The overview of fracture mechanics models for concrete

• Autorzy: Akram Amanda

Identyfikatory

DOI

10.21307/ACEE-2021-005

• Języki publikacji: EN

Abstrakty

EN

Fracture mechanics of concrete is a complex matter still thoroughly researched from different angles. It is not an easy task to describe fracture process in concrete, as there are many factors affecting crack development and propagation. Practical applications of fracture mechanics could allow engineers to design concrete structures more effectively and safely. At the minimum, it could help estimate the “safe” period of time left before the unstable, dangerous crack propagation. This utilitarian goal was the reason for many researchers to invent numerous theoretical models in order to describe the crack occurrence better. However, dealing with various analytical problems was not a simple matter and thus existing models of fracture mechanics for concrete have different limitations. Over the years first fracture theories for concrete were reviewed repeatedly. All of these investigations lead to modifications of older models in order to overcome found drawbacks, which proved not to be an easy task. Recently, new approaches to fracture analyses seemed to produce promising results, like universal size effect law (USEL) or modified two parameter fracture model (MTPM) with alternative ways for evaluating fracture parameters. In the paper some of them will be discussed together with other fracture models, starting from some of the very first ones introduced for concrete, like fictitious crack model (FCM) and crack band model (CBM).

Słowa kluczowe

EN

fracture mechanics; fracture of concrete; fracture model; cracking of concrete

PL

mechanika pękania; pękanie betonu; model pękania

• Wydawca: Silesian University of Technology
• Czasopismo: Architecture Civil Engineering Environment
• Rocznik: 2021
• Tom: Vol. 14, no. 1
• Strony: 47--58
• Opis fizyczny: Bibliogr. 54 poz.

Twórcy

autor

Akram Amanda

• MSc Eng.; Department of Structural Engineering; Faculty of Civil Engineering and Architecture; Lublin University of Technology; 40 Nadbystrzycka Street, 20-618 Lublin, Poland

