of strength of the National Academy of Sciences of Ukraine, Kyiv, Ukraine;<\/p>\n

Candidate of technical sciences;<\/p>\n

Senior Researcher<\/p>\n

https:\/\/www.scopus.com\/authid\/detail.uri?authorId=6504101245<\/a><\/p>\n

 <\/p>\n

 <\/p>\n

Reviewers: <\/strong><\/p>\n

Shukayev Sergiy Mykolaiovych<\/span><\/p>\n

National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine;<\/p>\n

Doctor of technical sciences;<\/p>\n

Professor;<\/p>\n

https:\/\/www.scopus.com\/authid\/detail.uri?authorId=6602981678<\/a><\/p>\n

Markovsky Pavlo Evgenovych<\/span><\/p>\n

Head of the department of Physics of strength and plasticity of heterogeneous metal materials G.V. Kurdyumov Institute for Metal Physics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;<\/p>\n

Doctor of technical sciences;<\/p>\n

Senior researcher;<\/p>\n

https:\/\/www.scopus.com\/authid\/detail.uri?authorId=6602146735<\/a><\/p>\n

\n
\u0420\u0456\u043a \u0432\u0438\u0434\u0430\u043d\u043d\u044f:<\/strong>\u00a02025<\/div>\n<\/div>\n
\n
\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438:<\/strong> 222<\/div>\n<\/div>\n
\n
ISBN:<\/strong> 978-966-360-542-5<\/div>\n<\/div>\n
\n
\u041c\u043e\u0432\u0430:<\/strong> Ukrainian<\/div>\n<\/div>\n
\n
\u0412\u0438\u0434\u0430\u0432\u0435\u0446\u044c:<\/strong> PH \u201cAkademperiodyka\u201d<\/div>\n<\/div>\n
\n
\u041c\u0456\u0441\u0446\u0435: <\/strong>Kyiv<\/div>\n<\/div>\n
DOI: <\/strong>https:\/\/doi.org\/10.15407\/akademperiodyka.542.222<\/a><\/div>\n
\n

