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Size effect on fracture resistance and fracture energy of concrete

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Abstract

A recent asymptotic approach dealing with the size effect on the fracture properties of a large plate is further developed to consider the influence of both the front and back free surfaces of small sized specimens. The new extension is applied to experimental results found in the literature, and good agreements have been found between the predictions and the fracture resistance and energy measured using geometrically similar specimens and specimens with identical size but different initial crack or notch lengths. The physics behind the size effect are discussed based on the modified asymptotic approach. It is found that both the specimen geometry and crack length contribute to the size effect on fracture properties besides its physical size. In particular, the ratio of a fracture process zone, size over its distance to a free surface plays a very important role.

Résumé

Une approche asymptotique, développée récemment pour étudier l’effet de taille sur les propriétés de la rupture d’une grande plaque, a été modifiée pour tenir compte de l’influence des surfaces libres, en avant et en arrière de la fissure dans le cas d’éprouvettes de petites dimensions. Cette nouvelle approche a été appliquée à des résultats expérimentaux trouvés dans la littérature. On a démontré qui’il y a une bonne concordance entre les prévisions fournies par cette approche modifiée et les valeurs des a résistance et de l’énergie de rupture mesurées d’une part sur des éprouvettes, géométriquement similaires et d’autre part sur des éprouvettes de même taille mais ayant des préfissures ou des entailles de longueurs différentes. L’origine physique de l’effet de taille est interprétée sur la base de cette approche asymptotique modifiée. On a trouvé que, non seulement la taille de l’éprouvette mais aussi sa géométrie et la longueur de la préfissure contribuent à l’effet de taille sur les propriétés de la rupture. En particulier, le rapport entre la taille de la zone d’endommagement et sa distance à une surface libre de l’éprouvette joue un rôle très important.

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References

  1. Kaplan, M. F., ‘Crack propagation and the fracture of concrete’,ACIJ.58 (1961), 591–610.

    Google Scholar 

  2. Walsh, P.F., ‘Fracture of plain concrete’,Indian Concr. J. 46 (1972).

  3. Higgins, D. D. and Bailey, J. E., ‘Fracture measurements on cement paste’,J. Mater. Sci. 11 (1976) 1995–2003.

    Article  Google Scholar 

  4. Mindess, S., ‘The effect of specimen size on the fracture energy of concrete’,Cem. Concr. Res. 14 (1984) 431–436.

    Article  Google Scholar 

  5. Bažant, Z.P., ‘Size effect in blunt fracture: concrete, rock, metal’,J. Eng. Mech. ASCE 110 [4] (1984) 518–535.

    Google Scholar 

  6. Bažant, Z.P. and Pfeiffer, P.A., ‘Determination of fracture energy from size effect and brittleness number’,ACI Mater. J. 84 (1987) 463–480.

    Google Scholar 

  7. Bažant, Z.P., ‘Size effect on strength: a review’,Arch. Appl. Mech.,69 (1999) 703–725.

    Article  MATH  Google Scholar 

  8. Nallathambi, P., Karihaloo, B.L. and Heaton, B.S., ‘Effect of specimen and crack sizes, water/cement ratio and coarse aggregate texture upon fracture toughness of concrete’,Mag. Concr. Res. 36 [129] (1984) 227–236.

    Article  Google Scholar 

  9. Nallathambi, P., Karihaloo B.L. and Heaton, B.S., ‘Various size effect in fracture of concrete’,Cem. Concr. Res. 15 (1985) 117–126.

    Article  Google Scholar 

  10. Wittmann, F.H. (ed.), ‘Fracture Mechanics of Concrete Structures’, Proc. FRAMCOS-2, Zurich, Switzerland, July 25–28, 1995 (Aedificatio Publishers, Freiburg, 1995).

    Google Scholar 

  11. Mihashi, H. and Rokugo, K. (eds.), ‘Fracture Mechanics of Concrete Structures’, Proc. FRAMCOS-3, Gifu, Japan, (Aedificatio Publishers, Freiburg, 1998).

    Google Scholar 

  12. Hu, X.Z., ‘Toughness measurements from crack close to free edge’,Inter. J. Fract. 86 (1997) L63–L68.

    Google Scholar 

  13. Hu, X.Z., ‘Size effects in toughness induced by crack close to free edge’, in Ref. [11] ‘, 2011–2020.

    Google Scholar 

  14. Hu, X.Z., ‘An asymptotic approach to size effect on fracture toughness and energy’, Proc. Inter. Workshop on Fracture Mechanics and Advanced Engineering Materials, Dec. 8–10, 1999, Sydney, ed. L. Ye and Y.W. Mai, 76–83.

  15. Hu, X.Z. and Wittmann, F.H., ‘Size effect on toughness induced by crack close to free surface’,Eng. Fract. Mech. 65 (2000) 209–221.

    Article  Google Scholar 

  16. Hu, X.Z., ‘An asymptotic approach to size effect on fracture toughness and fracture energy of composites’,Eng. Fract. Mech. (in press).

  17. Duan, K., Hu, X.Z. and Wittmann, F.H., ‘Explanation of size effect in concrete fracture using non-uniform energy distribution’,Mater. Struct. (in press).

