129
Views
0
CrossRef citations to date
0
Altmetric
Part A: Materials Science

Fractal fatigue crack

ORCID Icon
Pages 1048-1070 | Received 06 Oct 2022, Accepted 10 Feb 2023, Published online: 25 Mar 2023

References

  • X. Lin and G. Haicheng, Plastic energy dissipation model for lifetime prediction of zirconium and Zircaloy-4 fatigued at RT and 400∘C, Trans. ASME 120 (1998), pp. 112–118.
  • A. Das, Tackling flow stress of zirconium alloys, Arch. Comp. Meth. Engg. 28 (2021), pp. 2103–2131.
  • P.R. Pandarinathan and P. Vasudevan, Low-cycle fatigue studies on nuclear reactor Zircaloy-2 fuel tubes at room temperature, 300 and 350∘C, J. Nucl. Mater. 91 (1980), pp. 47–58.
  • T. Kubo, T. Motomiya, and Y. Wakashima, Low-cycle corrosion fatigue of Zircaloy-2 in iodine atmospheres, J. Nucl. Mater. 140 (1986), pp. 185–196.
  • M. Bocaarek, I. Alvarez-Armas, A.F. Armas, and C. Petersen, Low cycle deformation behaviour of Zircaloy-4 at elevated temperatures, Materwiss. Werksttech. 17 (1986), pp. 317–327.
  • A. Beloucif and J. Stolarz, Fatigue'96, Proceedings of the Sixth International Fatigue Congress, G. Lutjering, H. Nowack, eds., 6–10 May 1996, Berlin, Germany, Elservier, Oxford, 1996, p. 277.
  • X. Lin and G. Haicheng, Dislocation structures in Zirconium and Zircaloy-4 fatigued at different temperatures, Metall. Mater. Trans. 28A (1997), pp. 1021–1033.
  • X. Lin, G. Haicheng, and K. Zhenbang, Cyclic deformation behavior of Zircaloy-4 at different temperatures, Acta Metall. Sinica (English Letter) 8 (1995), pp. 219–225.
  • S.A. Nikulin, A.B. Rozhnov, A.Y. Gusev, T.A. Nechaykina, S.O. Rogachev, and M.Y. Zadorozhnyy, Fracture resistance of Zr-Nb alloys under low-cycle fatigue tests, J. Nucl. Mater. 446 (2014), pp. 10–14.
  • S.A. Nikulin, V.A. Markelov, A.Y. Gusev, T.A. Nechaykina, A.B. Rozhnov, S.O. Rogachev, and M.Y. Zadorozhnyy, Low-cycle fatigue tests of zirconium alloys using a dynamic mechanical analyzer, Int. J. Fat. 48 (2013), pp. 187–191.
  • A.J. Luevano, M.A. Przystupa, and J. Zhang, Accumulation of microstructural damage due to fatigue of high-strength aluminum alloys, J. Mater. Engg. Perf. 3 (1994), pp. 47–54.
  • B. Tomkins, Fatigue crack propagation – an analysis, Philos. Mag. 18 (1968), pp. 1041–1066.
  • A. Das, Magnetic properties of cyclically deformed austenite, J. Mag. Mag. Mater. 361 (2014), pp. 232–242.
  • A. Das, Dislocation configurations through austenite grain misorientations, Int. J. Fat. 70 (2015), pp. 473–479.
  • A. Das, Resurgence of texture in cyclically deformed austenite, Mater. Char. 123 (2017), pp. 315–327.
  • A. Das, Grain boundary engineering: Fatigue fracture, Philos. Mag. 97 (1017), pp. 867–916.
  • A. Das, Cyclic plasticity induced transformation of austenitic stainless steels, Mater. Char. 149 (2019), pp. 1–25.
  • P. Kotowski, G. Lesiuk, J.A. Correia, and A.M. de Jesus, Mixed mode (I+II) fatigue crack paths in S355J0 steel in terms of fractal geometry, in AIP Conference Proceedings, 2028 1, AIP Publishing LLC, 2018, p. 020005.
  • G.P. Cherepanov, A.S. Balankin, and V.S. Ivanova, Fractal fracture mechanics - a review, Engg. Fract. Mech. 51(6) (1995), pp. 997–1033.
  • B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, 1984.
  • M.A. Sadovskii and V.F. Pisarenko, Seismic Process in Bloc Medium (in Russian), Nauka, Moscow (1991).