Bibliografia

• [1] Griffith, A. A. (1920). The phenomena of rupture and flow in solids. Philosophical Transactions, Series A, 222, 163-198.
• [2] Irwin, G. R. (1948). Fracture Dynamics. Fracturing of Metals, 147-166.
• [3] Kurumatani, M., Terada, K., Kato, J., Kyoya, T., Kashiyama, K. (2016). An isotropic damage model based on fracture mechanics for concrete. Engineering Fracture Mechanics 155, 49-66.
• [4] Wang, J., Tao, M., Nie, X. (2017). Fracture Energy-based model for average crack spacing of reinforced concrete considering size effect and concrete strength variation. Construction and Building Materials, Volume 148, 398-410.
• [5] Xu, W., Waas, A. M. (2016). Modeling damage growth using the crack band model; effect of different strain measures. Engineering Fracture Mechanics 152, 126-138.
• [6] Xue, J., Kirane, K. (2019). Strength size effect and post-peak softening in textile composites analyzed by cohesive zone and crack band models. Engineering Fracture Mechanics 212, 106-122.
• [7] Zhao, L., Yan, T., Bai, X., Li, T., Cheng, J. (2013). Implementation of Fictitious Crack Model Using Contact Finite Element Method for the Crack Propagation in Concrete under Cyclic Load. Mathematical Problems in Engineering, vol. 2013, ID 726317.
• [8] Hilleborg, A., Modeer, M., Petersson, P. E. (1976). Analysis of Crack Formation and Crack Growth in Concrete by Means of Fract. Mech. and Finite Elements. Cement and Concrete Research, 6(6), 773-791.
• [9] Słowik, M. , Stroeven, P., Akram, A. (2020). Crack mechanisms in concrete - from micro to macro scale. Budownictwo i Architektura, 19(4), 53-66.
• [10] Bažant, Z.P., Oh, B.H. (1983). Crack band theory for fracture of concrete. Matériaux et Construction, 16, 155-177.
• [11] Bažant, Z.P. (editor) (1992). Fracture Mechanics of Concrete Structures. Elsevier Applied Science, London and New York, FraMCoS1.
• [12] Golewski, G. L. (2007). Analysis influence of Dmax on fracture mechanics parameters of concrete made of limestone aggregate at three point bending. Budownictwo i Architektura, 1, 5-16.
• [13] Mihashi, H., Nomura, N., Niiseki, S. (1991). Influence of aggregate size on fracture process zone of concrete detected with three dimensional acoustic emission technique. Cement and Concrete Research, 21(5), 737-744.
• [14] Woliński, S.,Hordijk, D. A., Reinhardt, H. W., Cornelissen, H. A.W. (1987). Influence of aggregate size on fracture mechanics parameters of concrete. International Journal of Cement Composites and Lightweight Concrete, 9(2), 95-103.
• [15] Woliński, S. (1991). Tensile behaviour of concrete and their applications in nonlinear fracture mechanics of concrete. Scientific Works of Rzeszow University of Technology, 15.
• [16] Słowik, M., Błazik-Borowa, E. (2011). Numerical study of fracture process zone width in concrete members. Architecture Civil Engineering Environment, 4(2), 73-78.
• [17] Wang, X., Saifullah, H.A., Nishikawa, H., Nakarai, K. (2020). Effect of water-cement ratio, aggregate type, and curing temperature on the fracture energy of concrete. Construction and Building Materials, 259, 119646.
• [18] Bažant, Z.P., Pfeiffer, P. A. (1987). Determination of Fracture Energy from Size Effect and Brittleness Number. ACI Materials Journal, 84(6), 463-480.
• [19] Bažant, Z. P. (2001). Concrete fracture models: Testing and practice. Engineering Fracture Mechanics, 69(2), 165-205.
• [20] Jenq, Y., Shah, S. P. (1985). Two parameter fracture model for concrete. Journal of Engineering Mechanics, 111(10), 1227-1241. https://doi.org/10.1061/(ASCE) 0733-9399(1985)111:10(1227).
• [21] Ince, R., Alyamaç, K. E. (2008). Determination of fracture parameters of concrete based on watercement ratio. Indian Journal of Engineering & Materials Sciences, 15, 14-22.
• [22] Karamloo, M., Mazloom, M., Payganeh, G. (2016). Influences of water to cement ratio on brittleness and fracture parameters of self-compacting lightweight concrete. Engineering Fracture Mechanics, 168, part A, 227-241.
• [23] Bharatkumar, B. H., Raghuprasad, B. K., Ramachandramurthy, D. S., Narayanan, R. , Gopalakrishnan, S. (2005). Effect of fly ash and slag on the fracture characteristics of high performance concrete. Materials and Structures volume, 38, 63-72.
• [24] Sundara, K.T., Iyengar, R., Raviraj, S., VenkateswaraGupta, A. (1995). Graphical method to determine the parameters of the two-parameter fracture model for concrete. Engineering Fracture Mechanics, 51(5), 851-859.
• [25] Jansen, D. C., Weiss, W. J., Schleuchardt, S. H. F. (2000). Modified Testing Procedure for the Two Parameter Fracture Model for Concrete. The Proceedings of the 14th Engineering Mechanics Conference (EM2000): Austin, TX.
• [26] Carpinteri, A., Berto, F., Fortese, G., Ronchei, C., Scorza, D., Vantadori, S. (2017). Modified two-parameter fracture model for bone. Engineering Fracture Mechanics, 174, 44-53.
• [27] Carpinteri, A., Fortese, G., Ronchei, C.,Scorza, D., Vantadori, S. (2017). Mode I fracture toughness of fibre reinforced concrete. Theoretical and Applied Fracture Mechanics, 91, 66-75.
