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Materials and Structures

, Volume 48, Issue 1–2, pp 235–247 | Cite as

Fiber-reinforced concrete in flexure: a cohesive/overlapping crack model application

  • A. Carpinteri
  • E. Cadamuro
  • G. Ventura
Original Article

Abstract

The analysis of fibre-reinforced concrete taking into account the nonlinear behaviour of the material in tension and compression is addressed by a numerical approach based on the Cohesive–Overlapping Crack Model, in order to reveal the influence of fibre content in the flexural behavior of beams. The results of a numerical analysis and of an experimental campaign are compared in order to validate the proposed model. The numerical curves show a good approximation to the experimental results; however a less good approximation is evidenced when the fibre content is set to very low values or very high values of fibres, where an embrittlement of the mechanical behaviour of the concrete is revealed.

Keywords

Fibre-reinforced concrete Cohesive crack Steel fibres Scale effects Structural instability 

References

  1. 1.
    Collepardi M, Coppola L (1990) Le fibre. Materiali Innovativi per Calcestruzzi Speciali, Cap. 8, ENCO, Spresiano (TV)Google Scholar
  2. 2.
    Carpinteri A (1981) A fracture mechanics model for reinforced concrete collapse. In: Proceedings of the IABSE colloquium. Delft University Press, Delft, pp 17–30Google Scholar
  3. 3.
    Carpinteri A (1984) Stability of fracturing process in RC beams. J Struct Eng (ASCE) 110(3):544–558CrossRefGoogle Scholar
  4. 4.
    Bosco C, Carpinteri A (1992) Fracture behaviour of beam cracked across reinforcement. Theor Appl Fract Mech 17:61–68CrossRefGoogle Scholar
  5. 5.
    Marshall DB, Cox BN, Evans AG (1985) The mechanics of matrix cracking in brittle–matrix fiber composites. Acta Metall Mater 33:2013–2021CrossRefGoogle Scholar
  6. 6.
    Jenq YS, Shah SP (1985) Two parameter fracture model for concrete. J Eng Mech 111(10):1227–1241CrossRefGoogle Scholar
  7. 7.
    Budiansky B, Hutchinson JW, Evans AG (1986) Matrix fracture in fiber-reinforced ceramics. J Mech Phys Solids 34:167–189CrossRefMATHGoogle Scholar
  8. 8.
    Foote RML, Mai Y-W, Cotterell B (1986) Crack growth resistance curves in strain-softening materials. J Mech Phys Solids 34(6):593–607CrossRefGoogle Scholar
  9. 9.
    Cox BN (1991) Extrinsic factors in the mechanics of bridged cracks. Acta Metall Mater 39:1189–1201CrossRefGoogle Scholar
  10. 10.
    Kendall K, Clegg WJ, Gregory RD (1991) Growth of tied cracks: a model for polymer crazing. J Mater Sci Lett 10:671–674CrossRefGoogle Scholar
  11. 11.
    Cox BN, Lo CS (1992) Load ratio, notch, and scale effects for bridged cracks in fibrous composites. Acta Metall Mater 40:69–80CrossRefGoogle Scholar
  12. 12.
    Barenblatt GI (1959) The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks. J Appl Math Mech 23(3):622–636CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. In: Dryden HL, von Karman T (eds) Advances in applied mechanics. Academic Press, New York, pp 55–129Google Scholar
  14. 14.
    Dugdale GS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104CrossRefGoogle Scholar
  15. 15.
    Bilby BA, Cottrell AH, Swinden KH (1963) The spread of plastic yield from a notch. Proc R Soc Lond A272:304–314CrossRefGoogle Scholar
  16. 16.
    Willis JR (1967) A comparison of the fracture criteria of Griffith and Barenblatt. J Mech Phys Solids 15:151–162CrossRefGoogle Scholar
  17. 17.
    Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35:379–386CrossRefGoogle Scholar
  18. 18.
    Smith E (1989) The size of the fully developed softening zone associated with a crack in a strain-softening material—I. A semi-infinite crack in a remotely loaded infinite solid. Int J Eng Sci 27(3):301–307CrossRefGoogle Scholar
  19. 19.
    Carpinteri A (1989) Cusp catastrophe interpretation of fracture instability. J Mech Phys Solids 37:567–582CrossRefMATHGoogle Scholar
  20. 20.
    Carpinteri A (1989) Size effects on strength, toughness, and ductility. J Eng Mech (ASCE) 115(7):1375–1392CrossRefGoogle Scholar
  21. 21.
    Bosco C, Carpinteri A (1995) Discontinuous constitutive response of brittle matrix fibrous composites. J Mech Phys Solids 43(2):261–274CrossRefMATHGoogle Scholar
  22. 22.
    Carpinteri A, Massabò R (1996) Bridged versus cohesive crack in the flexural behavior of brittle–matrix composites. Int J Fract 81:125–145CrossRefGoogle Scholar
  23. 23.
    Burakiewicz A (1978) Testing of fiber bond strength in cement matrix. In: Swamy RN (ed) Testing and test methods of fiber cement composites. The Construction Press Ltd., Lancaster, pp 355–369Google Scholar
  24. 24.
    Li VC, Liang E (1986) Fracture processes in concrete and fiber reinforced cementitious composites. J Eng Mech 112(2):566–586CrossRefGoogle Scholar
  25. 25.
    Comite Euro-International du Beton (1993) CEB-FIB Model Code 1990. CEB Bull d’Inf 213–214Google Scholar
  26. 26.
