Evaluation of the Strain-Softening Law of Concrete from the Fracture Test

Abstract:

This paper proposes a method for evaluating the linear stress-strain curve and bilinear stress-COD curve, suggested by Petersson, which can describe the tensile fracture behaviour of ordinary concrete satisfactorily. The two curves can be evaluated once modulus of elasticity (E), tensile strength (f_t) and fracture energy (G_F) are determined. It is proposed that the same fracture energy test suggested in the RILEM Recommendation be used to evaluate E, f_t and G_F. Firstly, the fracture energy was as usual evaluated from the area under the load-deflection curve. Secondly, the modulus of elasticity was calculated from the initial compliance in the same curve. Finally, the tensile strength was derived from the peak load. The proposed method was verified using some experimental data available in literature. The calculated values of the modulus of elasticity and the tensile strength were in good agreement with the corresponding experimental data. The method seems to provide a simple and practical way of evaluating the stress-strain and strain-softening curves of ordinary concrete, though further assessment is needed.

• Periodical: Advanced Materials Research (Volumes 535-537)
• Pages: 1868-1876
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.535-537.1868
• Online since: June 2012
• Authors: Wai Ching Tang, Hong Zhi Cui
• Keywords: Fictitious Crack Model, Fracture Energy, Modulus of Elasticity, Tensile Strength

References

[1] A.Hillerborg, M. Modeer. and P. E., Petersson Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite element, Cement and Concrete Research, vol.6 (1976), pp.773-781.

DOI: 10.1016/0008-8846(76)90007-7

[2] Z. P. Bazantand and B. H. Oh, Crack band theory for fracture of concrete, Material Structures, vol. 16 (1983), pp.155-177.

[3] L. Elfgren, Fracture Mechanics of Concrete Structures: from Theory to Applications, eport RILEM, FMA-90, Chapman and Hall, LTK (1989).

[4] A. Carpinteri, Application of fracture mechanics to reinforced concrete, Taylor & Francis (2007).

[5] J. Isenberg, Finite Element Analysis of Reinforced Concrete Structures II, American Society of Civil Engineers, New York, USA (1993).

[6] P. E. Petersson, Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials, Ph.D. Thesis, TVBM- 1006, Lund University, Sweden (1981).

[7] D. A. Hordijk, J. G. M. Van Mier, and H. W. Reinhardt, Fracture mechanics parameters of concrete from uni-axial tensile tests as influenced by specimen length, in 'Proceedings of the SEM- RILEM Int. Conf. on Fracture of Concrete and Rock', edited by S. P. Shah and S. E. Swartz, Houston, USA (1989), pp.138-149.

DOI: 10.1007/978-1-4612-3578-1_13

[8] J. G. Rots, and R. Borst, Analysis of concrete fracture in "direct" tension', International Journal of Solids and Structures, vol. 25(12) (1989), pp.1381-1394.

DOI: 10.1016/0020-7683(89)90107-8

[9] F. P. Zhou, Some Aspects of Tensile Fracture Behaviour and Structural Response of Cementitious Materials, Licentiate thesis, TVBM-1008, Lund University, Sweden, (1988).

[11] J. G. M. van Mier, Fracture Process of Concrete: Assessment of Materials Parameters for Fracture Models', CRC Press (1997).

[12] RILEM Draft Recommendation, Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams,' Materials Structures, vol. 18 (1985), pp.185-290.

DOI: 10.1007/bf02498757

[13] V. C. Li, C.M. Chan, and C. K. Y. Leung, Experimental determination of the tension-softening relations for cementitious composites', Cement and Concrete Research, vol. 17 (1987), pp.441-452.

DOI: 10.1016/0008-8846(87)90008-1

[14] F. H. Wittman, K. Rokugo, E. Bruhwiler, H. Mihashi, and P. Simoni, Fracture energy and strain softening of concrete as determined by means of compact tension specimens, Materials Structures, vol. 21 (1988), pp.21-32.

DOI: 10.1007/bf02472525

[15] P. E. Roelfstra, and F. H. Wittmann, numerical method to link strain softening with failure of concrete, in Fracture Toughness and Fracture Energy, edited by F. H. Wittmam, Elsevier, London (1986) pp.163-174.

[16] G. V. Guinea, J. Planas, and M. Elices, A general bilinear fit for the softening curve of concrete, Materials Structures, vol. 27 (1994), pp.99-105.

DOI: 10.1007/bf02472827

[17] D. A. Hordijk, Local approach to fatigue of concrete, Ph.D. thesis, Delft University of Technology, The Netherlands (1991).

[18] G. V. Guinea, J. Planas and M. Elices, Measurement of the fracture energy using three-point bend tests: Part 1- Influence of experimental procedures', Materials Structures, vol. 25 (1992) 212-218.

DOI: 10.1007/bf02473065

[19] Planas, J.. Elices, M. and Guinea, G. V., 'Measurement of the fracture energy using three-point bend tests: Part 2 - Influence of bulk energy dissipation', Materials Structures, vol. 25 (1992) 305-312.

DOI: 10.1007/bf02472671

[20] Zhou, F.P. and Balendran, R. V. Size effect on flexural, splitting tensile, and torsional strengths of high strength concrete, Cement and Concrete Research, vol. 28 (12) (1998), pp.1725-1736.

DOI: 10.1016/s0008-8846(98)00157-4

[21] A. M. Neville, Properties of concrete, 4th edition, Prentice Hall, England (2002).

[22] RILEM Draft Recommendation, TC 89-FMT fracture mechanics of concrete-test methods, Materials Structures, vol. 23 (1990), pp.457-460.

[23] B. L. Karihaloo, and P. Nallathambi, Notched beam test: mode I fracture toughness, in Fracture Mechanics Test Methods for Concrete, RILEM Report 5, edited by S. P. Shah and A. Carpinteri, Chapman and Hall, UK (1991) pp.1-86.

DOI: 10.1201/9781482267532-8

[24] S. P. Timoshenko, and J. N.Goodier, Theory of elasticity, McGraw-Hill (1970).

[25] H. Tada, P.C. Paris. and G. R. Irwin, The Stress Analysis of Crack Handbook, (Pel Research Corp, Hellertown (1975).

[26] A. Hillerborg, Application of fracture mechanics to concrete, TVBM-3030, Lund University, Sweden (1988).

[27] Z. P. Bazant, Fracture energy of heterogeneous materials and similitude, in SEMMLEM Int. Conference on Fracture of Concrete and Rock, edited by S. P. Shah and S. E. Swartz. (Martinus Nijhoff Publishers, USA (1987), pp.229-238.

[28] J. Planas, and M. Elices, Towards a measure of GF: an analysis of experimental results. In Fracture Toughness and Fracture Energy of Concrete, edited by F. H. Wittmam, Elsevier Science Publishers (1986), pp.38-390.

[29] W.C. Tang, T.Y. Lo and W K. Chan, Fracture Properties of Normal and Lightweight High Strength Concrete, Magazine of Concrete Research, Vol. 60(4) (2008), pp.237-244.

DOI: 10.1680/macr.2008.60.4.237

[30] M. Modeer, A Fracture Mechanics Approach to the Failure Analysis of Concrete Materials, Ph.D. Thesis, TVBM-1001. Lund University. Sweden (1979).