• [28] Xu, Sh., Reinhardt, H. W. (1999). Determination of double-K criterion for crack propagation in quasibrittle fracture, Part I: Experimental investigation of crack propagation. International Journal of Fracture, 98, 111-149.
• [29] Neimitz, A. (1998). Fracture Mechanics. PWN, Warszawa.
• [30] Xu, S., Reinhardt, H. W. (1999). Determination of double-K criterion for crack propagation in quasibrittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams. International Journal of Fracture, 98, 151-177.
• [31] Xu, S., Reinhardt, H. W. (1999). Determination of double-K criterion for crack propagation in quasibrittle fracture, Part III: Compact tension specimens and wedge splitting specimens. International Journal of Fracture, 98, 179-193.
• [32] Wang, B., Dai, J.G., Zhang, X.F., Xu, S.L. (2010). Experimental study on the double-k fracture parameters and brittleness of concrete with different strengths. Fracture Mechanics of Concrete and Concrete Structures - Assessment, Durability, Monitoring and Retrofitting of Concrete Structures - B. H. Oh, et al. (eds), Korea Concrete Institute, 703-708.
• [33] Kumar, S. ,Pandey, S. R., Srivastava, A.K.L. (2014). Determination of double-K fracture parameters of concrete using peak load method. Engineering Fracture Mechanics, 131, 471-484.
• [34] Kumar, S., Pandey, S. R.,Srivastava, A.K.L. (2013). Analytical methods for determination of double-K fracture parameters of concrete. Advances in Concrete Construction, 1(4), 319-340. DOI: http://dx.doi.org/10.12989/acc2013.1.4.319
• [35] Qing, L. B., Nie, Y. T., Wang, J., Hu,Y. (2017). A simplified extreme method for determining double-K fracture parameters of concrete using experimental peak load. Fatigue & Fracture of Engineering Materials & Structures 40(2), 254-266.
• [36] Qing, L. B., Nie, Y. T.(2020). The relationship between double-K parameters of concrete based on fracture extreme theory. Journal of Theoretical and Applied Mechanics, 58(1), 59-71.
• [37] Kumar, S., Barai, S.V. (2012). Size-effect of fracture parameters for crack propagation in concrete: a comparative study. Computers and Concrete, 9(1), 1-19.
• [38] Walraven, J.C. (2007). Fracture mechanics of concrete and its role in explaining structural behaviour. Fracture Mechanics of Concrete and Concrete Structures (FRAMCOS 6), 1265-1275.
• [39] Tang, T., Ouyang, C., Libardi, W., Shah, S.P. (1995). Determination of K Ics and CTOD c from peak loads and relationship between two-parameter fracture model and size effect model. Fracture Mechanics of Concrete Structures, 3 (Edited by F.H. Wittmann), 135-144.
• [40] Bhowmik, S., Ray, S. (2019). An experimental approach for characterization of fracture process zone in concrete. Engineering Fracture Mechanics, 211, 401-419.
• [41] Bažant, Z.P., Kazemi, M.T. (1991). Size dependence of concrete fracture energy determined by RILEM work-of-fracture method. Int. J.Fract., 51, 121-138.
• [42] Bažant, Z.P., Pfeiffer, P. A. (1987). Determination of Fracture Energy from Size Effect and Brittleness Number. ACI Materials Journal, 84(6), 463-480.
• [43] Hoover, C.G., Bažant, Z.P. (2014). Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests. Int J Fract 187, 133-143. https://doi.org/10.1007/s10704-013-9926-0
• [44] Carpinteri, A. (1992). Applications of Fracture Mechanics to Reinforced Concrete.CRC Press.
• [45] Cifuentes, H., Alcalde, M., Medina, F. (2013). Comparison of the Size-Independent Fracture Energy of Concrete obtained by Two Test Methods. In van Mier et al. (Eds). Proceedings of 8th International Conference on Fractur Mechanics of Concrete and ConcreteStructures (FraMCoS-8), 1-8.
• [46] Gustafsson, P. J., Hillerborg, A. (1988). Sensitivity in Shear Strength of Longitudinally Reinforced Concrete Beams to Fracture Energy of Concrete. Structural Journal, 85(3), 286-294.
• [47] Weibull, W. (1951). A Statistical Distribution Function of Wide Applicability. ASME Journal of Applied Mechanics, 18, 293-297.
• [48] Duan, K., Hu, X. Z., Wittmann, F. H. (2006). Scaling of quasi-brittle fracture: Boundary and size effect. Mech. Mater., 38, 128-141.
• [49] Hu, X. Z. (2002). An asymptotic approach to size effect on fracture toughness and fracture energy of composites. Engineering Fracture Mechanics, 69(5), 555-564.
• [50] Hoover, C. G., Bažant, Z. P. (2014). Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests. Journal of Engineering Mechanics, 140(3), 473-479.
• [51] Carpinteri, A., Chiaia, B., Ferro, G. (1995). Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder. Materials and Structures, 28, 311-317.
• [52] Carpinteri, A., Chiaia, B. (1997). Multifractal scaling laws in the breaking behaviour of disordered materials. Chaos, Solitons & Fractals, 8(2), 135-150.
• [53] Duan, K., Hu, X., Wittmann, F.H. (2003). Boundary effect on concrete fracture and non-constant fracture energy distribution. Engineering Fracture Mechanics, 70(16), 2257-2268.
• [54] Duan, K., Hu, X. (2004). Asymptotic analysis of boundary effect on strength of concrete. Conference: FraMCos-5, vol.1.