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.<\/p>\n

References to Chapter 1<\/strong>\u00a0<\/strong><\/p>\n

    \n
  1. T.Troschenko, G.V. Tsybanev, B.A. Gryaznov, Yu.S. Nalimov, Prochnost materialov i konstruktsiy<\/em>, T.2: Ustalost metallov. Vliyanie sostoyaniya poverhnosti i kontaktnogo vzaimodeystviya<\/em>, Institut problem prochnosti, Kiev (2009).<\/li>\n
  2. Klesnil, P. Lukas, Fatigue of metallic materials<\/em>, Elsevier, New York, (1980).<\/li>\n
  3. J. Miller, \u201cThe behaviour of short fatigue cracks and their initiation. Part II \u2013 general summary\u201d, Fatigue Fract Eng Mater Struct<\/em>, 10<\/strong>, 93\u2013113 (1987).<\/li>\n
  4. L. Davidson, K.S. Chan, \u201cCrystallography of fatigue crack initiation in Astroloy at ambient temperature\u201d, Acta Metall<\/em>, 37<\/strong>, 1089\u20131097 (1989).<\/li>\n
  5. S. Chan, \u201cA microstructure \u2013 based fatigue \u2013 crack \u2013 initiation model\u201d, Metall Mater Trans A<\/em>, 34A<\/strong>, 43\u201358 (2003).<\/li>\n
  6. S. Chan, \u201cVariability of large-crack fatigue-crack-growth thresholds in structural alloys\u201d, Metall Mater Trans A,<\/em> 35A<\/strong>, 3721\u20133735 (2004).<\/li>\n
  7. Lutjering, J. C. Williams, Titanium,<\/em> Springer, New York, (2003).<\/li>\n
  8. S. Chan, \u201cRoles of microstructure in fatigue crack initiation\u201d, Int J Fatigue,<\/em> 32<\/strong>, 1428\u20131447 (2010).<\/li>\n
  9. \u041a. Tanaka, T. Mura. \u201cA dislocation model for fatigue crack initiation\u201d, ASME J Appl Mech<\/em>, 48<\/strong>, 97\u2013103 (1981).<\/li>\n
  10. J. Miller, \u201cThe two thresholds of fatigue behaviour\u201d, Fatigue Fract Eng Mater Struct<\/em>, 16<\/strong>(9), 931\u2013939 (1993).<\/li>\n
  11. Schijve, \u201cFatigue of structures and materials in the 20th century and the state of the art\u201d, Int J Fatigue<\/em>, 25<\/strong>, 679\u2013702 (2003).<\/li>\n
  12. A. Ewing, J.C. Humfrey, \u201cThe Fracture of Metals under Repeated Alternations of Stress\u201d, Philos Trans R Soc<\/em>, 241\u2013250 (1903).<\/li>\n
  13. J. Forsyth, The Physical Basis of Metal Fatigue,<\/em> Blackie and Son, London, (1969).<\/li>\n
  14. Lukas, M. Klesnil., Corrosion Fatigue<\/em>, in: O. Devereux, A.J. McEvily, R.W. Staehle (Eds.), Chemistry, Mechanics and Microstructure, TX, Houston, 1\u201332 (1972).<\/li>\n
  15. Polak, \u201cMechanisms and kinetics of the early fatigue damage in crystalline materials\u201d, Materials Science and Engineering A<\/em>, 468\u2013470<\/strong>, 33\u201339. (2007).<\/li>\n
  16. Laird, D.J. Duquette, \u201cCorrosion Fatigue<\/em>\u201d, in: O. Devereux, A.J. McEvily, R.W. Staehle (Eds.), Chemistry, Mechanics and Microstructure, TX, Houston, 88\u2013117 (1972).<\/li>\n
  17. Mughrabi, Dislocations and properties of real materials<\/em>, The Institute of Metals, London, 244\u2013262 (1985).<\/li>\n
  18. Essmann, U. G\u00f6sele, H. Mughrabi, \u201cA model of extrusions and intrusions in fatigued metals I. Point-defect production and the growth of extrusions\u201d, Philos Mag A<\/em>, 44<\/strong>, 405\u2013426 (1981).<\/li>\n
  19. Polak, \u201cOn the role of point defects in fatigue crack initiation\u201d, Mater Sci Eng<\/em>, No. 92, 71\u201380 (1987).<\/li>\n
  20. Depres, C.F. Robertson, M.C. Fivel, \u201cCrack initiation in fatigue: experiments and three-dimensional dislocation simulations\u201d, Mater Sci Eng<\/em>, No. 387, 288\u2013291 (2004).<\/li>\n
  21. Schijve, Fatigue of Structures and Materials<\/em>, Springer, (2009).<\/li>\n
  22. P. Bullen, A.K. Head, W.A. Wood, \u201cStructural changes during the fatigue of metals\u201d, Proc Roy Soc<\/em>, No. 216, 332 (1953).<\/li>\n
  23. Ji\u0161a, P. Li\u0161kutin, T. Kruml, J. Polak, \u201cSmall fatigue crack growth in aluminium alloy EN-AW 6082\/T6\u201d, Int J Fatigue<\/em>, 32<\/strong>, 1913\u20131920 (2010).<\/li>\n
  24. Man, T. Vystave, A. Weidner, I. Kubena, M. Petrenec, T. Kruml, J. Polak. \u201cStudy of cyclic strain localization and fatigue crack initiation using FIB technique\u201d, Int J Fatigue<\/em>, 39<\/strong>, 44\u201353 (2012).<\/li>\n
  25. Polak, \u201cMechanisms and kinetics of the early fatigue damage in crystalline materials\u201d, Mater Sci Eng<\/em>, No. 468\u2013470, 33\u201339 (2007).<\/li>\n
  26. Polak, J. Man, M. Petrenec, \u201cDamage evolution during fatigue in structural materials\u201d, Procedia Materials Science<\/em>, No. 1, 3\u201312 (2012).<\/li>\n
  27. Suresh, Fatigue of materials. 2nd ed<\/em>., Cambridge University Press, 132\u2013164 (1998).<\/li>\n
  28. D. Taylor, O. Clancy, \u201cThe fatigue performance of machined surfaces\u201d, Fatigue Fract Eng Mater Struct<\/em>, 14<\/strong>, 329\u2013336 (1991).<\/li>\n
  29. M. Gell, G. Leverant, \u201cMechanisms of high-temperature fatigue\u201d, Fatigue at elevated temperatures<\/em>, ASTM STP 520, 37\u201367 (1973).<\/li>\n
  30. S. Nishijima, K. Kanazawa, \u201cStepwise S\u2013N curve and fish-eye failure in gigacycle fatigue\u201d, Fatigue Fract Eng Mater Struct<\/em>, 22<\/strong>, 601\u2013 607 (1999).<\/li>\n
  31. Y. Murakami, T. Nomoto, T. Ueda, \u201cFactors influencing the mechanism of superlong fatigue failure in steels\u201d, Fatigue Fract Eng Mater Struct<\/em>, 22<\/strong>, 581\u2013590 (1999).<\/li>\n
  32. Mughrabi, \u201cOn \u2018multi-stage\u2019 fatigue life diagrams and the relevant lifecontrolling mechanisms in ultrahigh-cycle fatigue\u201d, Fatigue Fract Eng Mater Struct<\/em>, 25<\/strong>, 755\u2013764 (2002).<\/li>\n
  33. Krupp, Fatigue crack propagation in metals and alloys: microstructural aspects and modelling concepts<\/em>, Wiley\u2013VCH, Weinheim (2007).<\/li>\n
  34. R. Mitchell, M. Meshii, \u201cFatigue and Microstructure\u201d, ASM, Metals Park, OH<\/em>, 385\u2013437, (1978).<\/li>\n
  35. F. Coffin Jr., \u201cA study of the effects of cyclic thermal stresses on a ductile metal\u201d, Trans ASME<\/em>, 76<\/strong>, 931\u2013950 (1954).<\/li>\n
  36. S. Manson, \u201cFatigue: a complex subject \u2013 some simple approximation\u201d, Exp Mech<\/em>, 5<\/strong>, 193\u2013226 (1965).<\/li>\n
  37. S. Cheng, C. Laird, \u201cFatigue life behavior of copper single crystals. Part II: model for crack nucleation in persistent slip bands\u201d, Fatigue Fract Eng Mater Struct<\/em>, 4<\/strong>, 343\u2013353 (1981).<\/li>\n
  38. Venkataraman, Y.W. Chung, T. Mura, \u201cApplication of minimum energy formalism in a multiple slip band model for fatigue-II. Crack nucleation and derivation of a generalised Coffin-Manson law\u201d, Acta Metall Mater,<\/em> 39<\/strong>, 2631\u20132638 (1991).<\/li>\n
  39. Saxena, S.D. Antolovich, \u201cLow cycle fatigue, fatigue crack propagation and substructures in a series of polycrystalline Cu-Al alloys\u201d, Metall Trans A<\/em>, 6A<\/strong>, 1809\u20131828 (1975).<\/li>\n
  40. Tanaka, T. Mura, \u201cA theory of fatigue crack initiation at inclusions\u201d, Metall Trans A<\/em>, 13A<\/strong>, 117\u2013123 (1982).<\/li>\n
  41. Venkataraman, Y.W. Chung, T. Mura, \u201cApplication of minimum energy formalism in a multiple slip band model for fatigue-I. Calculation of slip band spacings\u201d, Acta Metall Mater<\/em>, 39<\/strong>, 2621\u20132629 (1991).<\/li>\n
  42. R. Lin, M.E. Fine, T. Mura, \u201cFatigue crack initiation on slip bands: theory and experiment\u201d, Acta Metall<\/em>, 34<\/strong>, 619\u2013628 (1986).<\/li>\n
  43. Venkataraman, Y.W. Chung, Y. Nakasone, T. Mura, \u201cFree energy formulation of fatigue crack initiation along persistent slip bands: calculation of S\u2013N curves and crack depths\u201d, Acta Metall Mater<\/em>, 38<\/strong>, 31\u201340 (1990).<\/li>\n
  44. Mura, Y. Nakasone, \u201cA theory of fatigue crack initiation in solids\u201d, J Appl Mech<\/em>, 57<\/strong>, 1-6 (1990).<\/li>\n
  45. Mura, \u201cA theory of fatigue crack initiation\u201d, Mater Sci Eng<\/em>, A176<\/strong>, 61\u201370 (1994).<\/li>\n
  46. E. Harvey, P.G. Marsh, W.W. Gerberich, \u201cAtomic force microscopy and modeling of fatigue crack initiation in metals\u201d, Acta Metall Mater<\/em>, 42<\/strong>, 3493\u20133502 (1994).<\/li>\n
  47. N. Stroh, \u201cThe formation of cracks as a result of plastic flow\u201d, Proc Roy Soc<\/em>, No. 223, 404\u2013414 (1954).<\/li>\n
  48. R. Bache, \u201cA review of dwell sensitive fatigue in titanium alloys: the role of microstructure, texture and operating conditions\u201d, Fatigue<\/em>, 25<\/strong>, 1079\u20131087 (2003).<\/li>\n
