Crack mechanisms in concrete – from micro to macro scale
The paper discusses a fictitious crack model of concrete in tension proposed by Hillerborg. This model presents a concept that illustrates the mechanism of crack initiation and its propagation in concrete on meso-level. It has proven to be a very useful tool for practical use, for both numerical and experimental research. The model was derived from findings on crack mechanisms on more advanced micro- and macro-scale, as presented in this paper. One of the paramount issues regarding crack analysis is the influence of aggregate size on mechanical and fracture parameters of concrete, and also on micro-crack development and associated macro-crack formation. Although significant progress in recognizing crack mechanisms in concrete has been achieved, there are still some aspects that should be studied in depth, for example the role of aggregate particles on crack development. This problem is analysed in the paper as well.
concrete; crack mechanisms; fictitious crack model
Perlman A. B. and Sih G. C., “Elastostatic problems of curvilinear cracks in bonded dissimilar materials”, International Journal of Engineering Science, no. 5 (II), 1967, pp. 845-867.
Willis J. R., “Fracture mechanics of internal cracks”, Journ. Mech. Phys. Solids, no. 19(6), 1971, pp. 353-368.
Vile G. W. D., “The strength of concrete under short-term static biaxial stress”, Proc. Int. Conf. Structure of Concrete. (Eds. A.E. Brooks, K. Newman). Cem. Concr. Assoc., 1968, pp. 275-288.
Shah S. P. and Winter G., “Inelastic behaviour and fracture of concrete”, Journ. Am. Concr. Inst., no. 63(9), 1966, pp. 925-930.
Stroeven P., “Some aspects of the micromechanics of concrete”, PhD Thesis, Delft University of Technology, Delft Univ. Press, 1973.
Stroeven P., “Geometric probability approach to the examination of micro-cracking in plain concrete”, Journal of Materials Science 14, 1979, pp. 1141-1151.
Stroeven P., “Some observations on micro-cracking in concrete subjected to various loading regimes”, Engineering Fracture Mechanics, vol. 35(4/5), 1990, pp. 775-782.
Stroeven P., “Damage mechanisms in fiber reinforced concrete composites“, in Comptes rendus des neuvième journées nationales sur les composites (Eds. J.-P. Favre, A. Vautrin), AMAC, JNC 9 (in French), 1994, pp. 925-938.
Stroeven P. “Damage evolution in compressed concrete”, in: Proceedings of the International Conference on Fracture (Ed. A. Carpinteri), University of Turin, Italy (on CD), 2005.
Stroeven P., 50 years’ focus on concrete – from meter- to nano-scale, Media Center Rotterdam, 2015.
Perry C. and Gillott J. E., “The influence of mortar aggregate bond strength on the behaviour of concrete in compression”, Cement and Concrete Research, vol. 7(5), 1977, pp. 553-564.
Benkemoun N., Khazraji H. A., Poullain P., Choinska M. and Khelidj A., “3-D mesoscale simulation of crack-permeability coupling in the Brazilian splitting test”, International Journal for Numerical and Analytical Methods in Geomechanics, vol. 42(1), 2017, pp. 1-20.
Hillerborg A., Modeer M. and Petersson P. E., “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements”, Cement and Concrete Research, vol. 6, 1976, 773-782.
RILEM Draft Recommendation, Determination of the fracture energy of mortar and concrete by means of three-point bent tests on notched beams, Matériaux et Constructions, vol. 18(106), 1985, pp. 258-290.
Bažant Z. P. and Oh B. H., “Crack Band Theory for Fracture of Concrete”, Matériaux et Constructions, vol. 16(193), 1983, pp. 155-177.
Cedolin L., Poli S. D. and Iori I., “Experimental Determination of the Fracture Process Zone in Concrete”, Cement and Concrete Research, vol. 13, 1983, pp. 557-567.
CEB-FIP Model Code 1990, Bulletins d’information, no. 196.
