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Fracture energy and fracture process zone

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Abstract

The fracture energy Gf can be determined following a RILEM recommendation. However, it has been found that fracture energy depends on both size and geometry of the test specimen. The underlying fictitious crack model postulates that fracture energy, tensile strength, the critical opening of the fictitious crack, and the shape of the softening curve (softening factor) are constants for a given type of concrete. Here it is shown that a local fracture energy ccan be introduced. This local fracture energy varies with the width of the fracture process zone. As the crack approaches the back end of a specimen the fracture process zone becomes more and more confined and hence the local fracture energy decreases. Theoretical predictions are compared with experimental results obtained with the wedge splitting technique described earlier. It is shown that a local variation of the fracture energy leads to a size dependence of the global specific fracture energy.

Resume

L'énergie de rupture Gf peut être déterminée expérimentalement selon la méthode recommandée par la RILEM. On a déjà constaté que l'énergie de rupture dépend à la fois de la taille et de la géométrie du spécimen à tester. Le modèle de la fissure fictive postule que l'énergie de rupture, la résistance à la traction, l'ouverture critique de la fissure fictive et la forme du diagramme de radoucissement sont constants pour un type de béton donné.

On montre dans cet article qu'il est possible d'introduire une énergie de rupture locale gf. Cette énergie de rupture locale varie en fonction de la largeur de la zone d'endommagement. Au fur et à mesure que la fissure se propage dans le spécimen, la zone d'endommagement se confine de plus en plus et l'on assiste alors à une décroissance de l'énergie de rupture locale.

Les prévisions théoriques ont été confrontées aux résultats expérimentaux obtenus par ‘l'essai de fondage par coin’ (wedge splitting technique), méthode décrite précédemment. Il a été monté qu'une variation locale de l'énergie de rupture entraîne une dépendance de l'énergie de rupture spécifique globale de la taille du spécimen.

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References

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

    Article  Google Scholar 

  2. Hillerborg, A., ‘Analysis of one single crack’, in ‘Fracture Mechanics of Concrete’, edited by F. H. Wittmann (Elsevier, Amsterdam, 1983) pp. 223–249.

    Google Scholar 

  3. RILEM Draft Recommendation, ‘Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams’,Mater. Struct. 106 (1985) 286–290.

    Google Scholar 

  4. Rice, J. R., ‘A path independent integral and the approximate analysis of strain concentration by notches and cracks’,J. Applied Mech. (June 1968) 379–386.

  5. Li, V. C. in ‘Application of Fracture Mechanics to Cementitious Composites’, edited by S. P. Shah (Nijhoff, Dordrecht, 1985) p. 431.

    Google Scholar 

  6. Petersson, P. E., ‘Crack growth and development of fracture zones in plain concrete and similar materials’, Report TVBM-1006 (Division of Building Materials, Lund Institute of Technology, Sweden, 1981).

    Google Scholar 

  7. Bruhwiler, E., ‘Fracture mechanics of dam concrete subjected to quasi-static and seismic loading conditions’, Thesis No. 739 (Institute for Building Materials, Swiss Federal Institute of Technology, Lausanne, 1988).

    Google Scholar 

  8. Bruhwiler, E. and Wittmann, F. H., ‘The wedge splitting test, a method of performing stable fracture mechanics tests’,Eng. Frac. Mech. 35 (1990) 565–571.

    Article  Google Scholar 

  9. Carpinteri, A., Di Tommaso, A., Ferrara, G. and Melchiorri, G., ‘Experimental evaluation of concrete fracture energy through a new identification method’, in ‘Fracture Toughness and Fracture Energy of Concrete’, edited by F. H. Wittmann (Elsevier, Amsterdam, 1986) pp. 423–436.

    Google Scholar 

  10. Xu, S. L. and Zhao, G. F., ‘The determination of the fracture toughness and the fracture energy of concrete’, in ‘Fracture Toughness and Fracture Energy—Test Methods for Concrete and Rock’, International Workshop, Sendai, Japan, 1988, pp. 157–163.

  11. Hu, X. Z. and Wittmann, F. H., ‘Experimental method to determine extension of fracture process zone’,J. Mater. Civil Engng 2 (1990) 15–23.