  49. Davidson, K. Chan, R. McClung, S. Hudak, \u201cSmall Fatigue Cracks\u201d, Comprehensive Structural Integrity<\/em>, No. 4, 129\u2013164 (2003).<\/li>\n
  50. J. Miller, R.S. Piascik, J.C. Newman, N.E. Dowling, \u201cThe three thresholds for fatigue crack propagation\u201d, Fatigue and Fracture Mechanics<\/em>, ASTM STP 1296, No. 27, 267\u2013286 (1997).<\/li>\n
  51. C. Paris, F. Erdogan, \u201cA critical analysis crack propagation laws\u201d, Trans ASME, J Basic Eng<\/em>, No. 85, 528\u2013534 (1963).<\/li>\n
  52. Tanaka, \u201cFatigue Crack Propagation\u201d, Comprehensive Structural Integrity<\/em>, No. 4, 95\u2013127 (2003).<\/li>\n
  53. S. Suresh, R. Ritchie, \u201cThe propagation of short fatigue cracks\u201d, Metals Rev,<\/em> 29<\/strong>(6), 445\u2013476 (1984).<\/li>\n
  54. Santus, D. Taylor, \u201cPhysically short crack propagation in metals during high cycle fatigue\u201d, Int J Fatigue<\/em>, 31<\/strong>, 1356\u20131365 (2009).<\/li>\n
  55. Y. Akiniwa, K. Tanaka, \u201cStatistical characteristics of propagation of small fatigue crack in smooth specimens of aluminium alloy 2024-T3\u201d, Mater Sci Eng<\/em>, 104<\/strong>, 105\u2013115 (1988).<\/li>\n
  56. L. Davidson, K.S. Chan, R.C. McClung, \u201cCu-bearing high-strength low-alloy steels: The influence of microstructure on the initiation and growth of small fatigue cracks\u201d, Metall Trans A<\/em>, 27<\/strong>, 2540\u20132556 (1996).<\/li>\n
  57. Tokaji, T. Ogawa, Y. Kameyama, \u201cThe effects of stress ratio on the growth behaviour of small fatigue cracks in an aluminum alloy 7075-T6 (with special interest in stage i crack growth)\u201d, Fatigue Fract Eng Mater Struct<\/em>, 13<\/strong>(4), 411\u201321 (1990).<\/li>\n
  58. Taylor, J.F. Knott, \u201cFatigue crack propagation behaviour of short cracks; the effect of microstructure\u201d, Fatigue Fract Eng Mater Struct<\/em>, 4<\/strong>(2), 147\u2013155 (1981).<\/li>\n
  59. R. Yoder, L.A. Cooley, T.W. Crooker, \u201cOn microstructural control of near\u2013threshold fatigue crack growth in 7000\u2013series aluminium alloys\u201d, Scripta Metallurgica<\/em>, 16<\/strong>, 1021\u20131025 (1982).<\/li>\n
  60. A. Rodopoulus, E.R. de los Rios, \u201cTheoretical Analysis on the Behaviour of Short Fatigue Cracks\u201d, Int J Fatigue<\/em>, 24<\/strong>, 719\u2013724 (2002).<\/li>\n
  61. K. Sadananda, \u201cVasudevan Short crack growth and internal stresses\u201d, Int J Fatigue<\/em>, 19<\/strong>, Supp. No. 1, S99\u2013S108, (1997).<\/li>\n
  62. Mehanika razrusheniya i prochnost materialov<\/em>, Spravochnoe posobie: V 4 t., Pod red. V.Panasyuka, T.4, Nauk. dumka, Kiev (1990).<\/li>\n
  63. Hussain, E.R. de los Rios, \u201cTransition from small to long fatigue crack in C-Mn steel\u201d, Scripta metallurgica et Materialia<\/em>, 30<\/strong>, 53\u201358 (1994).<\/li>\n
  64. Obrtl\u0131k, J. Polak, M. Hajek, A. Vasek, \u201cShort fatigue crack behaviour in 316L stainless steel\u201d, Int J Fatigue<\/em>, 19<\/strong>(6), 471\u2013475 (1997).<\/li>\n
  65. S. Ravichandran, \u201cEffects of crack aspect ratio on the behavior of small surface cracks in fatigue: Part I. Simulation\u201d, Metal Mater Trans A<\/em>, 28a<\/strong>(1), 157\u2013169 (1997).<\/li>\n
  66. O. Ritchie, \u201cNear-Threshold Fatigue Crack Propagation in Ultra-High Strength Steel: Influence of Load Ratio and Cyclic Strength\u201d, Journal of Engineering Materials and Technology<\/em>, 7<\/strong>, 195\u2013204 (1977).<\/li>\n
  67. Lawson, E.Y. Chen, M. Meshii, \u201cNear-threshold fatigue: a review\u201d, Int J Fatigue<\/em>, 21<\/strong>, 15\u201334 (1999).<\/li>\n
  68. K. Liaw, T.R. Leax, W.A. Logsdon, \u201cNear-threshold fatigue crack growth behavior in metals\u201d, Acta Metall<\/em>, 31<\/strong>(10), 1581\u20131587 (1983).<\/li>\n
  69. Makhlouf, J.W. Jones, \u201cNear-threshold fatigue crack growth behaviour of a ferritic stainless steel at elevated temperatures\u201d, Int J Fatigue<\/em>, 14<\/strong>(2), 97\u2013104 (1992).<\/li>\n
  70. O. Ritchie, \u201cNear-threshold fatigue-crack propagation in steels\u201d, International Metals Reviews<\/em>, 5\u20136<\/strong>, 205\u2013230 (1979).<\/li>\n
  71. O. Ritchie, S. Suresh, \u201cThe fracture mechanics similitude concept: questions concerning its application to the behavior of short fatigue cracks\u201d, Materials Science and Engineering<\/em>, 57<\/strong>, L27\u2013L30 (1983).<\/li>\n
  72. Bantounas, D. Dye, T.C. Lindley, \u201cThe effect of grain orientation on fracture morphology during high-cycle fatigue of Ti-6Al-4V\u201d, Acta Materialia<\/em>, 57<\/strong>, 3584\u20133595 (2009).<\/li>\n
  73. C. Newman Jr., E.P. Phillips, M.H. Swain, \u201cFatigue-Life Prediction Methodology Using Small Crack Theory\u201d, Int J Fatigue<\/em>, 21<\/strong>, 109\u2013119 (1999).<\/li>\n
  74. L. McDowell, \u201cAn engineering model for propagation of small cracks in fatigue\u201d, Eng Fract Mech<\/em>, 56<\/strong>(3), 357\u2013377 (1997).<\/li>\n
  75. Vehoff, P. Neumann, \u201cLife Prediction based on the Propagation of Short Cracks\u201d, Steel Research<\/em>, 63<\/strong>, 372\u2013377 (1992).<\/li>\n
  76. J. Mc Evily, D. Eifler, E. Macherauch, \u201cAn analysis of the growth of short fatigue cracks\u201d, Eng Fract Mech<\/em>, 40<\/strong>, 571\u2013584 (1991).<\/li>\n
  77. L. DuQuesnay, T.H. Topper, M.T. Yu, \u201cThe effect of notch radius on the fatigue notch factor and the propagation of short cracks. The Behavior of Short Fatigue Cracks<\/em>\u201d, ESIS, London, 323\u2013335 (1986).<\/li>\n
  78. Grabowski, J.E. King, \u201cModelling short crack growth behaviour in nickel-base superalloys\u201d, Fatigue Fract Eng Mater Struct<\/em>, 15<\/strong>, 595\u2013606 (1992).<\/li>\n
  79. Bomas, J. H\u00fcnecke, S. Laue, P. Mayr, D. Sch\u00f6ne, \u201cAnrissleben sdauervorhersage am Beispiel glatter und gekerbter Proben des Werkstoffs Cm15\u201d, Materialwissenschaft und Werkstofftechnik<\/em>, 33<\/strong>, 230\u2013238 (2002).<\/li>\n
  80. D. Hobson, M.W. Brown, E.R. de los Rios, \u201cTwo Phases of Short Crack Growth in a Medium Carbon Steel\u201d, The Behavior of Short Fatigue Cracks<\/em>. ESIS, London, 441\u2013459 (1986).<\/li>\n
  81. Hussain, \u201cShort fatigue crack behaviour and analytical models. A Review\u201d, Eng Fract Mech<\/em>, 58<\/strong>, 327\u2013354 (1997).<\/li>\n
  82. S. Chan, J. Lankford, \u201cA Crack Tip Strain Model for the Growth of Small Fatigue Cracks\u201d, Scripta Metallurgica<\/em>, 17<\/strong>, 529\u2013532 (1983).<\/li>\n
  83. R. de los Rios, H.J. Mohamed, K.J. Miller, \u201cA micromechanics analysis for short fatigue crack growth\u201d, Fatigue Fract Eng Mater Struct,<\/em> 8<\/strong>, 49\u201363 (1985).<\/li>\n
  84. G. Foreman, V.E. Keary, R.M. Eagle, \u201cNumerical analysis of crack propagation in cyclic-loaded structures\u201d, J Basic Engineerin<\/em>, 89<\/strong>, 459\u2013463 (1967).<\/li>\n
  85. Weertman, \u201cRate of growth of fatigue cracks calculated from the theory of infinitesimal dislocations distributed on a plane\u201d, Int J Fracture<\/em>, 2<\/strong>, 460\u2013467 (1966).<\/li>\n
  86. Klesnil, P. Lukas, \u201cInfluence of strength and stress history on growth and stabilisation of fatigue cracks\u201d, Eng Fract Mech<\/em>, 4<\/strong>, 77\u201392 (1972).<\/li>\n
  87. J. McEvily, On closure in fatigue crack growth. Technical report, ASTM STP 982<\/em>, Philadelphia, 35<\/strong> (1988).<\/li>\n
  88. Elber, Fatigue Crack Propagation: Some Effects of Crack Closure on the Mechanism of Fatigue Crack Propagation under Cyclic Tension Loading. PhD Thesis<\/em>, University of New South Wales, New South Wales (1968).<\/li>\n
  89. Elber, The significance of fatigue crack closure, proc. damage tolerance in aircraft structures, ASTM STP 486<\/em>, Philadelphia, 230<\/strong> (1971).<\/li>\n
  90. L. Anderson, Fracture Mechanics: Fundamentals and Applications, 2nd edition<\/em>, CRC Press FL, Boca Raton (1995).<\/li>\n
  91. N. El Haddad, T.H. Topper, K.N. Smith, \u201cPrediction of non propagating cracks\u201d, Eng Fract Mech,<\/em> 11<\/strong>(3), 573\u2013584 (1979).<\/li>\n
  92. Kitagawa, S. Takahashi, Applicability of fracture mechanics to very small cracks or the cracks in the early stage. In: Proceedings of the second international conference of mechanical behavior of materials<\/em>, ASM STP, Philadelphia, 627\u2013631 (1976).<\/li>\n
