A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models

International Journal of Fracture

Volumn 161, Issue 1, 2010, Pages 41-52

  Carpinteri, Alberto ^a   Paggi, Marco ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Fatigue crack growth; Fatigue threshold; Fractals; Scaling laws; Short cracks

Indexed keywords

ANOMALOUS BEHAVIOR; ANOMALOUS SCALING; EXPERIMENTAL DATA; FATIGUE CRACK GROWTH; FATIGUE THRESHOLD; FRACTAL APPROACH; FRACTAL GEOMETRY; FRACTAL MODEL; GENERALIZED THEORY; OPEN PROBLEMS; SHORT CRACKS; SIZE DEPENDENCE; SIZE DEPENDENCY; SIZE EFFECTS; THEORETICAL FRAMEWORK; THEORETICAL MODELS;

FATIGUE CRACK PROPAGATION; FATIGUE OF MATERIALS; FRACTALS; PLASTIC DEFORMATION; SCALING LAWS;

CRACK DETECTION;

EID: 75549085758     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-009-9425-5     Document Type: Article

References (60)

1. ZP Bažant W Shell 1993 Fatigue fracture of high strength concrete and size effect ACI Mater J 90 472 478
2. ZP Bažant K Xu 1991 Size effect in fatigue fracture of concrete ACI Mater J 88 390 399
3. S Brown C Scholz 1985 Broad bandwidth study of the topography of natural rock surfaces J Geophys Res 90 12575 12582 10.1029/JB090iB14p12575 1985JGR....9012575B
4. Carpinteri Al (1994a) Fractal nature of material microstructure and size effects on apparent mechanical properties. Mech Mater 18:89-101. Internal Report, Laboratory of Fracture Mechanics, Politecnico di Torino, N. 1/92, 1992
5. Al Carpinteri 1994 Scaling laws and renormalization groups for strength and toughness of disordered materials Int J Solids Struct 31 291 302 0807.73050 10.1016/0020-7683(94)90107-4
6. Carpinteri Al (1994c) Strength and toughness in disordered materials: complete and incomplete similarity. In: Size-Scale effects in the failure mechanisms of materials and structures, Proceedings of the International Union of Theoretical and Applied Mechanics (IUTAM), Turin, Italy. E & FN Spon, London, pp 3-26
7. Al Carpinteri B Chiaia 1995 Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy RILEM Mater & Struct 28 435 443 10.1007/BF02473162
8. Al Carpinteri B Chiaia 1996 Power scaling laws and dimensional transitions in solid mechanics Chaos, Solitons Fractals 7 1343 1364 10.1016/0960-0779(96)00016-1 (Pubitemid 126377329)
9. Al Carpinteri B Chiaia P Cornetti 2002 A scale-invariant cohesive crack model for quasi-brittle materials Eng Fracture Mech 69 207 217 10.1016/S0013-7944(01)00085-6 (Pubitemid 34039668)
10. Al Carpinteri B Chiaia S Invernizzi 1999 Three-dimensional fractal analysis of concrete fracture at the meso-level Theoret Appl Fracture Mech 31 163 172 10.1016/S0167-8442(99)00011-7
11. Al Carpinteri P Cornetti S Puzzi 2006 Scaling laws and multi-scale approach to the mechanics of heterogeneous and disordered materials Appl Mech Rev 59 283 305 10.1115/1.2204076 (Pubitemid 46132201)
12. Al Carpinteri G Ferro 1994 Size effects on tensile fracture properties: a unified explanation based on disorder and fractalilty of concrete microstructure RILEM Mater & Struct 27 563 571 10.1007/BF02473124 1:CAS:528:DyaK2MXjt1Gmtbc%3D
13. Al Carpinteri M Paggi 2007 Self-similarity and crack growth instability in the correlation between the Paris' constants Eng Fracture Mech 74 1041 1053 10.1016/j.engfracmech.2006.12.007 (Pubitemid 46268132)
14. An Carpinteri A Spagnoli 2004 A fractal analysis of size effect on fatigue crack growth Int J Fatigue 26 125 133 1060.74611 10.1016/S0142-1123(03) 00142-7
15. An Carpinteri A Spagnoli S Vantadori 2002 An approach to size effect in fatigue of metals using fractal theories Fatigue Fract Eng Mater Struct 25 619 627 10.1046/j.1460-2695.2002.00506.x (Pubitemid 34806788)