  18. Trunk, B., ‘Influence of structural size on the fracture energy of concrete’, ETH Building Materials Reports No. 11, ETH Switzerland, 2000 (Aedificatio, Publishers, Freiburg, 2000) (in German).

    Google Scholar 

  19. Trunk, B. and Wittmann, F.H., ‘Experimental investigation into the size dependence of fracture mechanics parameters’, in Ref. [11] ‘, 1937–1948.

    Google Scholar 

  20. Hillerborg, A., ‘Results of three comparative test series for determining the fracture energyG F of concrete’,Mater. Struct. 18, (1985) 33–39.

    Google Scholar 

  21. Wittmann, F.H., Mihashi, H. and Nomura, N. ‘Size effect on fracture energy of concrete’,Eng. Fract. Mech. 35 (1990) 107–115.

    Article  Google Scholar 

  22. Carpinteri, A., Chiaia, B. and Ferro, G., ‘Multifractal nature of material microstructure and size effects on nominal strength’, in ‘Fracture of Brittle, Disordered Materials: Concrete, Rock and Ceramics’, Proc. IUTAM Symposium, Brisbane, September 1993, Eds. G. Baker & B.L. Karihaloo (E & FN Spon, London, 1995) 21–34.

    Google Scholar 

  23. Carpinteri, A., Ferro, G. and Invernizzi, S., ‘A truncated statistical model for analyzing the size-effect on tensile strength of concrete structures’, in Ref. [10] ‘, 557–570.

    Google Scholar 

  24. Carpinteri, A. and Chiaia, B., ‘Multifractal scaling law for the fracture energy variation of concrete structures’, in Ref. [10] ‘, 581–596.

    Google Scholar 

  25. Trunk, B. and Wittmann, F.H., ‘Influence of size on fracture energy of concrete’,Mater. Struct. 34 (239) (June 2001) 260–265.

    Article  Google Scholar 

  26. Hu, X.Z., ‘Fracture Process Zone and strain Softening in Cementitious Materials’, ETH Building Materials Reports No. 1, ETH Switzerland, 1990 (Aedificatio Publishers, Freiburg, 1995).

    Google Scholar 

  27. Hu, X.Z. and Wittmann, F.H., ‘Fracture energy and fracture process zone’,Mater. Struct. 25 (1992) 319–326.

    Article  Google Scholar 

  28. Cotterell, B. and Mai, Y.-W., ‘Crack growth resistancer curve and size effect in the fracture of cement paste’,J. Mater. Sci. 22 (1987) 2734–2738.

    Article  Google Scholar 

  29. Cotterell, B. and Mai, Y.-W., ‘Fracture Mechanics of Cementitious Materials’, (Blackie Academic & Professional 1996).

  30. Wittmann, X. and Zhong, H., ‘On Some Experiments to Study the Influence of Size on Strength and Fracture Energy of Concrete’, ETH Building Materials Reports No. 2, ETH Switzerland, 1994. (Aedificatio Publishers, Freiburg, 1996).

    Google Scholar 

  31. Wittmann, F.H., ‘Fracture process zone and fracture energy’, in ‘Fracture Mechanics of Concrete Structures’, Proc. FRAMCOS-1, Breackenridge, Colorado, USA, 1–5 June 1992, ed. Z.P. Bažant (Elsevier Applied Science) 391–403.

  32. Hillerborg, A., Modéer, M. and Petersson, P.-E., ‘Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements’,Cem. Concr. Res. 6 (1976) 773–782.

    Article  Google Scholar 

  33. Petersson, P.-E., ‘Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Structures’, Report TVBM-1006. (Division of Building Materials, Lund Institute of Technology, Sweden, 1981).

    Google Scholar 

  34. Hillerborg, A., ‘Analysis of one single crack’, in ‘Fracture Mechanics of Concrete’, ed. F.H. Wittmann (Elsvier, Amsterdam, 1983) 223–249.

    Google Scholar 

  35. RILEM TC 50-FMC, ‘Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams’,Mater. Struct. 18 (1985) 287–290.

    Google Scholar 

  36. Tada, H., Paris, P.C. and Irwin, G.R., ‘Stress analysis of cracks handbook’, 3rd Ed. (ASME Press, New York, 2000).

    Google Scholar 

  37. ASTM E399-90, ‘Standard Test Method for Plain-Strain Fracture Toughness of Metallic Materials’, American Society for Testing and Materials, Philadelphia, 1990.

  38. Duan, K., Hu, X.Z. and Wittmann, F.H., ‘Thickness effect on fracture energy of cementitious materials’, submitted toCem. Conr. Res.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Western Australia, 35 Stirling Highway, 6009, Crawley, WA, Australia

    K. Duan & X. -Z. Hu

  2. Institute for Building Materials, Swiss Federal Institute of Technology, CH-8093, Zürich, Switzerland

    F. H. Wittmann

Authors
  1. K. Duan
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  2. X. -Z. Hu
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  3. F. H. Wittmann
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Editorial Note Prof. Folker H. Wittmann is a RILEM Senior Member.

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Duan, K., Hu, X.Z. & Wittmann, F.H. Size effect on fracture resistance and fracture energy of concrete. Mat. Struct. 36, 74–80 (2003). https://doi.org/10.1007/BF02479520

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  • DOI: https://doi.org/10.1007/BF02479520

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