  93. E. Frost, K.L. Marsh, L.P. Pook, Metal Fatigue<\/em>, Clarendon Press, Oxford, (1974).<\/li>\n
  94. M. El Haddad, K.N. Smith, T.U. Topper, \u201cFatigue crack propagation of short cracks\u201d, Trans ASME, J Eng Mater Technol<\/em>, 101<\/strong>(1), 42\u201346 (1979).<\/li>\n
  95. D. Chapetti, \u201cFatigue propagation threshold of short cracks under constant amplitude loading\u201d, Int J Fatigue<\/em>, 25<\/strong>, 1319\u20131326 (2003).<\/li>\n
  96. Marines-Garcia, P.C. Paris, H. Tada, C. Bathias, \u201cFatigue crack growth from small to long cracks in VHCF with surface initiations\u201d, Int J Fatigue<\/em>, 29<\/strong>, 2072\u20132078 (2007).<\/li>\n
  97. W. Hertzberg, \u201cA simple calculation of da\/dN data in the near threshold regime and above\u201d, Int J Fract<\/em>, 64<\/strong>, R53\u2013R58 (1993).<\/li>\n
  98. T. Troshchenko, B.A. Gryaznov, Yu S. Nalimov, O.N. Gerasimchuk, O.M.\u00a0Ivasishin, P.E. Markovskii, “Fatigue strength and cyclic crack resistance of titanium alloy VT3-1 in different structural states. Communication 1. Study procedure and experimental results”, Strength Mater<\/em>, 27<\/strong>, 245\u2013251 (1995).<\/li>\n
  99. Standard Test Method for Measurements of Fatigue Crack Growth Rates<\/em>, E647, ASTM STP, Philadelphia (2000).<\/li>\n
  100. Palmgren, Die Lebensdauer von Kugellagern<\/em>, Veifahrenstechinik, Berlin, 68<\/strong>, 339-341 (1924).<\/li>\n
  101. A. Miner, \u201cCumulative damage in fatigue\u201d, Journal of Applied Mechanics<\/em>, 67<\/strong>, AI59-AI64 (1945).<\/li>\n
  102. Fatemi, L. Vang, \u201cCumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials\u201d, Int J Fatigue<\/em>, 20<\/strong>(1), 9-34 (1998).<\/li>\n
  103. Santecchia, M.S. Hamouda, F. Musharavati et al., \u201cA Review on fatigue life prediction methods for metals\u201d, Adv Mater Sci Eng,<\/em> 1-26 (2016).<\/li>\n
  104. A. Zakaria, S. Abdullah, M.J. Ghazali, \u201cA Review of the Loading Sequence Effects on the Fatigue Life Behaviour of Metallic Materials\u201d, Journal of Engineering Science and Technology Review<\/em>, 9<\/strong>(5), 189 \u2013 200 (2016).<\/li>\n
  105. Schijve, \u201cFatigue of structures and materials in the 20th century and the state of the art\u201d, Int J Fatigue<\/em>, 25<\/strong>, 679\u2013702 (2003).<\/li>\n
  106. J. French, \u201cFatigue and hardening of steels\u201d, Transactions, American Society of Steel Treating<\/em>, 21<\/strong>, 899-946 (1933).<\/li>\n
  107. B. Kommers, The effect of overstressing and understressing in fatigue, Proceedings ASTM<\/em>, 38<\/strong> (Part II). 249-268 (1938).<\/li>\n
  108. F. Langer, \u201cFatigue failure from stress cycles of varying amplitude\u201d, ASME J Appl Mech,<\/em> 59<\/strong>, AI60-AI62 (1937).<\/li>\n
  109. B. Kommers, \u201cThe effect of overstress in fatigue on the endurance life of steel\u201d, Proceedings ASTM<\/em>, 45<\/strong>, 532-541 (1945).<\/li>\n
  110. A. Bennett, \u201cA study of the damaging effect of fatigue stressing on X4130 steel\u201d, Proceedings ASTM,<\/em> 46<\/strong>, 693-714 (1946).<\/li>\n
  111. L. Henry, \u201cA theory of fatigue damage accumulation in steel\u201d, Transactions of the ASME<\/em>, 77<\/strong>, 913-918 (1955).<\/li>\n
  112. R. Gatts, \u201cApplication of a cumulative damage concept to fatigue\u201d, ASME Journal of Basic Engineering<\/em>, 83<\/strong>, 529-540 (1961).<\/li>\n
  113. R. Gatts, \u201cCumulative fatigue damage with random loading\u201d, ASME Journal of Basic Engineering<\/em>, 84<\/strong>, 439-467 (1962).<\/li>\n
  114. L. Bluhm, \u201cA note on fatigue damage\u201d, Materials Research and Standard<\/em>, 2<\/strong>(3), 122-123 (1962).<\/li>\n
  115. M. Marco, W.L. Starkey, \u201cA concept of fatigue damage\u201d, Transactions of the ASME<\/em>, 76<\/strong>, 627-632 (1954).<\/li>\n
  116. T. Corten, T.J. Dolan, \u201cCumulative fatigue damage\u201d, Proceedings of the International Conference on Fatigue of Metals: Institution of Mechanical Engineering and American Society of Mechanical Engineers. 235-246 (1956).<\/li>\n
  117. M. Freudenthal, R.A. Heller, \u201cOn stress interaction in fatigue and a cumulative damage rule\u201d, Journal of the Aerospace Sciences<\/em>, 26<\/strong>(7), 431-442 (1959).<\/li>\n
  118. A. Bennett,\u201cA study of the damaging effect of fatigue stressing on X4130 steel\u201d, Proceedings ASTM<\/em>, 46<\/strong>, 693-714 (1946).<\/li>\n
  119. L. Henry,\u201cA theory of fatigue damage accumulation in steel\u201d, Transactions of the ASME,<\/em> 77<\/strong>, 913-918 (1955).<\/li>\n
  120. Subramanyan, \u201cA cumulative damage rule based on the knee point of the S-N <\/em>curve\u201d, ASME Journal of Engineering Materials and Technology<\/em>, 98<\/strong>(4), 316-321 (1976).<\/li>\n
  121. Srivatsavan, S. Subramanyan, \u201cA cumulative damage rule based on successive reduction in fatigue limit\u201d, Journal of Engineering Materials and Technology<\/em>, Transactions of the ASME, 100(<\/strong>2), 212-214 (1978).<\/li>\n
  122. J. Grover, \u201cAn Observation Concerning the Cycle Ratio in Cumulative Damage. Fatigue of Aircraft Structures<\/em>\u201d, ASTM STP 274, Philadelphia, 120-124 (1960).<\/li>\n
  123. S. Manson, J.C. Freche, C.R., Ensign, \u201cApplication of a double linear damage rule to cumulative fatigue. Fatigue Crack Propagation<\/em>\u201d, ASTM STP 415, Philadelphia, 384-412 (1967).<\/li>\n
  124. S. Manson, G.R. Halford, \u201cPractical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage\u201d, Int J Fract,<\/em> 17<\/strong>(2), 169\u2013192 (1981).<\/li>\n
  125. S. Manson, G. R. Halford \u201cRe-examination of cumulative fatigue damage analysis – an engineering perspective\u201d, Eng Fract Mech<\/em>, 25(<\/strong>5\/6), 539-57I (1986).<\/li>\n
  126. D. Costaa, J.A.M. Ferreiraa, L.P. Borregob, et al., \u201cFatigue behaviour of AA6082 friction stir welds under variable loadings\u201d, Int J Fatigue<\/em>, 37<\/strong>, 8\u201316 (2012).<\/li>\n
  127. Rong Yuan, Haiqing Li, Hong-Zhong Huang et al., \u201cA nonlinear fatigue damage accumulation model considering strength degradation and its applications to fatigue reliability analysis\u201d, Int J Damage Mechanics<\/em>, 24<\/strong>(5), 646\u2013662 (2015).<\/li>\n
  128. M. Kachanov, \u201cTime to the rupture process under creep conditions\u201d, Izvestiia AN SSSR<\/em>, 8<\/strong>, 26-31 (1958).<\/li>\n
  129. N. Rabotnov, \u201cCreep Problems in Structural Members<\/em>\u201d, North-Holland, Amsterdam (1969).<\/li>\n
  130. Lemaitre, J.L. Chaboche, \u201cAspect phenomenologique de la ruptutre par endommagement\u201d, Journal Mecanique Appliquee<\/em>, 2<\/strong>(3), 317-365 (1978).<\/li>\n
  131. Lemaitre,\u00a0 A. Plumtree, \u201cApplication of damage concepts to predict creep-fatigue failures\u201d, ASME Journal of Engineering Materials and Technology<\/em>, 101<\/strong>, 284-292 (1979).<\/li>\n
  132. J. Miller, K.P. Zachariah, \u201cCumulative Damage laws for fatigue crack initiation and stage I propagation\u201d, Journal of strain analysis<\/em>, 11(<\/strong>4), 262-270 (1977).<\/li>\n
  133. E. Feltner, J.D. Morrow, \u201cMicroplastic Strain Hysteresis Energy as a Criteri on for Fatigue Fracture\u201d, ASME Journal of Basic Engineering<\/em>, 83<\/strong>, 5-22 (1961).<\/li>\n
  134. R. Halford, \u201cThe Energy Required for Fatigue\u201d, Journal of Materials<\/em>, 1(<\/strong>1), 3- 18 (1966).<\/li>\n
  135. Kujawski, F. Ellyin, \u201cA cumulative damage theory of fatigue crack initiation and propagation\u201d, Int J Fatigue<\/em>, 6<\/strong>(2), 83-88 (1984).<\/li>\n
  136. Kujawski, F. Ellyin, \u201cOn the concept of cumulative fatigue damage\u201d, Int J Fracture<\/em>, 37<\/strong>, 263-278, (1988).<\/li>\n
  137. T.Troshchenko, P.A. Fomichev, \u201cAn energy criterion for fatigue failure\u201d, Strength Mater,<\/em> 25<\/strong>, 1\u20137 (1993).<\/li>\n
  138. Golos, F. Ellyin, \u201cA total strain energy density theory for cumulative fatigue damage\u201d, ASME Journal of Pressure Vessel Technology<\/em>, 110<\/strong>, 36-41 (1988).<\/li>\n
  139. N. Leis, \u201cA nonlinear history-dependent damage model for low cycle fatigue. Low Cycle Fatigue\u201d, ASTM STP 942<\/em>, 143-159 (1988).<\/li>\n
  140. N. Smith, P. Watson, T.H. Topper, \u201cA stress-strain fun\u0441tion for the fatigue of metals\u201d, Journal of Materials<\/em>, 5<\/strong>(4), 767-778 (1970).<\/li>\n