  • A.S. Balankin, Physics of fracture and mechanics of self-affine cracks, Engg. Fract. Mech. 57 (1997), pp. 135–203.
  • V.S. Ivanova, Sinergetika. Prochnost' i razrushenie metallicheskih materialov [Synergetics. Strength and fracture of metallic materials] (Nauka, Moscow, 1992) (in Russian).
  • A. Das and S. Tarafder, Experimental investigation on martensitic transformation and fracture morphologies of austenitic stainless steel, Int. J. Plast. 25 (2009), pp. 2222–2247.
  • A. Das, S.K. Das, and S. Tarafder, Correlation of fractographic features with mechanical properties in systematically varied microstructures of Cu-strengthened high-strength low-alloy steel, Metall. Mater. Trans. A 13 (2009), pp. 3138–3146.
  • A. Das and J.K. Chakravartty, Correlation of fracture features with mechanical properties as a function of strain rate in zirconium alloys, Int. J. Mater. Res. 107 (2016), pp. 184–188.
  • A. Das, Fracture complexity of pressure vessel steels, Philos. Mag. 97 (2017), pp. 3084–3141.
  • A. Das and J.K. Chakravartty, Fractographic correlations with mechanical properties in ferritic martensitic steels, Surf. Topo. Metro. Prop. 5 (2017), p. 045006.
  • A. Das, Effect of stress-state on fracture features, Metall. Mater. Trans A 49 (2018), pp. 1425–1432.
  • A. Das and C.B. Basak, Fracture mechanisms of spinodal alloys, Philos. Mag. 98 (2018), pp. 3007–3033.
  • A. Das, Tessellated dimple geometry of high entropy alloy, Mater. Chem. Phys. 290 (2022), p. 126434.
  • C.R.F. Azevedo, R.R. Maia, E.A. Ariza, and A.P. Tschiptschin, Failure analysis of a martensitic stainless steel (CA-15M) roll manufactured by centrifugal casting. part I: material and fractographic characterization, Engg. Fail. Anal. 36 (2014), pp. 343–352.
  • Q. Zhong, Z. Zhao, and Z. Zhang, Development of fractography and research of fracture micromechanism, J. Mech. Streng. 27 (2005), pp. 358–370.
  • X. Lin and G.U. Haicheng, The relationship between plastic dissipated energy, fractal dimension and fatigue lifetime of zirconium and Zircaloy-4, Acta Metall. Sinica (English Letter) 34 (1998), pp. 705–712.
  • K. Slamecka, J. Pokluda, M. Kianicova, S. Major, and I. Dvorak, Quantitative fractography of fish-eye crack formation under bending-torsion fatigue, Int. J. Fat. 32 (2010), pp. 921–928.
  • W. Macek, R. Branco, M. Korpys, and T. Lagoda, Fractal dimension for bending-torsion fatigue fracture characterisation, Measurement 184 (2021), p. 109910.
  • Y.G. Cao, S.H. Zhang, and K. Tanaka, Calculation method for maximum low-cycle fatigue loads using FRASTA reconstruction data, Int. J. Fract. 182 (2013), pp. 157–166.
  • T.G. Mathia, P. Pawlus, and M. Wieczorowski, Recent trends in surface metrology, Wear 271 (2011), pp. 494–508.
  • K. Slamecka, J. Pokluda, P. Ponizil, S. Major, and P. Sandera, On the topography of fracture surfaces in bending-torsion fatigue, Engg. Fract. Mech. 75 (2008), pp. 760–767.
  • W. Macek, Post-failure fracture surface analysis of notched steel specimens after bending-torsion fatigue, Engg. Fail. Anal. 105 (2019), pp. 1154–1171.
  • F.C. del Angel, Fractal effect of corrosion on mechanical behavior of unprotected structural steel, in Developments in Corrosion Protection, 2014 Feb 20. Intech Open.
  • M. Ipohorski, Fractografía–Aplicación al análisis de falla, Informe CNEA 490 (1988), Buenos Aires, Argentina.
  • D. Avnir, D. Farin, and P. Pfeifer, Surface geometric irregularity of particulate materials: the fractal approach, J. Coll. Interf. Sci. 103 (1985), pp. 112–123.