16. W Cui 2002 A state-of-the-art review on fatigue life prediction methods for metal structures J Marine Sci Tech 7 43 56 10.1007/s007730200012 (Pubitemid 41389968)
17. K Donald PC Paris 1999 An evaluation of estimation procedure on 6061-T6 and 2024-T3 aluminum alloys Int J Fatigue 21 S47 S57 10.1016/S0142-1123(99) 00055-9 1:CAS:528:DC%2BD3cXhs1Srug%3D%3D
18. W Elber 1970 Fatigue crack closure under cyclic tension Eng Fract Mech 2 37 45 10.1016/0013-7944(70)90028-7
19. MH El Haddad T Topper K Smith 1979 Prediction of nonpropagating cracks Eng Fract Mech 11 573 584 10.1016/0013-7944(79)90081-X 1:CAS:528: DyaE1MXhslagtbk%3D (Pubitemid 9427959)
20. Forth SC, Johnston WM, Seshadri BR (2006) The effect of the laboratory specimen on fatigue crack growth rate. In: Proceedings of the 16th European Conference on Fracture, Alexandroupolis, Greece
21. Frost N (1966) The growth of fatigue cracks. In: Yokobori T (eds) Proceedings of the 1st international conference on fracture. The Japan society for strength and fracture of materials, Sendai, pp 1433-1459
22. NE Frost DS Dugdale 1958 The propagation of fatigue cracks in sheet specimens J Mech Phys Solids 6 92 110 10.1016/0022-5096(58)90018-8 1958JMPSo...6...92F
23. R Jones L Molent S Pitt 2007 Crack growth of physically small cracks Int J Fatigue 29 1658 1667 1140.74326 10.1016/j.ijfatigue.2007.01.031 (Pubitemid 47284438)
24. Kitagawa H, Takahashi S (1976) Applicability of fracture mechanics to very small cracks or the cracks in the early stage. In: Proceedings of 2nd international conference on mechanical behaviour of materials. American society for metals, Metal Park, pp. 627-631
25. H Kitagawa S Takahashi 1979 Fracture mechanical approach to very small fatigue cracks and to the threshold Trans Jpn Soc Mech Eng 45 1289 1303
26. D Kujawski 2001 Enhanced model of partial crack closure for correlation of R-ratio effects in aluminium alloys Int J Fatigue 23 95 102 10.1016/S0142-1123(00)00085-2 1:CAS:528:DC%2BD3MXktlyrsA%3D%3D (Pubitemid 32093246)
27. D Kujawski 2001 A fatigue crack driving force parameter with load ratio effects Int J Fatigue 23 S239 S246 10.1016/S0142-1123(01)00158-X
28. J Lankford 1982 The growth of small fatigue cracks in 7075-t6 aluminum Fatigue Eng Mater Struct 5 233 248 10.1111/j.1460-2695.1982.tb01251.x
29. Mandelbrot B (1982) The fractal geometry of nature. W.H. Freeman, New York
30. B Mandelbrot D Passoja A Paullay 1984 Fractal character of fractal surfaces of metals Nature 308 721 722 10.1038/308721a0 1:CAS:528: DyaL2cXktFWhsrY%3D 1984Natur.308..721M
31. J Masounave J Bailon 1976 Effect of grain size on threshold stress intensity factor in fatigue of a ferritic steel Scripta Materialia 10 165 170 10.1016/0036-9748(76)90142-3 1:CAS:528:DyaE28Xkt1Cis7s%3D
32. HSS Matsuoka K Ishikawa M Nihei 1992 Fractal characteristics of scanning tunneling microscopic images of brittle fracture surfaces on molybdenum Soc Mech Eng Int J 35 449 455
33. McClintock F (1963) On the plasticity of the growth of fatigue cracks. In: Drucker D, Gilman J (eds) Fracture of solids. Wiley, New York, pp 65-102
34. AJ McEvily M Endo Y Murakami 2003 On the √ area relationship and the short fatigue crack threshold Fatigue Fract Eng Mater Struct 26 269 278 10.1046/j.1460-2695.2003.00636.x
35. K Miller 1982 The short crack problem Fatigue Fract Eng Mater Struct 5 223 232 10.1111/j.1460-2695.1982.tb01250.x
36. L Molent R Jones S Barter S Pitt 2006 Recent developments in fatigue crack growth assessment Int J Fatigue 28 1759 1768 10.1016/j.ijfatigue.2006.01. 004 1:CAS:528:DC%2BD28XpslGhu7w%3D (Pubitemid 44344317)
37. th of small cracks emanating from small defects. In: Miller HJ, Rios ER (eds) The behaviour of short fatigue cracks. Mechanical Engineering Publications, London, pp 275-293