  141. J. Miller, K.P. Zachariah, \u201cCumulative damage laws for fatigue crock initiation and stage I propagation\u201d, Journal of Strain Analysis<\/em>, 12<\/strong>(4), 262-270 (1977).<\/li>\n
  142. F.E. Ibrahim, K. J. Miller, \u201cDetermination of fatigue crack initiation life\u201d, Fatigue Fract Eng Mater Struct<\/em>, 2<\/strong>, 351-360 (1980).<\/li>\n
  143. J. Miller, \u201cShort crack problem\u201d, Fatigue Fract Eng Mater Struct<\/em>, 5<\/strong>(3), 223-232 (1982).<\/li>\n
  144. T. Ma, C. Laird, \u201cOverview of fatigue behavior in copper single crystals -V. Short crack growth behavior and a new approach to summing cumulative damage and predicting fatigue life under variable amplitudes\u201d, Acta Metallurgica et Materialia<\/em>, 37<\/strong>(2), 369-379 (1989).<\/li>\n
  145. D\u00f6ring, J. Hoffmeyer, T. Seeger, M. Vormwald, \u201cShort fatigue crack growth under nonproportional multiaxial elastic\u2013plastic strains\u201d, Int J Fatigue<\/em>, 28<\/strong>, 972\u201382 (2006).<\/li>\n
  146. Hertel, M. Vormwald, \u201cShort-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading\u201d, Eng Fract Mech<\/em>, 78<\/strong>, 1614 \u20131627 (2011).<\/li>\n
  147. Vormwald, P. Heuler, T. Seeger, \u201cA fracture mechanics based model for cumulative damage assessment as part of fatigue life prediction\u201d, ASTM STP 1122.<\/em> Advances in fatigue lifetime prediction techniques<\/em>, 28\u201343 (1992).<\/li>\n
  148. Fatemi, D. Socie, \u201cA critical plane approach to multiaxial fatigue damage including out-of-phase loading\u201d, Fatigue Fract Eng Mater Struct<\/em>, 11<\/strong>, 149\u201365 (1988).<\/li>\n
  149. Laue, H. Bomas, \u201cSpectrum fatigue life assessment of notched specimens based on the initiation and propagation of short cracks\u201d, Int J Fatigue<\/em>, 28<\/strong>, 1011\u20131021 (2006).<\/li>\n
  150. Ahmadi, H. Zenner, \u201cLifetime simulation under multiaxial random loading with regard to the microcrack growth\u201d, Int J Fatigue<\/em>, 28<\/strong>, 954\u2013962 (2006).<\/li>\n
  151. D. Hobson, M.W. Brown, E.R. de los Rios, \u201cTwo phases of short crack growth in medium carbon steel. The behaviour of short fatigue cracks\u201d, EGF Publ.<\/em> London, 441\u2013459 (1986).<\/li>\n
  152. C. H. Ricardo, \u0421.A.J. Miranda, \u201cCrack simulation models in variable amplitude loading – a review\u201d, Frattura ed Integrit\u00e0 Strutturale<\/em>, 35<\/strong>, 456-471 (2016).<\/li>\n
  153. R.C. Murthy, G.S. Palani, N.R. Iyer, \u201cState of art review on fatigue crack growth analysis under variable amplitude loading\u201d, IEI Journal<\/em>, 118-129 (2004).<\/li>\n
  154. E. Wheeler, \u201cSpectrum loading and crack growth\u201d. Transactions of the ASME. Series D, J Basic Eng<\/em>, 94<\/strong>, 181-186 (1972).<\/li>\n
  155. D. Willenborg, R.M. Engle, H.A. Wood, \u201cA crack growth retardation model using an effective stress concept, AFFDL, TM-71-FBR<\/em>\u201d, Air Force Flight Dynamics Laboratory, Wright Patterson Air force Base, OH (1971).<\/li>\n
  156. R. Porter, \u201cMethod of analysis and prediction of variable amplitude fatigue crack growth\u201d, Eng Fract Mech<\/em>, 4<\/strong>(4) 717-736 (1972).<\/li>\n
  157. D. Gray, J.P. Gallagher, \u201cPredicting fatigue crack retardation following a single overload using a modified Wheeler model\u201d, ASTM STP 590<\/em> (1976).<\/li>\n
  158. P. Gallagher, T.F. Hughes, \u201cInfluence of the yield strength on overload fatigue crack growth behavior of 4340 steel, AFFDL \u2013 TR-74-27\u201d<\/em>, Air Force Flight Dynamics Laboratory, Wright Patterson Air force Base, OH (1974).<\/li>\n
  159. S. Johnson, \u201cMulti-parameter yield zone model for predicting spectrum crack growth\u201d, ASTM STP 748<\/em>, 85- 102 (1981).<\/li>\n
  160. B. Chang, R.M. Hiyama, M. Szamossi, \u201cImproved methods for predicting spectrum loadings effects, AFWAL-TR81-3092\u201d<\/em>, Air Force Flight Dynamics Laboratory, Wright Patterson Air force Base, OH (1984).<\/li>\n
  161. Elber,, \u201cThe significance of fatigue crack closure\u201d, ASTM STP 486<\/em>, 230- 242 (1971).<\/li>\n
  162. D. Bell, M. Creager, \u201cCrack growth analyses for arbitrary spectrum loading, AFFDL-TR-74-129\u201d<\/em>, Air Force Flight Dynamics Laboratory, Wright Patterson Air force Base, OH (1974).<\/li>\n
  163. C. Newman, \u201cA finite element analysis fatigue crack closure<\/em>\u00bb, NASA TM X 72005, NASA, Hampton, VA (1975).<\/li>\n
  164. D. Dill, C.R. Saff, \u201cSpectrum crack growth prediction method based on crack surface displacement and contact analyses, Fatigue crack growth under spectrum loads\u201d, ASTM STP 595<\/em>, 306\u2013319 (1976).<\/li>\n
  165. F. Kanninnen, C. Atkinson, C.E. Feddersen, \u201cA fatigue crack growth analysis method based on a single representation of crack tip plasticity\u201d, ASTM STP 637<\/em>, 122-140 (1977).<\/li>\n
  166. Budianski, J.W. Hucthinson, \u201cAnalysis of closure in fatigue crack\u201d growth, J Appl Mech<\/em>, 45<\/strong>, 267-276 (1978).<\/li>\n
  167. U. de Koning, \u201cA Simple crack closure model for predictions of fatigue crack growth rates under variable amplitude loading\u201d, ASTM STP 743<\/em>, 63-85 (1981).<\/li>\n
  168. S. Dugdale, \u201cYielding of steel sheets containing slits\u201d, J Mech Phys Solids<\/em>, 8<\/strong>(2), 100-104 (1960).<\/li>\n
  169. M. Hudson, H.F. Hardrath, \u201cEffects of changing stress amplitude on the rate of fatigue-crack propagation in two aluminum alloys\u201d, NASA TN D-960<\/em>. (1961).<\/li>\n
  170. G. Forman, V.E. Kearney, R.M. Engle, \u201cNumerical Analysis of Crack Propagation in Cyclically Loaded Structures\u201d, J Basic Eng<\/em>, 89<\/strong>(3), 459\u2013464 (1967).<\/li>\n
  171. Chahardehi, A. Mehmanparast, \u201cFatigue crack growth under remote and local compression \u2013 a state-of-the-art review\u201d, Frattura ed Integrit\u00e0 Strutturale<\/em>, 35<\/strong>, 41-49 (2016).<\/li>\n
  172. S. Silva, \u201cFatigue crack propagation after overloading and underloading at negative stress ratios\u201d, Int J Fatigue<\/em>, 29<\/strong>, 1757\u20131771 (2007).<\/li>\n
  173. D. Halliday, J.Z. Zhang, P. Poole, P. Bowen, \u201cIn situ observation on the contrasting effects of an overload on small fatigue crack growth at two different load ratios in 2024-T351 aluminium alloy\u201d, Int J Fatigue<\/em>, 19<\/strong>(4), 273\u2013282 (1997).<\/li>\n
  174. H. Noroozi, G. Glinka, S. Lambert, \u201cA two parameter driving force for fatigue crack growth analysis\u201d, Int J Fatigue<\/em>, 27<\/strong>, 1277\u20131296 (2005).<\/li>\n
  175. Mikheevskiy, G. Glinka, \u201cElastic\u2013plastic fatigue crack growth analysis under variable amplitude loading spectra\u201d, Int J Fatigue<\/em>, 31<\/strong>, 1828\u20131836 (2009).<\/li>\n
  176. W. Landgraf, J. Morrow, T. Endo, \u201cDetermination of the cyclic stress\u2013strain curve\u201d, J Mater<\/em>, 4<\/strong>(1), 176 (1969).<\/li>\n
  177. Technical report on low cycle fatigue properties: ferrous and nonferrous metals<\/em>. SAE Standard No. J1099, Society of Automotive Engineers (SAE), Warrendale, Pennsylvania, (1998).<\/li>\n
  178. N. Smith, P. Watson, T.H. Topper, \u201cA stress\u2013strain function for the fatigue of metals\u201d, J Mater<\/em>, 5<\/strong>(4), 767\u2013778 (1970).<\/li>\n
  179. K. Walker, \u201cThe 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\u201d, ASTM STP 462<\/em>. Philadelphia: American Society for Testing and Materials, 1-14 (1970).<\/li>\n
  180. Neuber, \u201cTheory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress\u2013strain law\u201d, ASME J Appl Mech<\/em>, 28<\/strong>, 544\u2013551 (1961).<\/li>\n
  181. Moftakhar, A. Buczynski, G. Glinka, \u201cCalculation of elastoplastic strains and Stresses in notched under multiaxial loading\u201d, Int J Fract<\/em>, 70<\/strong>(3), 357\u2013373 (1995).<\/li>\n
  182. Glinka, G. Shen, \u201cUniversal features of weight functions for cracks in mode I.\u201d, Eng Fract Mech<\/em>, 40<\/strong>(6), 1135\u20131146 (1991).<\/li>\n
  183. E. Dowling, \u201cMechanical behavior of materials<\/em>\u201d, Prentice Hall Inc., New Jersy (2006).<\/li>\n
  184. Abdelkader Miloudi, Zemri Mokhtar, Mohamed Benguediab, M. Mazari, Abdelwaheb Amrouche, \u201cCrack Propagation under Variable Amplitude Loading\u201d, Materials Research<\/em>, 16<\/strong>(5), 1161-1168 (2013).<\/li>\n<\/ol>\n

