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Scaling phenomena in fatigue and fracture

  • Conference paper
Advances in Fracture Research

Abstract

The general classification of scaling laws will be presented and the basic concepts of modern similarity analysis - intermediate asymptotics, complete and incomplete similarity - will be introduced and discussed. The examples of scaling laws corresponding to complete similarity will be given. The Paris scaling law in fatigue will be discussed as an instructive example of incomplete similarity. It will be emphasized that in the Paris law the powers are not the material constants. Therefore, the evaluation of the life-time of structures using the data obtained from standard fatigue tests requires some precautions.

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References

  • Barenblatt, G.I. and Botvina, L.R. (1981). Incomplete self-similarity of fatigue in the linear range of crack growth. Fatigue of Engineering Materials and Structures 3, 193–212.

    Google Scholar 

  • Barenblatt, G.I. and Zeldovich, Ya.B. (1971). Intermediate asymptotics in mathematical physics. Russian Mathematical Surveys 26(2), 45–61.

    Article  Google Scholar 

  • Barenblatt, G.I. and Zeldovich, Ya.B. (1972). Self-similar solutions as intermediate asymptotics. Ann. Rev. Fluid Mech. 4, 285–312.

    Article  Google Scholar 

  • Barenblatt, G.I. (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.

    MathSciNet  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • Barenblatt, G.I. (1996). Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Barenblatt, G.I. (2003). Scaling, Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Bažant, Z.P. and Planas, J. (1998). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press, Boston, London, New York, Washington, D.C.

    Google Scholar 

  • Bažant, Z.P. and Yavari, A. (2005). Is the cause of size effect on structural strength fractal or energeticstatistical? Engineering Fracture Mechanics 72, 1–31.

    Article  Google Scholar 

  • Bažant, Z.P. (1984). Size effect in blunt fracture: concrete, rock, metal. Journal of Engineering Mechanics ASCE 110(4), 518–535.

    Google Scholar 

  • Bažant, Z.P. (2002). Scaling of Structural Strength. Hermes Penton Science, London.

    Google Scholar 

  • Bažant, Z.P. (2004a). Probability distribution of energetic-statistical size effect in quasibrittle fracture. Probabilistic Engineering Mechanics 19, 307–319.

    Article  Google Scholar 

  • Bažant, Z.P. (2004b). Scaling theory for quasibrittle structural failure. Proceedings of the US National Academy of Sciences 101(37), 13400–13407.

    Article  Google Scholar 

  • Benbow, J.J. (1960). Cone cracks in fused silica. Proceeding of the Physics Society B75, 697–699.

    Article  Google Scholar 

  • Botvina, L.R. (1989). The Kinetics of Fracture of Structural Materials. Nauka, Moscow.

    Google Scholar 

  • Broberg, K.B. (2004). Significance of morphological changes at a propagating crack edge. International Journal of Fracture, 130, 723–742.

    Article  Google Scholar 

  • Carpinteri, A., Chiaia, B. and Cornetti, P. (2002). A scale-invariant cohesive crack model for quasi-brittle materials. Engineering Fracture Mechanics 69, 207–217.

    Article  Google Scholar 

  • Carpinteri, A., Cornetti, P., Barpi, F. and Valente, S. (2003). Cohesive crack model description of ductile to brittle size-scale transition: dimensional analysis vs. renormalization group theory. Engineering Fracture Mechanics 70, 1809–1839.

    Article  Google Scholar 

  • Carpinteri, A. and Massabo, R. (1996). Bridged versus cohesive crack in the flexural behaviour of brittle-matrix composites. International Journal of Fracture 81, 125–145.

    Article  Google Scholar 

  • Carpinteri, A. (1989). Cusp catastrophe interpretation of fracture instability. Journal of the Mechanics and Physics of Solids 37(5), 567–582.

    Article  Google Scholar 

  • Carpinteri, A. (1994). Scaling laws and renormalization groups for strength and toughness of disordered materials. International Journal of Solids and Structures 31(3), 291–302.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Carpinteri, A. (1997). Structural Mechanics-A United Approach. E. & F.N. Spon, London, et. al.

    Google Scholar 

  • Gardner, C.S.J., Greene, J.M., Kruskal, M.D. and Miura, R.M. (1967). A method for solving the Korteweg-de Vries equation. Physics Review Letters 19, 1095–1097.

    Article  Google Scholar 

  • Goldenfeld, N.D. (1992). Lectures on Phase Transition and the Renormalization Group. Perseus Publishing, Reading.

    Google Scholar 

  • Heiser, F.A. and Mortimer, W. (1972). Effects of thickness and orientation on fatigue crack growth rate in 4340 steel. Met. Trans. 3, 2119–2123.

    Google Scholar 

  • Irwin, G.R. (1960). Fracture made transition for a crack traversing a plate. Transactions of the ASME Series. D82, 417–425.

    Google Scholar 

  • Mandelbrot, B. (1975). Les Objects Fractals: Forme, Hasard et Dimension. Flammarion, Paris.

    Google Scholar 

  • Mandelbrot, B. (1977). Fractals, Form, Chance and Dimension. W.H. Freeman and Co., San Francisco.

    MATH  Google Scholar 

  • Mandelbrot, B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Co., San Francisco.

    MATH  Google Scholar 

  • Panasyuk, V.V. (1968). Limiting Equilibrium in Brittle Bodies with Cracks. Naukova Dumka, Kiev.

    Google Scholar 

  • Paris, P.C. and Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Basic Engineering Transactions ASME, Series D85, 528–534.

    Google Scholar 

  • Paris, P.C. and Gomez, M.P. and Anderson, W.P. (1961). A traditional analytic theory of fatigue. The Trend in Engineering 13, 9–14.

    Google Scholar 

  • Ritchie, R.O. and Knott, J.F. (1973). Mechanisms of fatigue crack growth in low alloy steel. Acta Metallurgica 21, 639–648.

    Article  Google Scholar 

  • Ritchie, R.O. (2005), Incomplete self-similarity and fatigue crack growth. International Journal of Fracture 132, 197–203.

    Article  Google Scholar 

  • Roesler, F. (1956). Brittle fracture near equilibrium. Proceeding of the Physics Society B69, 981–992.

    Article  Google Scholar 

  • Taylor, G.I. (1941) The formation of a blast wave by a very intense explosion. Report RC-210, Civil Defense Research Committee.

    Google Scholar 

  • Taylor, G.I. (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.

    Google Scholar 

  • Zheltov, Yu.P. and Christianovich, S.A. (1955). On the hydraulic fracture of oil stratum. Izvestiya, USSR Academic Science Technical Science 5, 3–41.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California and Lawrence Berkeley National Laboratory Berkeley, CA, 94720-3840, USA

    G. I. Barenblatt

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  1. G. I. Barenblatt
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Editor information

Editors and Affiliations

  1. Politecnico di Torino, Torino, Italy

    Alberto Carpinteri

  2. University of Sydney, Sydney, Australia

    Yiu-Wing Mai

  3. University of California, Berkeley, USA

    Robert O. Ritchie

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© 2006 Springer

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Barenblatt, G.I. (2006). Scaling phenomena in fatigue and fracture. In: Carpinteri, A., Mai, YW., Ritchie, R.O. (eds) Advances in Fracture Research. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5423-5_4

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  • DOI: https://doi.org/10.1007/978-1-4020-5423-5_4

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-4626-1

  • Online ISBN: 978-1-4020-5423-5

  • eBook Packages: EngineeringEngineering (R0)

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