Materials and Structures

, Volume 27, Issue 10, pp 563–571 | Cite as

Size effects on tensile fracture properties: a unified explanation based on disorder and fractality of concrete microstructure

  • Alberto Carpinteri
  • Giuseppe Ferro
Article

Abstract

Tests were carried out using three independent jacks orthogonally disposed, making it possible to apply a purely tensile force, so that the secondary flexural stresses, if kept under control, constitute a degree of error comparable with the values allowed for normal testing apparatus. The method enables a stress versus strain curve to be plotted with the descending (softening) branch up to the point where the cross-section of the tensile specimen breaks away. The principal purpose is to avoid any spurious effect that might provide a fallacious explanation of the recurring size effects on apparent tensile strength and fictitious fracture energy. Once the secondary effects have been excluded, only the disorder and fractality of the concrete microstructure remain to explain such fundamental trends. In the case of tensile strength, the dimensional decrement represents self-similar weakening of the material ligament, due to pores, voids, defects, cracks, aggregates, inclusions, etc. Analogously, in the case of fracture energy, the dimensional increment represents self-similar tortuosity of the fracture surface, as well as self-similar overlapping and distribution of microcracks in the direction orthogonal to that of the forming macrocrack.

Keywords

Fracture Energy Specimen Size Fractal Nature Plain Concrete Nominal Tensile Strength 