     <\/p>\n

     <\/p>\n

    References to Chapter 2<\/strong>\u00a0<\/strong><\/p>\n

      \n
    1. Standard Test Method for Measurements of Fatigue Crack Growth Rates<\/em>, ASTM STP, E647\u201300, Philadelphia (2000).<\/li>\n
    2. Guide to methods for assessing the acceptability of flaws in metallic structures<\/em>, British Standard BS 7910 (2005).<\/li>\n
    3. 50-345-82. Metodicheskie ukazaniya. Raschetyi i ispyitaniya na prochnost. Metodyi mehanicheskih ispyitaniy metallov. Opredelenie harakteristik treschinostoykosti (vyazkosti razrusheniya) pri tsiklicheskom nagruzhenii<\/em>, Vved. 01.01.83, Izd-vo standartov, M. (1983).<\/li>\n
    4. DSTU EN 10002-1:2006, MaterIali metalev<\/em>i<\/em>. Viprobuvannya na roztyag<\/em>, Derzhspozhivstandart Ukrayini, Kiyiv (2008) .<\/li>\n
    5. GOST 25.502-79 Raschetyi i ispyitaniya na prochnost v mashinostroenii. Metodyi mehanicheskih ispyitaniy metallov. Metodyi ispyitaniy na ustalost<\/em>, Izdatelstvo standartov, M. (1979).<\/li>\n
    6. GOST 25.504-82 Raschetyi i ispyitaniya na prochnost. Metodyi rascheta harakteristik soprotivleniya ustalosti, Izdatelstvo standartov, M. (1982).<\/li>\n
    7. GOST 25.507-85 Raschetyi i ispyitaniya na prochnost v mashinostroenii. Metodyi ispyitaniy na ustalost pri ekspluatatsionnyih rezhimah nagruzheniya. Obschie trebovaniya, Izdatelstvo standartov, M. (1985).<\/li>\n
    8. GOST 23207-78 Soprotivlenie ustalosti. Osnovnyie terminyi, opredeleniya i oboznacheniya<\/em>, Izdatelstvo standartov, M. (1978).<\/li>\n
    9. B.A. Gryaznov, U.S. Nalimov, G.V. Tsyban\u2019ov, O.M. Herasymchuk, O.M.Ivasishin, P.E. Markovskii, \u201cUpdating manufacture technology for critical parts of titanium alloy for increasing their fatigue characteristics\u201d, Proceedings of the International Seminar on Manufacturing Technology Beyond 2000, India, Bangalore (1999).<\/li>\n
    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<\/em>, 36<\/strong>, 225-230 (2004).<\/li>\n
    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<\/em>, 38<\/strong>, 651-658 (2006).<\/li>\n
    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<\/em>, 39<\/strong>, 408-414 (2007).<\/li>\n
    13. O.M. Herasymchuk, \u201cNonlinear relationship between the fatigue limit and quantitative parameters of material microstructure\u201d, Int J Fatigue<\/em>, 33<\/strong>, 649\u2013659 (2011).<\/li>\n
    14. P.E. Markovsky, V.I. Bondarchuk, O. Herasymchuk, \u201cInfluence of grain size, aging conditions and tension rate on the mechanical behavior of titanium low-cost metastable beta-alloy in thermally hardened condition\u201d, Mater Sci Eng A<\/em>, 645<\/strong>(1), 150\u2013162 (2015).<\/li>\n
    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<\/em>, 43<\/strong>, 282-293 (2011).<\/li>\n
    16. M. Herasymchuk, O.V. Kononuchenko, \u201cVpliv tehnologIchnih defektIv ta mIkrostrukturi na opIr vtomI kondensatIv Iz titanovogo splavu TI-6Al-4V, otrimanih metodom EV RVD\u201d, V kn.: Prochnost materialov i elementov konstruktsiy: Trudyi Mezhdunarodnoy nauchno-tehnicheskoy konferentsii. In-t problem prochnosti im. G.S.Pisarenko NAN Ukrainyi, Kyiv (2011).<\/li>\n
    17. M. Herasymchuk, O.V. Kononuchenko, “Effect of surface stress concentrators and microstructure on the fatigue limit of the material”, Strength Mater<\/em>, 43<\/strong>, 374-383 (2011).<\/li>\n
    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<\/em>, 47<\/strong>, 579-585 (2015).<\/li>\n
    19. M. Herasymchuk, O.V. Kononuchenko, V.I. Bondarchuk, \u201cFatigue life calculation for titanium alloys considering the influence of microstructure and manufacturing defects\u201d, Int J Fatigue<\/em>, 81<\/strong>, 257\u2013264 (2015).<\/li>\n
    20. M. Herasymchuk, P.E. Markovsky, V.I. Bondarchuk, \u201cCalculating the fatigue life of smooth specimens of two-phase titanium alloys subject to symmetric uniaxial cyclic load of constant amplitude, Int J Fatigue<\/em>, 83<\/strong>. 313\u2013322 (2016).<\/li>\n
    21. M. Herasymchuk, O.V. Kononuchenko, \u201cPeculiarities of short fatigue cracks growth from a blind hole in specimens made of steel 45. Part 1. Experimental results\u201d, Strength Mater<\/em>, 53<\/strong>, 213\u2013221 (2021).<\/li>\n
    22. M. Herasymchuk, O.V. Kononuchenko, “Theoretical estimation of fatigue life before crack initiation in metal materials”, Strength Mater,<\/em> 55<\/strong>, 457-468 (2023).<\/li>\n
    23. Tsvikker, Titan i ego splavyi<\/em>, Metallurgiya, M. (1979).<\/li>\n
    24. A. Borisova, G.A. Bochvar, M.Ya. Brun, Metallografiya titanovyih splavov<\/em>, Metallurgiya, M. (1980).<\/li>\n
    25. Lutjering, \u201cInfluence of processing on microstructure and mechanical properties of (\u03b1+\u03b2) titanium alloys\u201d, Mat Sci Eng<\/em>, A243<\/strong>, 32\u201345 (1998).<\/li>\n
    26. N. Gridnev, O. M. Ivasishin, S. P. Oshkaderov, Fizicheskie osnovyi skorostnogo termouprochneniya titanovyih splavov<\/em>, Nauk. Dumka, Kiev (1986).<\/li>\n
    27. M. Ivasishin, P.E. Markovsky, \u201cEnhancing the Mechanical Properties of Titanium Alloys with Rapid Heat Treatment (Overview)\u201d, JOM<\/em>, 7<\/strong>, 48\u201356 (1996).<\/li>\n
    28. M. Ivasishin, S.P. Oshkaderov, P.E. Markovskiy, \u201cIssledovaniya skorostnogo nagreva pod zakalku titanovyih splavov\u201d, Metallovedenie i termicheskaya obrabotka metallov<\/em>, No 1, 32\u201335 (1990).<\/li>\n
    29. O. Peters, G. Luetjering, O.M. Ivasishin, P.E. Markovsky, \u201cMechanical Properties of Fine- Grained Beta-Titanium Alloys\u201d, Proc. Of 3rd <\/sup>ASM Conf. On Synthesis, Processing and Modelling of Advanced Materials, 269\u2013274 (1997).<\/li>\n
    30. M. Ivasishin, S.L. Semiatin, \u201cRapid heat treatment of titanium alloys, In: Processing and Mechanical Properties of Titanium Alloys with Ultra-Fine Equiaxed Microstructure, \u00abTHERMEC\u00bb2000\u201d, Proceedings International Conference on Processing and Manufacturing of \u0430dvanced Materials las Vegas, USA. \u2013 CDROM. “Special Issue: Journal of Materials Processing Technology, Elsevier Science, UK, Section A1, 117<\/strong>\/3 (2000).<\/li>\n
    31. Lutjering, J.C. Williams, Titanium<\/em>, Springer, New York (2003).<\/li>\n
    32. Zarkades, F.R. Larson, \u201cEffect of textures on the charpy impact energy of some Ti alloy plate<\/em>\u201d, The Science, Technology and Application of Titanium, Pergamon Press, Oxford, UK (1970).<\/li>\n
    33. P. Jones, W.B. Hutchinson, \u201cStress-state dependence of slip in titanium-6Al-4V and other HCP metals\u201d, Acta Met<\/em>, 29<\/strong>, 951\u2013968 (1981).<\/li>\n
    34. Bantounas, D. Dye, T.C. Lindley, \u201cThe effect of grain orientation on fracture morphology during high-cycle fatigue of Ti-6Al-4V\u201d, Acta Mater<\/em>, 57<\/strong>, 3584\u20133595 (2009).<\/li>\n
    35. Venkatraman, S. Ghosh, V. Mills, \u201cA size dependent crystal plasticity finite\u2013element model for creep and load shedding in polycrystalline titanium alloys\u201d, Acta Mater<\/em>, 55<\/strong>, 3971\u20133986 (2007).<\/li>\n
    36. S. Ravichandran, \u201cNear threshold fatigue crack growth behavior of a titanium alloy: Ti-6A1-4V\u201d, Acta Metall Mater<\/em>, 39<\/strong>(3), 401\u2013410 (1991).<\/li>\n
    37. N. Gerasimchuk, Vyinoslivost i tsiklicheskaya treschinostoykost titanovogo splava VT3-1 v razlichnyih strukturnyih sostoyaniyah<\/em>. Dissertatsiya na soisk. uch.st. kand.tehn.nauk, Kiev (1995).<\/li>\n
    38. F. Savage, J. Tatalovich, M. Zupan, K.J. Hemker, M.J. Mills, \u201cDeformation mechanisms and microtensile behavior of single colony Ti-6242Si\u201d, Mater Sci Eng<\/em>, A319\u2013A321<\/strong>, 398\u2013403 (2001).<\/li>\n
    39. Sansoz, H. Ghonem, \u201cFatigue Crack Growth Mechanisms in Ti6242 Lamellar Microstructures: Influence of Loading Frequency and Temperatur\u201d, Metallurgical and Materials Transactions A<\/em>, 34a<\/strong>, 2565\u20132578 (2003).<\/li>\n
    40. Lin Xiao, \u201cTwinning behavior in the Ti\u20135 at.% Al single crystals during cyclic loading along [0 0 0 1]\u201d, Materials Science and Engineering A<\/em>, 394<\/strong>, 168\u2013175 (2005).<\/li>\n
    41. Mechanical Properties of a Titanium Blading Alloy,<\/em> EPRI CS-2933. Res. Proj. 1266-1, Final Report (1983).<\/li>\n
    42. A Movchan, \u201cNeorganicheskie materialyi, osazhdaemyie iz parovoy fazyi v vakuume<\/em>\u201d, Suchasne materIaloznavstvo HHI StorIchchya, Nauk. dumka, Kiev, 318\u2013332 (1998).<\/li>\n
    43. R. Smith, K. Kennedy, F.S. Boericke, \u201cMetallurgical Charactenstics of Titanium \u2013 Alloy Foil Prepared by Electron Beam Evaporation\u201d, J Vac Sci Technology<\/em>, 6<\/strong>, 48\u201351 (1970).<\/li>\n
    44. H. Froes, D. Eylon, Powder metallurgy of titanium alloys \u2013 a review.<\/em> Titanium. Technology: Present Status and Future Trends,<\/em> Warrendale, 49\u201359 (1985).<\/li>\n
    45. M. Hagivara, Y. Kaieda, Y. Kawade, Miura, \u201cProperty enhancement of titanium alloys by blended elemental P\/M method\u201d, Titanium 92, Science and Technology: Proc 7 World Conf on Titanium<\/em>, Warrendale, 1<\/strong>, 887\u2013894 (1993).<\/li>\n
    46. H. Fujii, K. Takahashi, K. Fujisawa, \u201cLow cost process of blended elemental powder metallurgy\u201d, Titanium 95, Science and Technology: Proc 8 World Conf on Titanium<\/em>, London, 1<\/strong>, 2547\u20132554 (1996).<\/li>\n
    47. Abkowits, D. Rowell, \u201cSuperior fatigue properties for blended elemental P\/M Ti\u20136Al\u20134V\u201d, J. Met.<\/em>, 8<\/strong>, 36\u201339. 1986.<\/li>\n
    48. A. Saltyikov, Stereometricheskaya metallografiya<\/em>, Metallurgiya, M. (1976).<\/li>\n
    49. H. Zuo, Z.G. Wang, E.H. Han, \u201cEffect of microstructure on ultra-high cycle fatigue behavior of Ti\u20136Al\u20134V\u201d, Materials Science and Engineering A<\/em>, 473<\/strong>, (2008).<\/li>\n
    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<\/em>, Institut problem prochnosti, Kiev (2009).<\/li>\n
    51. M. Babakov, Teoriya kolebaniy<\/em>, Nauka, M. (1965).<\/li>\n
    52. V. Prokopenko, M.V. Baumshtein, \u201cTheoretical estimate of the life of gas-turbine-engine compressor blades\u201d, Strength Mater,<\/em> 13<\/strong>, 575\u2013579 (1981).<\/li>\n
    53. Irvin, Osnovyi teorii rosta treschin i razruscheniya<\/em>, v kn: Razrushenie. \u2013 pod red. G. Libovitsa, T. 3., Mir, M. (1976).<\/li>\n
    54. Microstructure and Texture Effects on Titanium Alloys<\/em>, CS\u2013472. Project 1266\u201333, Interim. Report (1986).<\/li>\n
    55. M. Ivasishin, V.M. Anokhin, A.N. Demidik, D.G. Savvakin, \u201cCost-effective blended elemental powder metallurgy of titanium alloys for transport application\u201d, Key Eng Materials<\/em>, 188<\/strong>, 55\u201362 (2000).<\/li>\n
    56. M. Ivasishin, D.G. Savvakin, K.A. Bondareva, \u201cSintez splava Ti\u20136Al\u20134V s nizkoy ostatochnoy poristostyu metodom poroshkovoy metallurgii\u201d, Poroshkovaya metallurgiya<\/em>, No. 7\u20138, 54\u201364 (2002).<\/li>\n
    57. M. Ivasishin, D.G. Savvakin, V.S. Moxson, \u201cTitanium powder metallurgy for automotive components\u201d, Materials Techn Adv Perform Materials<\/em>, 17<\/strong>(1), 20\u201325 (2002).<\/li>\n
    58. Standard Test Methods for Determining Average Grain Size<\/em>, ASTM, E-112 (1996).<\/li>\n
    59. O.M. Herasymchuk, \u201cNonlinear relationship between the fatigue limit and quantitative parameters of material microstructure\u201d, Int J Fatigue,<\/em> 33<\/strong>, 649\u2013659 (2011).<\/li>\n<\/ol>\n

