Browse > Article
http://dx.doi.org/10.12989/cac.2015.15.2.199

Influence of softening curves on the residual fracture toughness of post-fire normal-strength concrete  

Yu, Kequan (College of civil engineering, Tongji University)
Lu, Zhoudao (College of civil engineering, Tongji University)
Publication Information
Computers and Concrete / v.15, no.2, 2015 , pp. 199-213 More about this Journal
Abstract
The residual fracture toughness of post-fire normal-strength concrete subjected up to $600^{\circ}C$ is considered by the wedge splitting test. The initial fracture toughness $K_I^{ini}$ and the critical fracture toughness $K_I^{un}$ could be calculated experimentally. Their difference is donated as the cohesive fracture toughness $K_I^c$ which is caused by the distribution of cohesive stress on the fracture process zone. A comparative study on determining the residual fracture toughness associated with three bi-linear functions of the cohesive stress distribution, i.e. Peterson's softening curve, CEB-FIP Model 1990 softening curve and Xu's softening curve, using an analytical method is presented. It shows that different softening curves have no significant influence on the fracture toughness. Meanwhile, comparisons between the experimental and the analytical calculated critical fracture toughness values further prove the validation of the double-K fracture model to the post-fire concrete specimens.
Keywords
post-fire; fracture toughness; bi-linear; softening curve; double-K fracture model;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Baker, G. (1996), "The effect of exposure to elevated temperatures on the fracture energy of plain concrete", RILEM Mater. Struct., 29(6), 383-388.   DOI
2 Bazant, Z.P. and Oh, B.H. (1983), "Crack band theory for fracture of concrete", RILEM Mater Struct, 16(93), 155-177.
3 Bazant, Z.P. and Prat, P.C. (1988), "Effect of temperatures and humidity on fracture energy of concrete", ACI Mater. J., 85(4), 262-271.
4 Bazant, Z.P. and Kazemi, M.T. (1990), "Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete", Int. J. Fract., 44(2), 111-131.   DOI
5 Bretschneider, N., Slowik, V., Villmann, B. and Mechtcherine, V. (2011), "Boundary effect on the softening curve of concrete", Eng. Fract. Mech., 78(17), 2896-2906.   DOI
6 Bueckner, H.F. (1970), "A novel principle for the computation of stress intensity factors", Z. Angew. Math. Mech., 50(2), 529-546.
7 Bulletin D' Information (1993), CEB-Comite Euro-international du Beton-CEB-FIP Model Code 1990, Lausanne.
8 Chen, H.H. and Su, R.K.L. (2013), "Tension softening curves of plain concrete", Constr. Build. Mater., 44(7), 440-451.   DOI
9 Glinka, G. and Shen, G. (1991). "Universal features of weight functions for cracks in Mode I", Eng. Fract. Mech., 40(6), 1135-1146.   DOI
10 Gopalaratnam, V.S. and Shah, S.P. (1985), "Softening response of plain concrete in direct tension", ACI Mater. J., 82(3), 310-323.
11 Hillerboerg, A., Modeer, M. and Peterson P.E. (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6(6), 773-782.   DOI
12 Hilsdorf, H.K. and Brameshuber, W. (1991), Current Trends in Concrete Fracture Research. Springer, Netherlands.
13 Hisham, A.F. and Sameer, A.H. (1997), "Variation of the fracture toughness of concrete with temperature", Constr. Build. Mater., 11(2), 105-108.   DOI
14 Jenq, Y.S. and Shah, S.P. (1985a), "Two parameter fracture model for concrete", J Eng Mech, ASCE, 111(10), 1227-1241.   DOI
15 Jenq, Y.S. and Shah, S.P. (1985b), "A fracture toughness criterion for concrete", Eng. Fract. Mech., 21(5), 1055-1069.   DOI
16 Kumar, S. and Barai, S.V. (2012), "Size-effect of fracture parameters for crack propagation in concrete: a comparative study", Comput. Concr., 9(1), 1-19.   DOI   ScienceOn
17 Kumar, S. and Barai, S.V. (2010), "Determining the double-K fracture parameters for three-point bending notched concrete beams using weight function", Fatigue Fract. Eng. Mater Struct, 33(10), 645-660.   DOI
18 Kumar, S. and Barai, S.V. (2009), "Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function", Eng. Fract. Mech., 76(7), 935-946.   DOI
19 Kumar, S. and Barai, S.V. (2008a), "Influence of specimen geometry and size-effect on the $K_R$-curve based on the cohesive stress in concrete", Int. J. Fract., 152(2), 127-148.   DOI
20 Kumar, S. and Barai, S.V. (2008b), "Influence of specimen geometry on determination of double-K fracture parameters of concrete: a comparative study", Int. J. Fract, 149(1), 47-66.   DOI
21 Kwon, S.H., Zhao, Z.F. 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(8), 1061-1069.   DOI
22 Nallathambi, P. and Karihaloo, B.L. (1986), "Determination of specimen-size independent fracture toughness of plain concrete", Mag. Concr. Res., 38(135), 67-76.   DOI
23 Nielsen, C.V. and Bicanic, N. (2003), "Residual fracture energy of high-performance and normal concrete subject to high temperatures", RILEM Mater. Struct., 36(8), 515-521.   DOI
24 Petersson, P.E. (1981), Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials, Division of Building Materials, Lund Institute of Technology, Report TVBM-1006, Sweden.