Kleinschrodt H. D. and Winkler H., “The Influence of the Maximum Aggregate Size and the Size of Specimen on Fracture Mechanics Parameters”, Fracture Toughness and Fracture Energy of Concrete. Ed. by F. H. Wittmann, Elsevier Science Publishers B. V., Amsterdam, 1986, pp. 391-402.
Słowik M., “The analysis of failure in concrete and reinforced concrete beams with different reinforcement ratio”, Archive of Applied Mechanics, vol. 89, 2019, pp. 885-895.
Kwon H., Zhao Z. and Shah S. P., “Effect of specimen size on fracture energy and softening curve of concrete: Part II. Inverse analysis and softening curve”, Cement and Concrete Research, vol. 38 (8-9), 2008, pp. 1061-1069.
Kumar S. and Bara V. S., “Size-effect of fracture parameters for crack propagation in concrete: a comparative study”, Computers and Concrete, vol. 9(1), 2012, pp. 1-19.
Hoover C. G. and Bažant Z. P., “Cohesive Crack, Size Effect, Crack Band and Work-of-Fracture Models Compared to Comprehensive Concrete Fracture Tests”, International Journal of Fracture, vol. 187(1), 2014, pp. 133-143.
Słowik M., “The analysis of Crack Formation in Concrete and Slightly Reinforced Concrete Member in Bending”, in Brittle Matrix Composites 8. Edited by A.M. Brandt, V. C. Li, I. H. Marshall, Woodhead Publishing Limited, Cambridge and Zturek Research-Scientific Institute, Warsaw, 2006, pp. 351-360.
Słowik M. and Błazik-Borowa E., “The Influence of Aggregate Size on the Width of Fracture Process Zone in Concrete Members”, in Brittle Matrix Composites 9, Woodhead Publishing Limited, Cambridge and IFTR, Warsaw, 2009, pp. 429-438.
Słowik M., “Numerical analysis of the width of fracture process zone in concrete beams”, Computational Materials Science, vol. 50, 2011, pp. 1347-1352.
Hu X. Z. and Wittmann F. H., “Fracture energy and fracture process zone”, Materials and Structures, vol. 25, 1992, pp. 319-326.
Bažant Z. P. and Planas, J., Fracture and Size Effect in Concrete and Other Quasibrittle Materials. London: CRC Press, 1998.
Rossello C., Elices M. and Guinea G. V., “Fracture of model concrete: 2. Fracture energy and characteristic length”, Cement and Concrete Research, vol. 36(7), 2006, pp. 1345-1353.
Mechanical Behavior of Concrete, Edited by Torrenti J. M., Pijaudier-Cabot G. and Reynouard J. M., John Wiley & Sons, Inc., 2013, pp. 63-120.
Carloni C., “Analyzing bond characteristics between composites and quasi-brittle substrates in the repair of bridges and other concrete structures”, Advanced Composites in Bridge Construction and Repair, vol. 3, 2014, pp. 61-93.
Zhong H., Li H., Ooi E. T. and Song C., “Hydraulic fracture at the dam-foundation interface using the scaled boundary finite element method coupled with the cohesive crack model”, Engineering Analysis with Boundary Elements, vol. 88, 2018, pp. 41-53. https://doi.org/10.1016/j.enganabound.2017.11.009
Carloni C., Cusatis G., Salviato M., Le J.-L., Hoover C.G. and Bažant Z. P., “Critical comparison of the boundary effect model with cohesive crack model and size effect law”, Engineering Fracture Mechanics, vol. 215, 2019, pp. 193-210. https://doi.org/10.1016/j.engfracmech.2019.04.036
Cornetti P., Muñoz-Reja M., Sapora A. and Carpinteri A., “Finite fracture mechanics and cohesive crack model: Weight functions vs. cohesive laws”, International Journal of Solids and Structures, vol. 156-157, 2019, pp. 126-136. https://doi.org/10.3390/met9050602
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Budownictwo i Architektura supports the open science program. The journal enables Open Access to their publications. Everyone can view, download and forward articles, provided that the terms of the license are respected.
Publishing of articles is possible after submitting a signed statement on the transfer of a license to the Journal.