       <\/p>\n

      References to Chapter 3<\/strong>\u00a0<\/strong><\/p>\n

        \n
      1. E. Stromeyer, \u201cThe determination of fatigue limits under alternating stress conditions\u201d. Proc of the Royal Society of London. Series A, containing papers of a mathematical and physical character<\/em>, 90<\/strong>(620), 411\u201325 (1914).<\/li>\n
      2. \u041a. Tanaka, T. Mura, \u201cA dislocation model for fatigue crack initiation\u201d, ASME J Appl Mech<\/em>, 48<\/strong>, 97\u2013103 (1981).<\/li>\n
      3. S Chan, \u201cA microstructure \u2013 based fatigue \u2013 crack \u2013 initiation model\u201d, Metall Mater Trans A<\/em>, 34A<\/strong>, 43\u201358 (2003).<\/li>\n
      4. Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials<\/em>, ASTM E466-15 (2015).<\/li>\n
      5. O. Herasymchuk, \u201cNonlinear relationship between the fatigue limit and quantitative parameters of material microstructure\u201d, Int J Fatigue<\/em>, 33<\/strong>, 649\u2013659 (2011).<\/li>\n
      6. D. Chapetti, \u201cFatigue propagation threshold of short cracks under constant amplitude loading\u201d, Int<\/em> J<\/em> Fatigue<\/em>, 25<\/strong>, 1319\u20131326 (2003).<\/li>\n
      7. M.H. El Haddad, T.H. Topper, K.N. Smith, \u201cPrediction of non propagating cracks\u201d, Eng<\/em> Fract<\/em> Mech<\/em>, 11(<\/strong>3), 573\u2013584 (1979).<\/li>\n
      8. J. McEvily, M. Endo, Y. Murakami, \u201cOn the relationship and the short fatigue threshold\u201d, Fatigue Fract Eng Mater Struct<\/em>, 26<\/strong>, 269\u2013278 (2003).<\/li>\n
      9. Kitagawa, S. Takahashi, \u201cApplicability of fracture mechanics to very small cracks or the cracks in the early stage\u201d, in: Proc. of the Second Int. Conf. of Mechanical Behavior of Materials. Metals Park (OH): ASM, 627\u2013631 (1976).<\/li>\n
      10. U. Krupp, Fatigue Crack Propagation in Metals and Alloys: Microstructural Aspects and Modeling Concepts<\/em>, Wiley\u2013VCH, Weinheim (2007).<\/li>\n
      11. W. Hertzberg, \u201cA simple calculation of da\/dN<\/em> data in the near threshold regime and above\u201d, Int J Fract<\/em>, 64<\/strong>, 53\u201358 (1993).<\/li>\n
      12. M. Herasymchuk, O.V. Kononuchenko, P.E. Markovsky, V.I. Bondarchuk, \u201cCalculating the fatigue life of smooth specimens of two-phase titanium alloys subject to symmetric uniaxial cyclic load of constant amplitude\u201d, Int J Fatigue<\/em>, 83<\/strong>, 313\u2013322 (2016).<\/li>\n
      13. M. Herasymchuk, \u201cMicrostructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth\u201d, Int J Fatigue<\/em>, 81<\/strong>, 148\u2013161 (2015).<\/li>\n
      14. P. Lukas, W.W. Gerberich, \u201cA proposed criterion for fatigue threshold: dislocation substructure approach\u201d, Fatigue Fract<\/em> Eng Mater Struct<\/em>, 6<\/strong>, 271\u201380 (1983).<\/li>\n
      15. Hanlon, E.D. Tabachnikova, S. Suresh, \u201cFatigue behavior of nanocrystalline metals and alloys\u201d, Int J Fatigue<\/em>, 27<\/strong>, 1147\u20131158 (2005).<\/li>\n
      16. O. Peters, B.L. Boyce, X. Chen, et.al., \u201cOn the application of the Kitagawa\u2013Takahashi diagram to foreign-object damage and high-cycle fatigue\u201d, Eng Fract Mech<\/em>, 69<\/strong>, 1425\u20131446 (2002).<\/li>\n
      17. M. Herasymchuk, O.V. Kononuchenko, \u201cPeculiarities of short fatigue cracks growth from a blind hole in specimens made of steel 45. Part 1. Experimental results”, Strength Mater<\/em>, 53<\/strong>, 213\u2013221 (2021).<\/li>\n
      18. Tanaka, Y. Nakai, Y. Yamashita, \u201cFatigue growth threshold of small cracks\u201d, Int J Fract<\/em>, 17(5)<\/strong>, 519\u201333 (1981).<\/li>\n
      19. S. Park, S.J. Kim, K. H. Kim, et.al.,\u201cA microstructural model for predicting high cycle fatigue life of steels\u201d, Int J Fatigue<\/em>, 27<\/strong>, 1115\u20131123 (2005).<\/li>\n
      20. N. Hanlon, W.M. Rainforth, \u201cSome observations on cyclic deformation structures in the high-strength commercial aluminum alloy AA 7150\u201d, Metall Mater Trans A<\/em>, 29A<\/strong>, 2727\u20132736 (1998).<\/li>\n
      21. Akiniwa, K. Tanaka, \u201cStatistical characteristics of propagation of small fatigue crack in smoth specimens of aluminium alloy 2024-T3\u201d, Mater Sci Eng<\/em>, A104<\/strong>, 105\u2013115 (1988).<\/li>\n
      22. Tokaji, M. Kamakura, Y. Ishiizumi, N. Hasegawa, \u201cFatigue behaviour and fracture mechanism of a rolled AZ31 magnesium alloy\u201d, Int J Fatigue<\/em>, 26<\/strong>, 1217\u20131224 (2004).<\/li>\n
      23. J. McEvily, M. Endo, K. Yamashita, et al., \u201cFatigue notch sensitivity and the notch size effect\u201d, Int J Fatigue<\/em>, 30<\/strong>, 2087\u20132093 (2008).<\/li>\n
      24. S. Chan, \u201cVariability of large-crack fatigue-crack-growth thresholds in structural alloys\u201d, Metall Mater Trans A<\/em>, 35A<\/strong>, 3721\u20133735 (2004).<\/li>\n
      25. Sun, Z. Lei, Y. Hong, \u201cEffects of stress ratio on crack growth rate and fatigue strength for high cycle and very-high-cycle fatigue of metallic materials\u201d, Mech Mater<\/em>, 69<\/strong>, 227\u2013236 (2014).<\/li>\n
      26. \u201cStandard Test Method for Measurements of Fatigue Crack Growth Rates<\/em>\u201d, ASTM STP, E647\u201300 (2000).<\/li>\n
      27. Lukas, M. Klesnil, \u201cFatigue limit of notched bodies\u201d, Mater Sci Eng<\/em>, 34<\/strong>, 61\u201366 (1978).<\/li>\n
      28. M. Herasymchuk, O.V. Kononuchenko, \u201cPeculiarities 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\u201d, Strength Mater<\/em>, 53<\/strong>, 405\u2013416 (2021).<\/li>\n
      29. Tanaka, Y. Akiniwa, \u201cResistance curve method for predicting propagation threshold of short fatigue cracks at notches\u201d, Eng Fract Mech, <\/em>30<\/strong>, 863\u2013876 (1988).<\/li>\n
      30. Atzori, P. Lazzarin, G. Meneghetti, \u201cFracture mechanics and notch sensitivity\u201d, Fatigue Fract Eng Mater Struct, <\/em>26<\/strong>, 257\u2013267 (2003) .<\/li>\n
      31. M. Ciavarella, G. Meneghetti, \u201cOn fatigue limit in the presence of notches: classical vs. recent unified formulations\u201d, Int<\/em> J<\/em> Fatigue<\/em>, 26<\/strong>, 289\u2013298 (2004).<\/li>\n
      32. C. Ting, F.V. Lawrence, \u201cA crack closure model for predicting the threshold stresses of notches\u201d, Fatigue Fract Eng Mater Struct,<\/em> 16<\/strong>, 93\u2013114 (1993).<\/li>\n
      33. Sadananda, S. Sarkar, D. Kujawski, A.K. Vasudevan, \u201cA two-parameter analysis of S\u2013N<\/em> fatigue life using and \u201d, Int J Fatigue<\/em>, 31<\/strong>, 1648\u20131659 (2009).<\/li>\n
      34. M. Herasymchuk, O.V. Kononuchenko, \u201cThe range of use of the critical distance concept to predict the endurance limit in the presence of stress raisers\u201d, Strength Mater<\/em>, 52<\/strong>, 722-730 (2020).<\/li>\n
      35. Maierhofer, H.P. Ganser, R. Pippan, \u201cModified Kitagawa\u2013Takahashi diagram accounting for finite notch depths\u201d, Int J Fatigue<\/em>, 70<\/strong>, 503\u2013509 (2015).<\/li>\n<\/ol>\n

