Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue

Chaos, Solitons and Fractals

Volumn 40, Issue 3, 2009, Pages 1136-1145

  Paggi, Marco ^a   Carpinteri, Alberto ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

FATIGUE OF MATERIALS; FRACTALS; FRACTURE MECHANICS; SCALING LAWS;

ANOMALOUS BEHAVIOR; ANOMALOUS SCALING; FATIGUE THRESHOLD; FRACTAL GEOMETRY; GENERALIZED THEORY; MULTI FRACTALS; THEORETICAL FORMULATION; THEORETICAL MODELING;

CRACKS;

EID: 65349150552     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.08.068     Document Type: Article

References (54)

1. Taylor D. Fatigue thresholds (1981), Butterworth, London
2. Miller K.J. The short crack problem. Fatigue Fract Eng Mater Struct 5 (1982) 223-232
3. Suresh S., and Ritchie R.O. Propagation of short fatigue cracks. Int Met Rev 29 (1984) 445-476
4. Pearson S. Initiation of fatigue cracks in commercial aluminum alloys and the subsequent propagation of very short cracks. Eng Fract Mech 7 (1975) 237-247
5. Lankford J. The growth of small fatigue cracks in 7075-T6 aluminum. Fatigue Eng Mater Struct 5 (1982) 233-248
6. McClintock F.A. On the plasticity of the growth of fatigue cracks. In: Drucker D.C., and Gilman J.J. (Eds). Fracture of solids (1963), Wiley, New York 65-102
7. Paris P.C., Gomez M.P., and Anderson W.P. A rational analytic theory of fatigue. Trend Eng 13 (1961) 9-14
8. Paris P.C., and Erdogan F. A critical analysis of crack propagation laws. ASME J Basic Eng 85D (1963) 528-534
9. Radhakrishnan V.M. Quantifying the parameters in fatigue crack propagation. Eng Fract Mech 13 (1980) 129-141
10. Frost NE. The growth of fatigue cracks. In: Yokobori T, editor. Proceedings of the first international conference on fracture. Sendai: The Japan Society for Strength and Fracture of Materials; 1966. p. 1433-59.
11. Usami S., and Shida S. Elastic-plastic analysis of the fatigue limit for a material with small flaws. Fatigue Fract Eng Mater Struct 1 (1979) 471-481
12. Kitagawa H, Takahashi S. Applicability of fracture mechanics to very small cracks or the cracks in the early stage. In: Proceedings of second international conference on mechanical behaviour of materials. Metal Park: American Society for Metals; 1976. p. 627-31.
13. Kitagawa H., and Takahashi S. Fracture mechanical approach to very small fatigue cracks and to the threshold. Trans Jpn Soc Mech Eng 45 (1979) 1289-1303
14. Carpinteri A. Fractal nature of material microstructure and size effects on apparent mechanical properties. Mech Mater 18 (1994) 89-101 [Internal Report, Laboratory of Fracture Mechanics, Politecnico di Torino, N. 1/92; 1992]
15. Carpinteri A. Scaling laws and renormalization groups for strength and toughness of disordered materials. Int J Solids Struct 31 (1994) 291-302
16. Carpinteri A. Strength and toughness in disordered materials: complete and incomplete similarity. Size-scale effects in the failure mechanisms of materials and structures. Proceedings of the international union of theoretical and applied mechanics (IUTAM), Turin, Italy (1994), E&FN Spon, London 3-26
17. Carpinteri A., and Ferro G. Size effects on tensile fracture properties: a unified explanation based on disorder and fractalilty of concrete microstructure. RILEM Mater Struct 27 (1994) 563-571
18. Carpinteri A., and Chiaia B. Fractals, renormalization group theory and scaling laws for strength and toughness of disordered materials. Proceedings of the workshop probabilities and materials: tests, models and applications (PROBAMAT), Cachan, France, November 1993 (1994), Kluwer, Dordrecht 141-150
19. Carpinteri A., and Chiaia B. Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy. RILEM Mater Struct 28 (1995) 435-443
20. Mandelbrot B.B., Passoja D.E., and Paullay A.J. Fractal character of fractal surfaces of metals. Nature 308 (1984) 721-722
21. Williford R.E. Multifractal fracture. Scripta Metal Mater 22 (1988) 1749-1754
22. Underwood EE, Banerjee K. Fractal analysis of fracture surfaces, ASM Handbook, vol. 12: Fractography. Metals Park, Ohio, USA: ASM International; 1987, p. 211-5.
23. Panagiotopoulos P.D. Introduction. Chaos, Solitons and Fractals 8 (1997) vii-viii
24. Carpinteri A., and Chiaia B. Power scaling laws and dimensional transitions in solid mechanics. Chaos, Solitons and Fractals 7 (1996) 1343-1364