38. JC Newman Jr EP Phillips MH Swain 1999 Fatigue-life prediction methodology using small-crack theory Int J Fatigue 21 109 119 10.1016/S0142-1123(98)00058-9 1:CAS:528:DyaK1MXhsFyhtLY%3D
39. JC Newman Jr A Brot C Matias 2004 Crack-growth calculations in 7075-T7351 aluminum alloy under various load spectra using an improved crack-closure model Eng Fract Mech 71 2347 2363 10.1016/j.engfracmech.2004.01.004 (Pubitemid 38662441)
40. P Paris F Erdogan 1963 A critical analysis of crack propagation laws ASME J Basic Eng 85D 528 534
41. P Paris M Gomez W Anderson 1961 A rational analytic theory of fatigue Trend Eng 13 9 14
42. S Pearson 1975 Initiation of fatigue cracks in commercial aluminum alloys and the subsequent propagation of very short cracks Eng Fract Mech 7 237 247
43. R Pippan O Kolednik M Lang 1994 A mechanism for plasticity-induced crack closure under plane strain conditions Fatigue Fract Eng Mater Struct 17 721 726 10.1111/j.1460-2695.1994.tb00269.x
44. N Pugno M Ciavarella P Cornetti Al Carpinteri 2006 A generalized Paris' law for fatigue crack growth J Mech Phys Solids 54 1333 1349 1120.74779 10.1016/j.jmps.2006.01.007 1:CAS:528:DC%2BD28Xkt1ygur0%3D 2006JMPSo..54.1333P
45. N Pugno P Cornetti Al Carpinteri 2007 New unified laws in fatigue: from the Wöhlers to the Paris regime Eng Fract Mech 74 595 601 10.1016/j.engfracmech.2006.07.009 (Pubitemid 44848168)
46. V Radhakrishnan 1979 Parameter representation of fatigue crack growth Eng Fract Mech 11 359 372 10.1016/0013-7944(79)90011-0 1:CAS:528:DyaE1MXitVynur0%3D (Pubitemid 9424582)
47. V Radhakrishnan 1980 Quantifying the parameters in fatigue crack propagation Eng Fract Mech 13 129 141 10.1016/0013-7944(80)90048-X
48. A Spagnoli 2004 Fractality in the threshold condition of fatigue crack growth: an interpretation of the kitagawa diagram Chaos, Solitons and Fractals 22 589 598 1116.74421 10.1016/j.chaos.2004.02.034
49. A Spagnoli 2005 Self-similarity and fractals in the Paris range of fatigue crack growth Mech Mater 37 519 529 10.1016/j.mechmat.2004.04.003 (Pubitemid 40120702)
50. S Suresh R Ritchie 1984 Propagation of short fatigue cracks Int Metals Rev 29 445 476
51. Tanaka K (2003) Fatigue crack propagation. In: Ritchie R, Murakami Y (eds) Comprehensive structural integrity, vol 4, cyclic loading and fatigue. Elsevier, Amsterdam, pp 95-127
52. Taylor D (1981) Fatigue thresholds. Butterworths, London
53. Underwood E, Banerjee K (1987) Fractal analysis of fracture surfaces. In: ASM Handbook, vol 12: fractography, ASM International, Metals Park, Ohio, USA
54. S Usami S Shida 1979 Elastic-plastic analysis of the fatigue limit for a material with small flaws Fatigue Fract Eng Mater Struct 1 471 481 10.1111/j.1460-2695.1979.tb01334.x 1:CAS:528:DyaL3cXis1Cnug%3D%3D
55. AK Vasudevan K Sadananda N Louat 1994 A review of crack closure, fatigue crack threshold and related phenomena Mater Sci Eng A 188 1 22 10.1016/0921-5093(94)90351-4
56. Verhoeven J (1975) Fundamentals of physical metallurgy. John Wiley, New York
57. R Williford 1988 Multifractal fracture Scripta Metallurgica et Materialia 22 1749 1754 1:CAS:528:DyaL1cXmtlGntL0%3D
58. R Williford 1990 Fractal fatigue Scripta Metallurgica et Materialia 24 455 460
59. K Wilson 1971 Renormalization group and critical phenomena Phys Rev B 4 3174 3205 10.1103/PhysRevB.4.3174 1971PhRvB...4.3174W
60. Yokobori T (1979) A critical evaluation of mathematical equations for fatigue crack growth with special references to ferrite grain size and monotonic yield strenght dependence. In: Fongi J(ed) Fatigue mechanics, ASTM STP 675. Am Soc Test Mater, pp 683-706