    Carpinteri A, Ferro G, Ventura G (2003) Size effects on flexural response of reinforced concrete elements with a nonlinear matrix. Eng Fract Mech 70:995–1013CrossRefGoogle Scholar
  27. 27.
    Carpinteri A, Corrado M, Paggi M, Mancini G (2007) Cohesive versus overlapping crack model for a size effect analysis of RC elements in bending. In: Carpinteri A, Gambarova P, Ferro G, Plizzari G (eds) Proceedings of the 6th international FraMCoS conference, vol 2. Taylor and Francis, Leiden, pp 655–663Google Scholar
  28. 28.
    Carpinteri A, Corrado M, Paggi M, Mancini G (2009) New model for the analysis of size-scale effects on the ductility of reinforced concrete elements in bending. J Eng Mech 135(3):221–229CrossRefGoogle Scholar
  29. 29.
    Carpinteri A (1985) Interpretation of the Griffith instability as a bifurcation of the global equilibrium. In: Shah SP (ed) Proceedings of the NATO advanced research workshop on application of fracture mechanics to cementitious composites. Martinus Nijhoff Publishers, Dordrecht, pp 287–316Google Scholar
  30. 30.
    Planas J, Elices M (1992) Asymptotic analysis of a cohesive crack: 1. Theoretical background. Int J Fract 55:153–177CrossRefGoogle Scholar
  31. 31.
    Bazant ZP, Beisel S (1994) Smeared-tip superposition method for cohesive fracture with rate effect and creep. Int J Fract 65:277–290Google Scholar
  32. 32.
    Ruiz G, Elices M, Planas J (1999) Size effects and bond-slip dependence of lightly reinforced concrete beams. In: Carpinteri A (ed) Minimum reinforcement in concrete members. Elsevier Science Ltd., Oxford, pp 127–180Google Scholar
  33. 33.
    Brincker R, Henriksen MS, Christensen FA, Heshe G (1999) Size effects on the bending behaviour of reinforced concrete beams. In: Carpinteri A (ed) Minimum reinforcement in concrete members. Elsevier Science Ltd., Oxford, pp 127–180CrossRefGoogle Scholar
  34. 34.
    Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773–782CrossRefGoogle Scholar
  35. 35.
    Carpinteri A, Colombo G, Ferrara G, Giuseppetti G (1989) Numerical simulation of concrete fracture through a bilinear softening stress–crack opening displacement law. In: Shah SP, Swartz SE (eds) Proceedings of the SEM-RILEM international conference, Houston, USA, 1987. Springer, New York, pp 131–141Google Scholar
  36. 36.
    van Vliet M, van Mier J (1996) Experimental investigation of concrete fracture under uniaxial compression. Mech Cohesive-Frict Mater 1(1):115–127CrossRefGoogle Scholar
  37. 37.
    Jansen DC, Shah SP (1997) Effect of length on compressive strain softening of concrete. J Eng Mech 123(1):25–35CrossRefGoogle Scholar
  38. 38.
    Hillerborg A (1990) Fracture mechanics concepts applied to moment capacity and rotational capacity of reinforced concrete beams. Eng Fract Mech 35:233–240CrossRefGoogle Scholar
  39. 39.
    Bažant ZP (1989) Identification of strain-softening constitutive relation from uniaxial tests by series coupling model for localization. Cem Concr Res 19:973–977CrossRefGoogle Scholar
  40. 40.
    Markeset G, Hillerborg A (1995) Softening of concrete in compression—localization and size effects. Cem Concr Res 25:702–708CrossRefGoogle Scholar
  41. 41.
    Palmquist SM, Jansen DC (2001) Postpeak strain–stress relationship for concrete in compression. ACI Mater J 98:213–219Google Scholar
  42. 42.
    Suzuki M, Akiyama M, Matsuzaki H, Dang TH (2006) Concentric loading test of RC columns with normal- and high-strength materials and averaged stress–strain model for confined concrete considering compressive fracture energy. In: Proceedings of the 2nd FIB congress, 5–8 June 2006, Naples, ItalyGoogle Scholar
  43. 43.
    RILEM Technical Committee TC89-FMT on Fracture Mechanics of Concrete (1990) Determination of fracture parameters (K ICS and CTODc) of plain concrete using three-point bend tests. Draft Recomm Mater Struct 23:457–460CrossRefGoogle Scholar
  44. 44.
    RILEM Technical Committee TC-50 on Fracture Mechanics of Concrete (1985) Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Draft Recomm Mater Struct 18:285–290Google Scholar
  45. 45.
    Guinea GV, Planas J, Elices M (1992) Measurement of the fracture energy using three-point bend tests: 1.—Influence of experimental procedures. Mater Struct 25(148):212–218CrossRefGoogle Scholar
  46. 46.
    Guinea GV, Planas J, Elices M (1992) Measurement of the fracture energy using three-point bend tests: 2.—Influence of bulk energy dissipation. Mater Struct 25(149):305–312Google Scholar
  47. 47.
    Guinea GV, Planas J, Elices M (1992) Measurement of the fracture energy using three-point bend tests: 3.—Influence of cutting the P-δ tail. Mater Struct 25:327–334CrossRefGoogle Scholar
  48. 48.
    Petersson PE (1981) Crack growth and development of fracture zones in plain concrete and similar materials. Lund Institute of Technology Report TVBM-1006Google Scholar

Copyright information

© RILEM 2013

Authors and Affiliations

  1. 1.Department of Structural and Geotechnical EngineeringPolitecnico di TorinoTurinItaly

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