         <\/p>\n

        References to Chapter 4<\/strong><\/p>\n

          \n
        1. Depres, C.F. Robertson, M.C. Fivel, \u201cCrack initiation in fatigue: experiments and three-dimensional dislocation simulations\u201d, Mater Sci Eng<\/em>, 387<\/strong>, 288\u2013291 (2004).<\/li>\n
        2. P. Hirth, J.Lothe, Theory of dislocations (2 ed.)<\/em>, USA, Wiley (1982).<\/li>\n
        3. Bridier, P. Villechaise, J. Mendez, \u201cAnalysis of the different slip systems activated by tension in a a\/b titanium alloy in relation with local crystallographic orientation\u201d, Acta Mater<\/em>, 53<\/strong>, 555\u2013567 (2005).<\/li>\n
        4. J. Caton, R. John, W.J. Porter, M.E. Burba, \u201cStress ratio effects on small fatigue crack growth in Ti\u20136Al\u20134V\u201d, Int J Fatigue<\/em>, 38<\/strong>, 36\u201345 (2012).<\/li>\n
        5. Akiniwa, K. Tanaka, \u201cStatistical characteristics of propagation of small fatigue crack in smooth specimens of aluminium alloy 2024-T3\u201d, Mater Sci Eng<\/em>, 104<\/strong>, 105\u2013115 (1988).<\/li>\n
        6. T. Lee, M. Peters, G. Wirth, \u201cEffects of thermomechanical treatment on microstructure and mechanical properties of blended elemental Ti-6Al-4V compacts\u201d, Mater Sci Eng<\/em>, A102<\/strong>, 105\u2013114 (1988).<\/li>\n
        7. T. Lee, M. Peters. G. Welsch, \u201cElastic moduli and tensile and physical properties of heat-treated and quenched powder metallurgical Ti-6Al-4V alloy\u201d, Metall Trans A<\/em>, 22A<\/strong>, 709\u2013713 (1991).<\/li>\n
        8. W. Hertzberg, \u201cA simple calculation of da\/dN data in the near threshold regime and above\u201d, Int J Fract<\/em>, 64<\/strong>, R53\u2013R58 (1993).<\/li>\n
        9. S. Chan, \u201cVariability of large-crack fatigue-crack-growth thresholds in structural alloys\u201d, Metall Mater Trans A<\/em>, 35A<\/strong>, 3721\u20133735 (2004).<\/li>\n
        10. Tanaka, Y. Akiniwa, \u201cResistance curve method for predicting propagation threshold of short fatigue cracks at notches,\u201d Eng Fract Mech<\/em>, 30<\/strong>, 863\u2013876 (1988).<\/li>\n
        11. Maierhofer, H.P. Ganser, R. Pippan, \u201cModified Kitagawa\u2013Takahashi diagram accounting for finite notch depths,\u201d Int J Fatigue<\/em>, 70<\/strong>, 503\u2013509 (2015).<\/li>\n
        12. M. Herasymchuk, \u201cMicrostructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth,\u201d Int J Fatigue<\/em>, 81<\/strong>, 148\u2013161 (2015).<\/li>\n
        13. Leopold, Y. Nadot, T. Billaudeau, J. Mendez, \u201cInfluence of artificial and casting defects on fatigue strength of moulded components in Ti-6Al-4V alloy\u201d, Fatigue Fract Eng Mater Struct<\/em>, 38<\/strong>, 1026\u20131041 (2015).<\/li>\n
        14. British Standard: Guide to methods for assessing the acceptability of flaws in metallic structures.<\/em> BS 7910 (2005).<\/li>\n
        15. Bantounas, D. Dye, T.C. Lindley, \u201cThe effect of grain orientation on fracture morphology during high-cycle fatigue of Ti-6Al-4V\u201d, Acta Materialia<\/em>, 57<\/strong>, 3584\u20133595 (2009).<\/li>\n
        16. Pol\u00e1k, J. Man, \u201cExperimental evidence and physical models of fatigue crack initiation\u201d, Int J Fatigue<\/em>, 91<\/strong>, 294\u2013303 (2016).<\/li>\n
        17. C. Newman, Jr. and I. S. Raju, \u201cStress-intensity factor equations for cracks in three-dimensional finite bodies\u201d, NASA Technical Memorandum 83200<\/em>, (1981).<\/li>\n
        18. Schijve, \u201cFatigue of structures and materials in the 20th century and the state of the art\u201d, Int J Fatigue<\/em>, 25<\/strong>, 679\u2013702 (2003).<\/li>\n
        19. Rege, D.G. Pavlou, \u201cA one-parameter nonlinear fatigue damage accumulation model\u201d, Int J Fatigue<\/em>, 98<\/strong>, 234\u2013246 (2017).<\/li>\n
        20. Santecchia, A.M.S. Hamouda, F. Musharavati et al., \u201cA Review on fatigue life prediction methods for metals\u201d, Adv Mater Sci Eng<\/em>, 1\u201326 (2016).<\/li>\n<\/ol>\n

           <\/p>\n

           <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

          Authors: Herasymchuk Oleh Mykolaiovych Head of department of Fatigue and crack resistance of structural materials, G.S.Pisarenko Institute for problems of strength of the National Academy of Sciences of Ukraine, Kyiv, Ukraine; Doctor of technical sciences; Senior researcher; https:\/\/www.scopus.com\/authid\/detail.uri?authorId=57197739466       Kononuchenko Oleh Vasyliovych Senior researcher of department of Fatigue and crack resistance of structural […]<\/p>\n","protected":false},"author":3,"featured_media":6329,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,21],"tags":[],"class_list":["post-6328","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-books","category-scientific_monographs"],"_links":{"self":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/6328","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/comments?post=6328"}],"version-history":[{"count":6,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/6328\/revisions"}],"predecessor-version":[{"id":6420,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/6328\/revisions\/6420"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media\/6329"}],"wp:attachment":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media?parent=6328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/categories?post=6328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/tags?post=6328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}