25. Carpinteri A., and Chiaia B. Multifractal scaling laws in the breaking behavior of disordered materials. Chaos, Solitons and Fractals 8 (1997) 135-150
26. Meisner M.J., and Frantziskonis G.N. Heterogeneous materials - scaling phenomena relevant to fracture and to fracture toughness. Chaos, Solitons and Fractals 8 (1997) 151-170
27. Carpinteri A., Chiaia B., and Invernizzi S. Applications of fractal geometry and renormalization group to the italian seismic activity. Chaos, Solitons and Fractals 14 (2002) 917-928
28. Carpinteri A., and Paggi M. A fractal interpretation of size-scale effects on strength, friction and fracture energy of faults. Chaos, Solitons and Fractals 39 (2009) 540-546
29. Carpinteri An., Spagnoli A., and Vantadori S. An approach to size effect in fatigue of metals using fractal theories. Fatigue Fract Eng Mater Struct 25 (2002) 619-627
30. Carpinteri An., and Spagnoli A. A fractal analysis of size effect on fatigue crack growth. Int J Fatigue 26 (2004) 125-133
31. Spagnoli A. Self-similarity and fractals in the Paris range of fatigue crack growth. Mech Mater 37 (2005) 519-529
32. Spagnoli A. Fractality in the threshold condition of fatigue crack growth: an interpretation of the Kitagawa diagram. Chaos, Solitons and Fractals 22 (2004) 589-598
33. Mandelbrot B.B. The fractal geometry of nature (1982), W.H. Freeman and Company, New York
34. Sumiyoshi H., Matsuoka S., Ishikawa K., and Nihei M. Fractal characteristics of scanning tunneling microscopic images of brittle fracture surfaces on molybdenum. Soc Mech Eng Int J 35 (1992) 449-455
35. Brown S.R., and Scholz C.H. Broad bandwidth study of the topography of natural rock surfaces. J Geophys Res 90 (1985) 12575-12582
36. Carpinteri A., Chiaia B., and Invernizzi S. Three-dimensional fractal analysis of concrete fracture at the meso-level. Theor Appl Fract Mech 31 (1999) 163-172
37. Wilson K. Renormalization group and critical phenomena. Phys Rev B 4 (1971) 3174-3205
38. Barenblatt GI. Scaling, self-similarity and intermediate asymptotics. Consultant Bureau, New York; 1979.
39. Carpinteri A., Cornetti P., and Puzzi S. Scaling laws and multi-scale approach to the mechanics of heterogeneous and disordered materials. Appl Mech Rev 59 (2006) 283-305
40. Carpinteri A., Chiaia B., and Cornetti P. A scale-invariant cohesive crack model for quasi-brittle materials. Eng Fract Mech 69 (2002) 207-217
41. Carpinteri A., and Cornetti P. A fractional calculus approach to the description of stress and strain localization in fractal media. Chaos, Solitons and Fractals 13 (2002) 85-94
42. Carpinteri A., Chiaia B., and Ferro G. Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder. RILEM Mater Struct 28 (1995) 311-317
43. Carpinteri A., and Chiaia B. Size effects on concrete fracture energy: dimensional transition from order to disorder. RILEM Mater Struct 29 (1996) 259-266
44. Bouchaud E. Scaling properties of cracks. J Phys: Condens Mat 9 (1997) 4319-4344
45. Williford R.E. Fractal fatigue. Scripta Metal Mater 24 (1990) 455-460
46. Yokobori T. A critical evaluation of mathematical equations for fatigue crack growth with special references to ferrite grain size and monotonic yield strength dependence. In: Fongi J.T. (Ed). Fatigue mechanics. ASTM STP vol. 675 (1979), American Society for Testing and Materials 683-706
47. Bažant Z.P., and Xu K. Size effect in fatigue fracture of concrete. ACI Mater J 88 (1991) 390-399
48. Bažant Z.P., and Shell W.F. Fatigue fracture of high strength concrete and size effect. ACI Mater J 90 (1993) 472-478
49. El Haddad M.H., Topper T.H., and Smith K.N. Prediction of nonpropagating cracks. Eng Fract Mech 11 (1979) 573-584
50. Carpinteri A., and Paggi M. Self-similarity and crack growth instability in the correlation between the Paris' constants. Eng Fract Mech 74 (2007) 1041-1053
51. Verhoeven J.D. Fundamentals of physical metallurgy (1975), John Wiley & Sons, NY (USA)
52. Masounave J., and Bailon J.P. Effect of grain size on threshold stress intensity factor in fatigue of a ferritic steel. Scripta Mater 10 (1976) 165-170
53. Radhakrishnan V.M. Parameter representation of fatigue crack growth. Eng Fract Mech 11 (1979) 359-372
54. Tanaka K. Fatigue crack propagation. In: Ritchie R.O., and Murakami Y. (Eds). Comprehensive structural integrity. Cyclic loading and fatigue vol. 4 (2003), Elsevier, Amsterdam 95-127