Scaling phenomena in fatigue and fracture

International Journal of Fracture

Volumn 138, Issue 1-4, 2006, Pages 19-35

  Barenblatt, G I ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dynamic cracks; Fatigue advanced similarity analysis; Fatigue cracks; Fracture advanced similarity analysis; Fracture cracks; Incomplete similarity; Pan's law; Scaling laws in fatigue; Scaling laws in fracture

Indexed keywords

CRACKS; FATIGUE OF MATERIALS; FATIGUE TESTING; LIFE CYCLE;

DYNAMIC CRACKS; INCOMPLETE SIMILARITY; PAN'S LAW; SIMILARITY ANALYSIS;

FRACTURE;

EID: 33745277590     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-006-0036-0     Document Type: Conference Paper

References (39)

1. G.I. Barenblatt L.R. Botvina 1981 Incomplete self-similarity of fatigue in the linear range of crack growth Fatigue of Engineering Materials and Structures 3 193-212
2. G.I. Barenblatt Ya.B. Zeldovich 1971 Intermediate asymptotics in mathematical physics Russian Mathematical Surveys 26 2 45-61 10.1070/ rm1971v026n02ABEH003819
3. G.I. Barenblatt Ya.B. Zeldovich 1972 Self-similar solutions as intermediate asymptotics Ann. Rev. Fluid Mech. 4 285-312 10.1146/ annurev.fl.04.010172.001441 1972AnRFM...4..285B
4. G.I. Barenblatt 1956 On certain problems of the theory of elasticity which arise in the theory of the hydraulic fracture of the oil stratum Journal of Applied Mathametics in Mechanical (PMM) 20 4 475-486 81696
5. Barenblatt, G.I. (1959). On the equilibrium cracks formed in brittle fracture. Journal of Applied Mathametic Mechanics (PMM) (3) 434-444, (4) 706-721, (5) 893-900
6. G.I. Barenblatt 1996 Scaling, Self-Similarity, and Intermediate Asymptotics Cambridge University Press Cambridge
7. G.I. Barenblatt 2003 Scaling Cambridge University Press Cambridge
8. Z.P. Bažant J. Planas 1998 Fracture and Size Effect in Concrete and Other Quasibrittle Materials CRC Press Boston, London, New York, Washington, D.C
9. Z.P. Bažant A. Yavari 2005 Is the cause of size effect on structural strength fractal or energetic-statistical? Engineering Fracture Mechanics 72 1-31 10.1016/j.engfracmech.2004.03.004
10. Z.P. Bažant 1984 Size effect in blunt fracture: Concrete, rock, metal Journal of Engineering Mechanics ASCE 110 4 518-535
11. Z.P. Bažant 2002 Scaling of Structural Strength Hermes Penton Science London
12. Z.P. Bažant 2004a Probability distribution of energetic-statistical size effect in quasibrittle fracture Probabilistic Engineering Mechanics 19 307-319 10.1016/j.probengmech.2003.09.003
13. Z.P. Bažant 2004b Scaling theory for quasibrittle structural failure Proceedings of the US National Academy of Sciences 101 37 13400-13407 10.1073/pnas.0404096101 2004PNAS..10113400B
14. J.J. Benbow 1960 Cone cracks in fused silica Proceeding of the Physics Society B75 697-699 10.1088/0370-1328/75/5/308
15. L.R. Botvina 1989 The Kinetics of Fracture of Structural Materials Nauka Moscow
16. K.B. Broberg 2004 Significance of morphological changes at a propagating crack edge International Journal of Fracture 130 723-742 10.1007/ s10704-004-2825-7
17. A. Carpinteri B. Chiaia P. Cornetti 2002 A scale-invariant cohesive crack model for quasi-brittle materials Engineering Fracture Mechanics 69 207-217 10.1016/S0013-7944(01)00085-6
18. A. Carpinteri P. Cornetti F. Barpi S. Valente 2003 Cohesive crack model description of ductile to brittle size-scale transition: Dimensional analysis vs. renormalization group theory Engineering Fracture Mechanics 70 1809-1839 10.1016/S0013-7944(03)00126-7
19. A. Carpinteri R. Massabo 1996 Bridged versus cohesive crack in the flexural behaviour of brittle-matrix composites International Journal of Fracture 81 125-145 10.1007/BF00033178
20. A. Carpinteri 1989 Cusp catastrophe interpretation of fracture instability Journal of the Mechanics and Physics of Solids 37 5 567-582 0695.73036 10.1016/0022-5096(89)90029-X
21. A. Carpinteri 1994 Scaling laws and renormalization groups for strength and toughness of disordered materials International Journal of Solids and Structures 31 3 291-302 0807.73050 10.1016/0020-7683(94)90107-4
22. Carpinteri, A. (1996). Strength and toughness in disordered materials: complete and incomplete similarity. In Size-Scale Effects in the Failure Mechanisms of Materials and Structures Edited by Carpinteri A. E. & F.N. Spon, London, et. al., 3-26
23. Carpinteri, A. (1997). Structural Mechanics - A United Approach. E. & F.N. Spon, London, et. al.
24. C.S.J. Gardner J.M. Greene M.D. Kruskal R.M. Miura 1967 A method for solving the Korteweg-de Vries equation. Physics Review Letters 19 1095-1097
25. Goldenfeld, N.D. (1992). Lectures on Phase Transition and the Renormalization Group. Perseus Publishing, Reading
26. F.A. Heiser W. Mortimer 1972 Effects of thickness and orientation on fatigue crack growth rate in 4340 steel Met. Trans. 3 2119-2123
27. G.R. Irwin 1960 Fracture made transition for a crack traversing a plate Transactions of the ASME Series D82 417-425
28. Mandelbrot, B. (1975). Les Objects Fractals: Forme, Hasard et Dimension. Flammarion, Paris.
29. B. Mandelbrot 1977 Fractals, Form, Chance and Dimension W.H. Freeman and Co. San Francisco
30. B. Mandelbrot 1982 The Fractal Geometry of Nature W.H. Freeman and Co. San Francisco
31. Panasyuk, V.V. (1968). Limiting Equilibrium in Brittle Bodies with Cracks. Naukova Dumka, Kiev.
32. P.C. Paris F. Erdogan 1963 A critical analysis of crack propagation laws Journal of Basic Engineering Transactions ASME, Series D85 528-534
33. P.C. Paris M.P. Gomez W.P. Anderson 1961 A traditional analytic theory of fatigue The Trend in Engineering 13 9-14
34. R.O. Ritchie J.F. Knott 1973 Mechanisms of fatigue crack growth in low alloy steel Acta Metallurgica 21 639-648 10.1016/0001-6160(73)90073-4
35. R.O. Ritchie 2005 Incomplete self-similarity and fatigue crack growth International Journal of Fracture 132 197-203 10.1007/s10704-005-2266-y
36. F. Roesler 1956 Brittle fracture near equilibrium Proceeding of the Physics Society B69 981-992 10.1088/0370-1301/69/10/303 1956PPSB...69..981R
37. Taylor, G.I. (1941) The formation of a blast wave by a very intense explosion. Report RC-210, Civil Defense Research Committee.
38. G.I. Taylor 1950 The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945 Proceeding of the Royal Society A201 175-186 0036.26404 1950RSPSA.201..175T
39. Yu.P. Zheltov S.A. Christianovich 1955 On the hydraulic fracture of oil stratum Izvestiya. USSR Academic Science Technical Science 5 3-41