25 Park, K., Paulino, H.G. and Roesler, J.R. (2008), "Determination of the kink point in the bilinear softening model for concrete", Eng. Fract. Mech., 75(13), 3806-3818.   DOI
26 Phillips, D.V. and Zhang, Z. (1993), "Direct tension tests on notched and un-notched plain concrete specimens", Mag. Concr. Res., 45(162), 25-35.   DOI
27 Prokopski, G. (1995), "Fracture toughness of concretes at high temperature", J Mater. Sci., 30(6), 1609-1612.   DOI
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.   DOI
29 Roesler, J., Paulino, G.H., Park, K. and Gaedicke, C. (2007), "Concrete fracture prediction using bilinear softening", Cement Concrete Compos., 29(4), 300-312.   DOI
30 Tada, H., Paris, P.C. and Irwin, G. (1985), The stress analysis of cracks handbook. Paris Productions Incorporated, St. Louis, Paris, France.
31 Xu, S. and Reinhardt, H.W. (1999a), "Determination of double-K criterion for crack propagation in quasi-brittle materials, Part I: Experimental investigation of crack propagation", Int. J. Fract., 98(2), 111-149.   DOI
32 Xu. S and Reinhardt, H.W. (1999b), "Determination of double-K criterion for crack propagation in quasi-brittle materials, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams", Int. J. Fract, 98(2), 151-177.   DOI
33 Xu, S. and Reinhardt, H.W. (1999c), "Determination of double-K criterion for crack propagation in quasi-brittle materials, Part III: Compact tension specimens and wedge splitting specimens", Int. J. Fract., 98(2), 179-193.   DOI
34 Yu, J.T., Yu, K.Q. and Lu, Z.D. (2012), "Residual fracture properties of concrete subjected to elevated temperatures", RILEM Mater. Struct., 45 (8), 1155-1165.   DOI
35 Yu, K.Q. and Lu, Z.D. (2014), "Determining residual double-K fracture toughness of post-fire concrete using analytical and weight function method", RILEM Mater. Struct., 47(5), 839-852.   DOI   ScienceOn
36 Zhang, B., Bicanic, N., Pearce, C.J. and Balabanic, G. (2000), "Residual fracture properties of normal and high-strength concrete subject to elevated temperatures", Mag. Concr. Res., 52(2), 123-136.   DOI
37 Zhang, B. and Bicanic, N. (2006), "Fracture energy of high-performance concrete at high temperatures up to $450^{\circ}C$: the effects of heating temperatures and testing situations (hot and cold)", Mag. Concr. Res., 58(5), 277-288.   DOI
38 Zhang, B., Bicanic, N., Pearce, C.J. and Balabanic, G. (2000), "Assessment of toughness of concrete subjected to elevated temperatures from complete load-displacement curve- Part II: Experimental Investigation", ACI Mater., 97(5), 556-566.
39 Zhang, B., Bicanic, N., Pearce, C.J. and Phillips, D.V. (2002), "Relationship between brittleness and moisture loss of concrete exposed to high temperatures", Cement Concrete Res., 32(3), 363-371.   DOI
40 Zhang, B., Bicanic, N., Pearce, C.J. and Balabanic, G. (2000), "Assessment of toughness of concrete subjected to elevated temperatures from complete load-displacement curve- Part I: General introduction", ACI Mater., 97(5), 550-555.