    Google Scholar 

  12. Idem ‘Fracture process zone andK r-curve of hardened cement paste and mortar’, in ‘Fracture of Concrete and Rock: Recent Developments’ edited by S. P. Shah, S. E. Swartz and B. Barr (Elsevier, London, 1989) pp. 307–316.

    Google Scholar 

  13. Idem, ‘An analytical method to determine the bridging stress transferred within the fracture process zone’,Cement Concr. Res. 21 (1991) 1118–1128.

    Article  Google Scholar 

  14. Hu, X. Z., ‘Fracture Process Zone and Strain-Softening in Cementitious Materials’, Postdoctoral Research Report (Institute for Building Materials, Swiss Federal Institute of Technology, Zurich, 1991).

    Google Scholar 

  15. Bažant, Z. B. and Cedolin, L., ‘Blunt crack band propagation in finite element analysis’,J. Eng. Mech. Div. ASCE 105 (1979) 297–315.

    Google Scholar 

  16. Bažant, Z. B. and Oh, B. H. ‘Crack band theory for fracture of concrete’,Mater. Struct. 16 (1983) 155–177.

    Google Scholar 

  17. Nomura, N., Mihashi, H. and Izumi, M., ‘Numerical analysis of crack extension process of concrete’, in ‘Fracture Toughness and Fracture Energy—Test Methods for Concrete and Rock’, International Workshop, Sendai, Japan, 1988, pp. 338–347.

  18. Wittmann, F. H., Mihashi, H. and Nomura, N., ‘Size effect on fracture energy of concrete’,Eng. Frac. Mech. 35 (1990) 107–116.

    Article  Google Scholar 

  19. Evans, A. G., Heuer, A. H. and Porter, D. L., ‘The fracture toughness of ceramics’, in ‘Fracture’ Vol. 1, edited by D. M. R. Taplin (University of Waterloo Press, Ontario, 1977) pp. 529–556.

    Google Scholar 

  20. Wecharatana, M. and Shah, S. P., ‘A model for predicting fracture resistance in reinforced concrete’,Cement Concr. Res.13 (1983) 819–329.

    Article  Google Scholar 

  21. Foote, R. M. L., Mai, Y. W. and Cotterell, B., ‘Crack growth resistance curves in strain-softening materials’,J. Mech. Phys. Solids 34 (1986) 593–607.

    Article  Google Scholar 

  22. Steinbrech, R. W., Reichl, A. and Schaarwachter ‘R-curve behaviour of long cracks in alumina’,J. Amer. Ceram. Soc. 73 (1990) 2009–2015.

    Article  Google Scholar 

  23. Rodel, J., Kelly, J. F. and Lawn, B. R., ‘In Situ measurements of bridged crack interfaces in SEM,J. Amer. Ceram. Soc. 73 (1990) 3313–3318.

    Article  Google Scholar 

  24. Hu, X. Z. and Mai, Y. W. ‘A general method for determination of crack-interface bridging stresses’,J. Mater. Sci. in press.

  25. Hu, X. Z., Lutz, E. and Swain, M. V., ‘Crack tip bridging stresses in ceramic materials’,J. Amer. Ceram. Soc. 74 (1991) 1828–1832.

    Article  Google Scholar 

  26. Swartz, S. and Refai, T., ‘Cracked surface revealed by dye and its utility in determining fracture parameters’, in ‘Fracture Toughness and Fracture Energy—Test Methods for Concrete and Rock, International Workshop, Sendai, Japan, 1988 pp. 393–405.

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Authors and Affiliations

  1. Centre for Advanced Materials Technology, Department of Mechanical Engineering, University of Sydney, 2006, NSW, Australia

    X. -Z. Hu

  2. Institute for Building Materials, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093, Zurich, Switzerland

    F. H. Wittmann

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  1. X. -Z. Hu
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  2. F. H. Wittmann
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Hu, X.Z., Wittmann, F.H. Fracture energy and fracture process zone. Materials and Structures 25, 319–326 (1992). https://doi.org/10.1007/BF02472590

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