The effect of crack rate on the tensile stress–crack width relation of fibre reinforced concrete is studied experimentally, using the three-point bending test, where the post-peak flexural response of the material is determined over a range of loading rates covering 5 orders of magnitude. The tetralinear stress–crack opening (σ–w) relations are subsequently obtained from inverse analyses. Concretes with hooked-ended steel fibres at different dosages and with polypropylene fibres have been studied. The results show that the tensile strength is reduced and the initial drop in cohesive stresses is less steep at slower loading rates, with the changes being more significant in concretes with lower toughness. Numerical analysis shows that the fracture process zone at crack initiation extends further as the loading becomes slower. The variation in the σ–w relation with crack rate has been modelled empirically based on the rate-dependence of the concrete matrix and the tensile strength of the FRC. The general variation of flexural toughness with the loading rate has also been identified, reflecting the moderating influence due to steel fibres, especially at higher dosages.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Soufeiani L, Raman SN, Bin Jumaat MZ, Alengaram UJ, Ghadyani G, Mendis P (2016) Influences of the volume fraction and shape of steel fibers on fiber-reinforced concrete subjected to dynamic loading—a review. Eng Struct 124:405–417. https://doi.org/10.1016/j.engstruct.2016.06.029
Naaman AE, Gopalaratnam VS (1983) Impact properties of steel fibre reinforced concrete in bending. Int J Cem Compos Light Concr 5:225–233. https://doi.org/10.1016/0262-5075(83)90064-7
Bažant ZP, Gettu R (1992) Rate effects and load relaxation in static fracture of concrete. ACI Mater J 89:457–468
Rosa AL, Yu RC, Ruiz G, Saucedo L, Sousa JLAO (2012) A loading rate dependent cohesive model for concrete fracture. Eng Fract Mech 82:195–208. https://doi.org/10.1016/j.engfracmech.2011.12.013
Mechtcherine V (2009) Fracture mechanical behavior of concrete and the condition of its fracture surface. Cem Concr Res 39:620–628. https://doi.org/10.1016/j.cemconres.2009.03.011
Banthia N (1990) A study of some factors affecting the fiber-matrix bond in steel fiber reinforced concrete. Can J Civ Eng 17:610–620. https://doi.org/10.1016/j.cemconres.2014.05.008
Babafemi AJ, Boshoff WP (2017) Pull-out response of macro synthetic fibre from concrete matrix: effect of loading rate and embedment length. Constr Build Mater 135:590–599. https://doi.org/10.1016/j.conbuildmat.2016.12.160
Nieuwoudt PD, Boshoff WP (2017) Time-dependent pull-out behaviour of hooked-end steel fibres in concrete. Cem Concr Compos 79:133–147. https://doi.org/10.1016/j.cemconcomp.2017.02.006
Babafemi AJ, du Plessis A, Boshoff WP (2018) Pull-out creep mechanism of synthetic macro fibres under a sustained load. Constr Build Mater 174:466–473. https://doi.org/10.1016/j.conbuildmat.2018.04.148
Zhang XX, Abd Elazim AM, Ruiz G, Yu RC (2014) Fracture behaviour of steel fibre-reinforced concrete at a wide range of loading rates. Int J Impact Eng 71:89–96. https://doi.org/10.1016/j.ijimpeng.2014.04.009
Meng W, Yao Y, Mobasher B, Khayat KH (2017) Effects of loading rate and notch-to-depth ratio of notched beams on flexural performance of ultra-high-performance concrete. Cem Concr Compos 83:349–359. https://doi.org/10.1016/j.cemconcomp.2017.07.026
Bernad C, Gettu R, Barragan BE, Antunes JL (2002) Study of the effect of loading rate and relaxation on the behaviour of steel fibre reinforced concrete. In: Report of tests performed within sub-task 5.2 creep in the post- cracked region: Brite Project (BRPR.CT98.0813)
Sousa JLAO, Gettu R (2006) Determining the tensile stress–crack opening curve of concrete by inverse analysis. J Eng Mech 132:141–148. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:2(141)
Olesen JF (2001) Fictitious crack propagation in fibre reinforced concrete beams. J Eng Mech 127:272–280
Stephen SJ, Raphael B, Gettu R, Jose S (2019) Determination of the tensile constitutive relations of fiber reinforced concrete using inverse analysis. Constr Build Mater 195:405–414. https://doi.org/10.1016/j.conbuildmat.2018.11.014
EN 14651 (2005) Test method for metallic fibre concrete-Measuring the flexural tensile strength (limit of proportionality (LOF), residual). European Standards, Brussels
Raphael B, Smith IFC (2003) A direct stochastic algorithm for global search. Appl Math Comput 146:729–758. https://doi.org/10.1016/S0096-3003(02)00629-X
dos Santos FLG, Sousa JLAO (2015) Determination of parameters of a viscous-cohesive fracture model by inverse analysis. IBRACON Struct Mater J 8:669–706. https://doi.org/10.1590/S1983-41952015000500007
Nayar SK (2015) Design of fibre reinforced concrete slabs-on-grade and pavements, Ph.D. thesis, Department of Civil Engineering, Indian Institute of Technology Madras, Chennai
ACI Committee 544.7R (2016) Report on design and construction of fiber-reinforced precast concrete tunnel segments. American Concrete Institute, Farmington Hills
Stephen SJ, Gettu R, Ferreira LET, Jose S (2018) Assessment of the toughness of fibre-reinforced concrete using the R-curve approach. Sādhanā. https://doi.org/10.1007/s12046-018-0838-6
The authors are grateful to Prof. Benny Raphael for programming the optimization algorithm for the inverse analysis. The first author is thankful to the Ministry of Human Resource Development (MHRD), Govt. of India, for providing an assistantship during her doctoral studies. The FIST Grant SR/FST/ETII-054/2012 from DST, Govt. of India, is acknowledged for the experimental work performed in the Laboratory for Mechanical Performance of Civil Engineering Materials, IIT Madras. M/s Bekaert and W.R. Grace provided the fibers used in this study.
Conflict of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
About this article
Cite this article
Stephen, S.J., Gettu, R. Rate-dependence of the tensile behaviour of fibre reinforced concrete in the quasi-static regime. Mater Struct 52, 107 (2019). https://doi.org/10.1617/s11527-019-1405-2
- Loading rate effect
- Inverse analysis
- σ–w curve
- Fracture process zone
- Fibre reinforced concrete