  • N.A. Davies, N.K. Harrison, R.H.K. Morris, S. Noble, M.J. Lawrence, L.A. D'Silva, L. Broome, M.R. Brown, K.M. Hawkins, P.R. Williams, and S. Davidson, Fractal dimension (df) as a new structural biomarker of clot microstructure in different stages of lung cancer, Thromb. Haemos. 114 (2015), pp. 1251–1259.
  • A. Das, Fractal-property correlation of hierarchical 3D nanolayered α/β-Zr networks, Scr. Mater, 218 (2022), p. 114833.
  • Z.Q. Mu and C.W. Lung, Studies on the fractal dimension and fracture toughness of steel, J. Phys. D: Appl. Phys. 21 (1988), p. 848.
  • C.S. Pande, L.E. Richards, N. Louat, B.D. Dempsey, and A.J. Schwoeble, Fractal characterization of fractured surfaces, Acta Metall. 35 (1987), pp. 1633–1637.
  • K. Ishikawa, Fractals in dimple patterns of ductile fracture, J. Mater. Sci. Lett. 9 (1990), pp. 400–402.
  • S. Talu, S. Stach, V. Sueiras, and N.M. Ziebarth, Fractal analysis of AFM images of the surface of bowman's membrane of the human corne, Ann. Biomed. Engg. 43 (2015), pp. 906–916.
  • B. Mandelbrot, D. Passoja, and A. Paullay, Fractal character of fractal surfaces of metals, Nature 308 (1984), pp. 721–722.
  • J.J. Mecholski and T.J. Mackin, Fractal analysis of fracture in Ocala chert, J. Mater. Sci. Lett. 7 (1988), pp. 1145–1147.
  • R.H. Dauskardt, F. Haubensak, and R.O. Ritchie, On the interpretation of the fractal character of fracture surfaces, Acta Metall. Mater. 38(2) (1990), pp. 143–159.
  • J.C.M. Li, A theoretical limit of fracture toughness, Scripta Metall. 22 (1988), pp. 837–838.
  • J.H. Bulloch, A study concerning material fracture toughness and some small punch test data for low alloy steels, Engg. Fract. Mech. 11 (2004), pp. 635–653.
  • S. Chatterjee, D. Dey, and S. Munshi, Recent Trends in Computer-Aided Diagnostic Systems for Skin Diseases: Theory, Implementation, and Analysis, Academic Press - Elsevier Science, London, UK, 2022. https://doi.org/10.1016/C2020-0-03671-6.
  • D. Tang and A.G. Marangoni, Understanding and controlling the microstructure of complex foods, D. Julian McClements, ed., Woodhead Publishing, 2007, pp. 67–88. eBook ISBN: 9781845693671.
  • A. Carpinteri, Scaling laws and renormalization groups for strength and toughness of disordered materials, Int. J. Sol. Str. 31 (1994), pp. 291–302.
  • A. Carpinteri and M. Paggi, A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models, Inter. J. Fract. 161 (2010), pp. 41-–52.
  • A. Carpinteri and B. Chiaia, Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy, RILEM Mater. & Struct. 28 (1995), pp. 435–443.
  • R. Williford, Multifractal fracture, Scr. Metall. Mater. 22 (1988), pp. 1749–1754.
  • R. Williford, Fractal fatigue, Scr. Metall. Mater. 24 (1990), pp. 455–460.
  • E. Underwood and K. Banerjee, Fractal analysis of fracture surfaces, in ASM Handbook, Vol 12: fractography, ASM International, Metals Park, Ohio, USA, 1987.
  • B. Mandelbrot, Self-affine fractals and the fractal dimension, Phys. Scripta 32 (1985), pp. 257–260.
  • C.S. Pande, N. Louat, R.A. Masumura, and S. Smith, Fractal characterization of rough surfaces using secondary electrons, Philos. Mag. Lett. 55 (1987), pp. 99–104.
  • A.M. Gokhale, W.J. Drury, and S. Mishra, Recent developments in quantitative fractography in fractography of modern engineering materials: Composites and metals, Vol. 2, ASTM STP 1203, E. Masters and L. N. Gilbertson, eds., American Society for Testing and Materials, Philadelphia, 1993, p. 3.
  • O.A. Hilders, N.D. Pena, M. Ramos, L. Saenz, L. Berrio, R.A. Caballero, and A. Quintero, Stress triaxiality dimple fracture morphology and fractal dimension relations for several aluminum alloys, Mater. Sci. For. 396 (2002), pp. 1321–1328.