Resume

L'expérience a été conduite en utilisant trois vérins indépendants placés orthogonalement. Celà a permis d'appliquer une charge de traction pure de façon que les contraintes secondaires de fléxion, si elles sont contrôlées, donnent des erreurs dont l'ordre de grandeur est comparable au valeurs tolérées pour les appareils utilisés normalement. Ce gendre de méthode expérimentale permet de suivre la partie descendante (écrouissage négatif) de la courbe effort-déformation jusqu'au point où la section transversale de l'échantillon sous traction se casse. Le but principal est d'éviter tous les faux effets qui peuvent nous conduire à des explications erronées à propos des effets d'échelle récurrents sur l'allure de la résistance à la traction apparente et de l'énergie de rupture fictive. Une fois que les effets secondaires ont été exclus, seuls le désordre et le caractère fractal de la microstructure du béton permettent de justifier cette tendance fondamentale. Dans le cas de la résistance à la traction, la diminution dimensionnelle représente un affaiblissement des liaisons du matériau, dû aux pores, aux vides, aux défauts, aux fissures, aux granulats, aux inclusions, etc. D'une manière analogue, dans le cas de l'énergie de rupture, l'accroissement dimensionnel représente la sinuosité de la surface de rupture, ainsi que la superposition et la distribution des microfissures dans la direction perpendiculaire à celle des microfissures en formation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L'Hermite, R., ‘Idées actuelles sur la technologie du béton’, Collection de l'Institut Technique du Bâtiment et des Travaux Publics, Paris, 1955.Google Scholar
  2. 2.
    Rusch, H. and Hilsdorf, H. K., ‘Deformation characteristics of concrete under axial tension’,Voruntersuchungen 44 (1963).Google Scholar
  3. 3.
    Hughes, B. P. and Chapman, G. P., ‘The complete stress-strain curves for concrete in direct tension’,RILEM Bull. 30 (1966) 95–97.Google Scholar
  4. 4.
    Evans, R. H. and Marathe, M. S., ‘Microcracking and stress-strain curves for concrete in tension’,Mater. Struct. 1 (1968) 61–64.Google Scholar
  5. 5.
    Heilmann, H. G., Hilsdorf, H. K. and Finsterwalder, K., ‘Festigkeit und Verformung von Beton unter Zugspannungen’,Deutsch. Ausschuss Stahlbeton 203 (1969).Google Scholar
  6. 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, 1981).Google Scholar
  7. 7.
    Gopalaratnam, V. S. and Shah, S. P., ‘Softening response of plain concrete in direct tension’,J. ACI 82 (1985) 310–323.Google Scholar
  8. 8.
    Reinhardt, H. W., Cornelissen, A. W. and Hordijk, D. A., ‘Tensile tests and failure analysis of concrete’,J. Struct. Eng. 112 (1986) 2462–2477.CrossRefGoogle Scholar
  9. 9.
    Phillips, D. V. and Zhang, B., ‘Fracture energy and brittleness of plain concrete specimens under direct tension’, in ‘Fracture Behaviour and Design of Materials and Structures’, edited by D. Firrao, Proceedings of the 8th European Conference on Fracture, Torino, Italia, October, 1990 (EMAS, Warley, 1991) pp. 646–652.Google Scholar
  10. 10.
    van Mier, J. G. M., ‘Scaling in tensile and compressive fracture of concrete’, in ‘Applications of Fracture Mechanics to Reinforced Concrete’, edited by A. Carpinteri (Chapman and Hall, London, 1992) pp. 19–31.Google Scholar
  11. 11.
    Saouma, V. E., Barton, C. C. and Gamaleldin, N. A., ‘Fractal characterization of fracture surfaces in concrete’,Engng Fract. Mech. 35 (1990) 47–53.CrossRefGoogle Scholar
  12. 12.
    Mandelbrot, B. B., ‘The Fractal Geometry of Nature’ (W. H. Freeman and Company, New York, 1982).MATHGoogle Scholar
  13. 13.
    Falconer, K., ‘Fractal Geometry: Mathematical Foundations and Applications’ (Wiley, Chichester, 1990).MATHGoogle Scholar
  14. 14.
    Griffith, A. A., ‘The phenomena of rupture and flow in solids’,Phil. Trans. R. Soc. Lond. A221 (1921) 163–198.Google Scholar
  15. 15.
    Weibull, W., ‘A Statistical Theory of the Strength of Materials’ (Swedish Royal Institute for Engineering Research, Stockholm, 1939).Google Scholar
  16. 16.
    Freudenthal, A. M., ‘Statistical approach to brittle fracture’, in ‘Fracture’ edited by H. Liebowitz, Vol. 2 (Academic Press, New York, 1968) pp. 591–619.Google Scholar
  17. 17.
    Jayatilaka, A. S., ‘Fracture of Engineering Brittle Materials’ (Applied Science, London, 1979).Google Scholar
  18. 18.
    Carpinteri, A., ‘Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics’,Int. J. Solids Struct. 25 (1989) 407–429.CrossRefGoogle Scholar
  19. 19.
    Idem, ‘Mechanical Damage and Crack Growth in Concrete: Plastic Collapse to Brittle Fracture’ (Martinus Nijhoff, Dordrecht, 1986).MATHGoogle Scholar
  20. 20.
    Mandelbrot, B. B., Passoja, D. E. and Paullay, A. J., ‘Fractal character of fracture surfaces of metals’,Nature 308 (1984) 721–722.CrossRefGoogle Scholar
  21. 21.
    RILEM Technical Committee 50, ‘Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams’, Draft RecommendationMater. Struct. 18 (1985) 287–290.Google Scholar
  22. 22.
    Meakin, P., ‘Models for material failure and deformation’,Science 252 (1991) 226–234.Google Scholar
  23. 23.
    Carpinteri, A., ‘Experimental determination of fracture toughness parametersK IC andJ IC and aggregative materials’ Proceedings of the Fifth International Conference on Fracture (Pergamon Press, Oxford, 1981) pp. 1491–1498.Google Scholar
  24. 24.
    Idem, ‘Static and energetic fracture parameters for rocks and concretes’,Mater. Struct. 14 (1981) 151–162.Google Scholar
  25. 25.
    Idem, ‘Notch sensitivity in fracture testing of aggregative materials’,Engng Fract. Mech. 16 (1982) 467–481.CrossRefGoogle Scholar
  26. 26.
    Idem, ‘Interpretation of the Griffith instability as a bifurcation of the global equilibrium’, in ‘Applications of Fracture Mechanics to Cementitious Composities’, edited by S. P. Shah (Martinus Nijhoff, Dordrecht, 1985), pp. 287–316.Google Scholar
  27. 27.
    Idem, ‘Limit analysis for elastic-softening structures: scale and slenderness influence on the global brittlenes’, in ‘Brittle Matrix Composites’, edited by A. M. Brandt and I. H. Marshall (Elsevier Applied Science, London, 1986) pp. 497–508.Google Scholar
  28. 28.
    Idem., ‘Cusp catastrophe interpretation of fracture instability’,J. Mech. Phys. Solids 37 (1989) 567–582.MATHCrossRefGoogle Scholar
  29. 29.
    Tang, T., Shah, S. P. and Ouyang, C., ‘Fracture mechanics and size effect of concrete in tension’,J. Struct. Engng, ASCE 118 (1992) 3169–3185.Google Scholar
  30. 30.
    Lange, D. A., Jennings, H. M. and Shah, S. P., ‘Relationship between fracture surface roughness and fracture behavior of cement paste and mortar’,J. Am. Ceram. Soc. 76 (1993) 589–597.CrossRefGoogle Scholar
  31. 31.
    Wilson, K. G., ‘Renormalization group and critical phenomena’,Phys. Rev. B4 (1971) 3174–3205.CrossRefGoogle Scholar
  32. 32.
    Herrmann, H. J. and Roux, S., ‘Statistical Models for the Fracture of Disordered Media’ (North-Holland, Amsterdam, 1990).Google Scholar

Copyright information

© RILEM 1994

Authors and Affiliations

  • Alberto Carpinteri
    • 1
  • Giuseppe Ferro
    • 1
  1. 1.Dip. di Ingegneria StrutturalePolitecnico di TorinoTorinoItaly

Personalised recommendations