Advances in concrete construction

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Analytical methods for determination of double-K fracture parameters of concrete

  • Kumar, Shailendra (Department of Civil Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya, Central University) ;
  • Pandey, Shashi Ranjan (Department of Civil Engineering, National Institute of Technology) ;
  • Srivastava, A.K.L. (Department of Civil Engineering, National Institute of Technology)
  • Received : 2013.07.06
  • Accepted : 2013.12.10
  • Published : 2013.12.25
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Abstract

This paper presents a comparative study on the double-K fracture parameters of concrete obtained using four existing analytical methods such as Gauss-Chebyshev integral method, simplified Green's function method, weight function method and simplified equivalent cohesive force method. Two specimen geometries: three point bend test and compact tension specimen for sizes 100-500 mm at initial notch length to depth ratios 0.25 and 0.4 are used for the comparative study. The required input parameters for determining the double-K fracture parameters are derived from the developed fictitious crack model. It is found that the cohesive toughness and initial cracking toughness determined using weight function method and simplified equivalent cohesive force method agree well with those obtained using Gauss-Chebyshev integral method whereas these fracture parameters determined using simplified Green's function method deviates more than by 11% and 20% respectively as compared with those obtained using Gauss-Chebyshev integral method. It is also shown that all the fracture parameters related with double-K model are size dependent.