  • S. Morel, E. Bouchaud, J. Schmittbuhl, and G. Valentin, R-curve behavior and roughness development of fracture surfaces, Int. J. Fract. 114 (2002), pp. 307–325.
  • A.A. Shaniavski and M.A. Artamonov, Fractal dimensions for fatigue fracture surfaces performed on micro- and meso-scale levels, Inter. J. Fract. 128 (2004), pp. 309–314.
  • W. Tang and Y. Wang, Fractal characterization of impact fracture surface of steel, Appl. Surf. Sci.258 (2012), pp. 4777–4781.
  • M. Paggi and O. Plekhov, On the dependency of the parameters of fatigue crack growth from the fractal dimension of rough crack profiles, Proc. Inst. Mech. Eng. Part C: J. Mech. Engg. Sci. 228(12) (2014), pp. 2059–2067.
  • O. Hilders and N. Zambrano, The effect of aging on impact toughness and fracture surface fractal dimension in SAF 2507 super duplex stainless steel, J. Micros. Ultrastr. 2 (2014), pp. 236–244.
  • M. Tanaka, M. Tagami, R. Kato, H. Akiyama, N. Oyama, and J. Ono, Quantitative evaluation of the impact fracture surfaces of SS400 steel by the three-dimensional geometrical analysis, ISIJ Int. 47 (2017), pp. 178–186.
  • W. Macek, Z. Marciniak, R. Branco, D. Rozumek, and G.M. Krolczyk, A fractographic study exploring the fracture surface topography of S355J2 steel after pseudo-random bending-torsion fatigue tests, Measurement 178 (2021), pp. 109443.
  • C. Guerrero, E. Reyes, and V. Gonzalez, Fracture surface of plastic materials: the roughness exponent, Polymer 43 (2002), pp. 6683–6693.
  • H. Liu, Y. Zuo, Z. Wu, W. Sun, L. Zheng, Y. Lou, J. Lin, and R. Wan, Fractal analysis of mesoscale failure evolution and microstructure characterization for sandstone using DIP, SEM-EDS, and micro-CT, Int. J. Geomech. 21 (2021), pp. 04021153.
  • L.F. Richardson, Fractals. In The Collected Papers of Lewis Fry Richardson: Meteorology and Numerical Analysis, Vol. 1, O.M. Ashford, H. Charnock, P.G. Drazin, eds., Cambridge University Press, 1993, pp. 45–46. ISBN 0-521-38297-1.
  • P. McAnulty, L.V. Meisel, and P.J. Cote, Hyperbolic distributions and fractal character of fracture surfaces, Phy. Rev. A 46 (1992), p. 3523.
  • C.W. Lung and Z.Q. Mu, Fractal dimension measured with perimeter-area relation and toughness of materials, Phy. Rev. B 38 (1988), pp. 11781.
  • B.J. Florio, P.D. Fawell, and M. Small, The use of the perimeter-area method to calculate the fractal dimension of aggregates, Pow. Tech. 343 (2019), pp. 551–559.
  • L. Carney and J. Mecholsky, Relationship between fracture toughness and fracture surface fractal dimension in AISI 4340 steel, Mater. Sci. Appl. 4 (2013), pp. 258–267.
  • A.F. Costa, G. Humpire-Mamani, and A.J. Traina, An efficient algorithm for fractal analysis of textures, in 2012 25th SIBGRAPI Conference on Graphics, Patterns and Images, IEEE, 2012 Aug 22, pp. 39–46. DOI:10.1109/SIBGRAPI.2012.15
  • O.A. Hilders, N. Zambrano, and R. Caballero, Microstructure, strength, and fracture topography relations in AISI 316L stainless steel, as seen through a fractal approach and the Hall–Petch law, Int. J. Met. 2015 (2015), Article ID: 624653, 10 pages. DOI: 10.1155/2015/624653
  • S. Morel, J. Schmittbuhl, E. Bouchaud, and G. Valentin, Scaling of crack surfaces and implications for fracture mechanics, Phys. Rev. Lett. 85 (2000), p. 1678.
  • M.P. Black and R.L. Higginson, Investigation into the use of electron back scattered diffraction to measure recrystallised fraction, Scripta Mater. 41 (1999), pp. 125–129.
  • S.H. Kang, H.H. Jin, J. Jang, Y.S. Choi, K.H. Oh, D.C. Foley, and X. Zhang, A quantitative evaluation of microstructure by electron back-scattered diffraction pattern quality variations, Micros. Microanal. 19 (2013), pp. 83–88.
  • A.A. Griffith, The phenomena of rupture and flow in solids, Philos. Trans. Roy. Soc. Lon. A221(582–593) (1921), pp. 163–198.
  • G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech.24 (1957), pp. 361–364.
  • Z. Sekeresova and H. Lauschmann, Multi-fractal features of fatigue crack surfaces in relation to crack growth rate, Mater. Sci. For. 567 (2008), pp. 129–132.
  • R. Brighenti, A. Carpinteri, A. Spagnoli, and D. Scorza, Crack path dependence on inhomogeneities of material microstructure, Frattura ed Integrità Strutturale 6 (2012), pp. 6–16.
  • A. Carpinteri, L. Montanari, and A. Spagnoli, Fatigue fractal crack propagating in a self-balanced microstress field. Available at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1028.1657&rep=rep1&type=pdf.
  • S.F.D. Santos and J.D.A. Rodrigues, Correlation between fracture toughness, work of fracture and fractal dimensions of Alumina–mullite–zirconia composites, Mater. Res. 6 (2003), pp. 219–226.
  • J.A. Rodrigues and V.C. Pandolfelli, Insights on the fractal-fracture behaviour relationship, Mater. Res. 1 (1998), pp. 47–52.
  • D. Hull, Fractography-Observing, Measuring and Interpreting Fracture Surface to Topography, Cambridge University Press, Cambridge, 1999, pp. 91–150.
  • H. Hadraba, O. Nemec, and I. Dlouhy, Conversion of transgranular to intergranular fracture in NiCr steels, Engg. Fract. Mech. 75 (2008), pp. 3677–3691.
  • I. Dlouhy and B. Strnadel, The effect of crack propagation mechanism on the fractal dimension of fracture surfaces in steels, Engg. Fract. Mech. 75 (2008), pp. 726–738.
  • C.R.F. Azevedo and E.R. Marques, Three-dimensional analysis of fracture, corrosion and wear surfaces, Engg. Fail. Anal. 17 (2010), pp. 286–300.
  • A. Carpinteri, A. Spagnoli, S. Vantadori, and D. Viappiani, Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals, Engg. Fract. Mech. 75 (2008), pp. 579–589.
  • Z. Zhang, Quantitative characterization on fatigue fracture features of A6005 aluminum alloy welded joints, Engg. Fail. Anal. 129 (2021), p. 105687.
  • Z.X. Zhang, S.Q. Kou, J.H. Yu, Y. Yu, L.G. Jiang, and P.A. Lindqvist, Effects of loading rate on rock fracture, Int. J. Rock Mech. Min. Sci. 36 (1999), pp. 597–611.
  • G.C. Kirby III and P. Matic, A complex systems approach to metallic fracture surface characterization, Engg. Fract. Mech. 40 (1991), pp. 1105–1122.
  • P. Maruschak, Automated fractal analysis of a network of thermal fatigue cracks, Mater. Tech. 46 (2012), pp. 193–195.
  • L. Xiao, H.C. Gu, and Z.B. Kuang, Study of fractal characteristics of fatigued fracture surface at elevated temperature in Zircaloy-4 by secondary electron line scanning, Rare Met. Mater. Engg. 24 (1995), pp. 22–26.
  • Y. Hao, Z. Wang, and Y. Kang, Fractal analysis on the fatigue fracture surface along the crack propagation direction, Int. J. Fat. 17 (1995), pp. 584–587.
  • P. Kotowski, Fractal dimension of metallic fracture surface, Int. J. Fract. 141 (2006), pp. 269–286.
  • Z.G. Wang, D.L. Chen, X.X. Jiang, S.H. Ai, and C.H. Shih, Relationship between fractal dimension and fatigue threshold value in dual-phase steels, Scripta Metall. 22 (1988), pp. 827–832.
  • J.A. Griggs, Using fractal geometry to examine failed implants and prostheses, Dent. Mater. 34 (2018), pp. 1748–1755.
  • J.G. Yun, C.Q. Ma, J.J. Yi, and X.W. Li, Qualitative and quantitative characterizations of fracture surfaces of AL6XN super-austenitic stainless steel fatigued at different stress amplitudes, Prog. Nat. Sci. Mater. Int. 22 (2012), pp. 48–52.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.