Keywords

References

  1. ASTM International Standard E399-06 (2006), Standard test method for linear-elastic method plane-strain fracture toughness KIC of metallic materials, Copyright ASTM International, West Conshohocken, U.S., 1-32.
  2. Bazant, Z.P. and Oh, B.H. (1983), "Crack band theory for fracture of concrete", Mater. Struct., 16(93), 155-177.
  3. Bazant, Z.P., Kim, J.K. and Pfeiffer, P.A. (1986), "Determination of fracture properties from size effect tests", J. Struct. Eng. ASCE, 112(2), 289-307. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:2(289)
  4. Carpinteri, A. (1989), "Cusp catastrophe interpretation of fracture instability", J. Mech. Phy. Solids, 37(5), 567-582. https://doi.org/10.1016/0022-5096(89)90029-X
  5. Cusatis, G. and Schauffert, E.A. (2009), "Cohesive crack analysis of size effect", Eng. Fract. Mech.,76, 2163-2173. https://doi.org/10.1016/j.engfracmech.2009.06.008
  6. Elices, M., Rocco, C. and Roselló, C. (2009), "Cohesive crack modeling of a simple concrete: Experimental and numerical results", Eng. Frac. Mech., 76, 1398-1410. https://doi.org/10.1016/j.engfracmech.2008.04.010
  7. Hillerborg, A., Modeer, M. and Petersson, P.E. (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6, 773-782. https://doi.org/10.1016/0008-8846(76)90007-7
  8. Hu S. and Lu J. (2012), "Experimental research and analysis on double-K fracture parameters of concrete", Adv. Sci. Lett., 12(1), 192-195. https://doi.org/10.1166/asl.2012.2806
  9. Hu S., Mi Z. and Lu J. (2012), Effect of crack-depth ratio on double-K fracture parameters of reinforced concrete", Appl. Mech. Mater., 226-228, 937-941. https://doi.org/10.4028/www.scientific.net/AMM.226-228.937
  10. Jenq, Y.S. and Shah, S.P. (1985), "Two parameter fracture model for concrete", J. Eng. Mech. ASCE, 111 (10), 1227-1241. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:10(1227)
  11. Kaplan, M.F. (1961), "Crack propagation and the fracture of concrete", Am. Concrete Inst., 58(5), 1961, 591-610.
  12. Karihaloo, B.L. and Nallathambi, P. (1991), Notched Beam Test: Mode I Fracture Toughness, Report of RILEM Technical Committee 89-FMT (Eds. Shah, P. and Carpinteri, A.), Chamman & Hall, London, 1-86.
  13. Kumar, S. and Barai, S.V. (2008a), "Influence of specimen geometry on determination of double-K fracture parameters of concrete: A comparative study", Int. J. Fract., 149, 47-66. https://doi.org/10.1007/s10704-008-9227-1
  14. Kumar, S. and Barai, S.V. (2008b), "Cohesive crack model for the study of nonlinear fracture behaviour of concrete", J. Inst. Engng. (India), 89, 7-15.
  15. Kumar, S. and Barai, S.V. (2009a), "Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function", Eng. Fract. Mech., 76, 935-948. https://doi.org/10.1016/j.engfracmech.2008.12.018
  16. Kumar, S. and Barai, S.V. (2009b), "Influence of loading condition and size-effect on the KR-curve based on the cohesive stress in concrete", Int. J. Fract., 156, 103-110. https://doi.org/10.1007/s10704-009-9349-0
  17. Kumar, S. and Barai, S.V. (2009c), "Effect of softening function on the cohesive crack fracture parameters of concrete CT specimen", Sadhana-Acad. Proc. Eng. Sci., 36(6), 987-1015.
  18. Kumar, S. and Barai, S.V. (2010a), "Determining the double-K fracture parameters for three-point bending notched concrete beams using weight function", Fatigue Fract. Engng. Mater. Struct., 33(10), 645-660. https://doi.org/10.1111/j.1460-2695.2010.01477.x
  19. Kumar, S. and Barai, S.V. (2010b), "Size-effect prediction from the double-K fracture model for notched concrete beam", Int. J. Damage Mech., 19, 473-497. https://doi.org/10.1177/1056789508101187
  20. Kumar, S. and Pandey, S.R. (2012), "Determination of double-K fracture parameters of concrete using splittension cube test", Comp. Concr. An Int. J., 9(1), 1-19. https://doi.org/10.12989/cac.2012.9.1.001
  21. Kwon, S.H., Zhao, Z. and Shah, S.P. (2008), "Effect of specimen size on fracture energy and softening curve of concrete: Part II. Inverse analysis and softening curve", Cement Concrete Res., 38, 1061-1069. https://doi.org/10.1016/j.cemconres.2008.03.014
  22. Murthy, A.R., Iyer N.R. and Prasad B.K.R (2012), "Evaluation of fracture parameters by double-G, double-K models and crack extension resistance for high strength and ultra high strength concrete beams", Comput. Mater. Continua., 31(3), 229-252.
  23. Murakami, Y. (1987), Stress Intensity Factors Hand Book, Committee on Fracture Mechanics, The Society of Materials Science, Japan Vol-1, Pergamon Press, Oxford.
  24. Nallathambi, P. and Karihaloo, B.L. (1986), "Determination of specimen-size independent fracture toughness of plain concrete", Mag. Concrete Res., 38(135), 67-76. https://doi.org/10.1680/macr.1986.38.135.67
  25. Park, K., Paulino, G. H. and Roesler, J.R. (2008), "Determination of the kink point in the bilinear softening model for concrete", Eng. Frac Mech., 7, 3806-3818.
  26. Petersson, P.E. (1981), Crack Growth and Development of Fracture Zone in Plain Concrete and Similar Materials, Report No. TVBM-100, Lund Institute of Technology.
  27. Planas, J. and Elices, M. (1991), "Nonlinear fracture of cohesive material", Int. J. Fract., 51, 139-157.
  28. Reinhardt, H.W., Cornelissen, H.A.W. and Hordijk, D.A. (1986), "Tensile tests and failure analysis of concrete", J. Struct. Eng., ASCE, 112(11), 2462-2477. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:11(2462)
  29. RILEM Draft recommendation (50-FMC) (1985), "Determination of the fracture energy of mortar and concrete by means of three-point bend test on notched beams", Mater. Struct., 18, 285-290. https://doi.org/10.1007/BF02472917
  30. RILEM Draft Recommendations (TC89-FMT) (1990), "Determination of fracture parameters ($K_{Ic}\;^s$ and $CTOD_c$) of plain concrete using three-point bend tests", Mater. Struct., 23(138), 457-460. https://doi.org/10.1007/BF02472029
  31. Roesler J., Paulino, G.H., Park, K. and Gaedicke, C. (2007), "Concrete fracture prediction using bilinear softening", Cement Concrete Compos., 29, 300-312. https://doi.org/10.1016/j.cemconcomp.2006.12.002
  32. Tada, H., Paris, P.C. and Irwin, G. (1985), The Stress Analysis of Cracks Handbook, Paris Productions Incorporated, St. Louis, Missouri, USA.
  33. Xu, S. and Reinhardt, H.W. (1998), "Crack extension resistance and fracture properties of quasi-brittle materials like concrete based on the complete process of fracture", Int. J. Fract. 92, 71-99. https://doi.org/10.1023/A:1007553012684
  34. Xu, S. and Reinhardt, H.W. (1999a), "Determination of double-K criterion for crack propagation in quasibrittle materials, Part I: Experimental investigation of crack propagation", Int. J. Fract., 98, 111-149. https://doi.org/10.1023/A:1018668929989
  35. Xu, S. and Reinhardt, H.W. (1999b), "Determination of double-K criterion for crack propagation in quasibrittle materials, Part II: analytical evaluating and practical measuring methods for three-point bending notched beams", Int. J. Fract., 98, 151-177. https://doi.org/10.1023/A:1018740728458
  36. Xu, S. and Reinhardt, H.W. (1999c), "Determination of double-K criterion for crack propagation in quasibrittle materials, Part III: compact tension specimens and wedge splitting specimens", Int. J. Fract., 98, 179-193. https://doi.org/10.1023/A:1018788611620
  37. Xu, S. and Reinhardt, H.W. (2000), "A simplified method for determining double-K fracture meter parameters for three-point bending tests", Int. J. Fract., 104, 181-209. https://doi.org/10.1023/A:1007676716549
  38. Xu, S. and Zhang, X. (2008), "Determination of fracture parameters for crack propagation in concrete using an energy approach", Engng. Fract. Mech., 75, 4292-4308. https://doi.org/10.1016/j.engfracmech.2008.04.022
  39. Xu, S. and Zhu, Y. (2009), "Experimental determination of fracture parameters for crack propagation in hardening cement paste and mortar", Int. J. Fract., 157, 33-43. https://doi.org/10.1007/s10704-009-9315-x
  40. Zhang, X., Xu, S. and Zheng, S. (2007), "Experimental measurement of double-K fracture parameters of concrete with small-size aggregates", Front. Archit. Civ. Eng. China, 1(4), 448-457. https://doi.org/10.1007/s11709-007-0061-8
  41. Zhang, X. and Xu, S. (2011), "A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis", Eng. Fract. Mech.,78, 2115-2138. https://doi.org/10.1016/j.engfracmech.2011.03.014
  42. Zhao, Y. and Xu, S. (2002), "The influence of span/depth ratio on the double-K fracture parameters of concrete", J China Three Georges Univ. (Nat. Sci.), 24(1), 35-41.
  43. Zhao, Z., Kwon, S.H. and Shah, S.P. (2008), "Effect of specimen size on fracture energy and softening curve of concrete: Part I. Experiments and fracture energy", Cement Concrete Res., 38, 1049-1060. https://doi.org/10.1016/j.cemconres.2008.03.017
  44. Zi. G. and Bazant, Z.P. (2003), "Eignvalue method for computing size effect of cohesive cracks with residual stress, with application to kink-bands in composites", Int. J. Eng. Sci., 41, 1519-1534. https://doi.org/10.1016/S0020-7225(03)00033-8

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