Issue 39

J. Klon et alii, Frattura ed Integrità Strutturale, 39 (2017) 17-28; DOI: 10.3221/IGF-ESIS.39.03 27 C ONCLUSIONS he paper presents a new simple model based on two parameters which has an ambition to describe the quasi- brittle fracture in a way that does not depend on the specimen size, shape and boundary conditions. This approach models the nonlinear fracture process via a separation of the dissipated energy into the amount released for the propagation of the effective crack and the amount dissipated in the volume of FPZ. Parameters of this rather simplified model of quasi-brittle crack growth, namely the resistance to the effective crack propagation (or the fracture energy) G f and the density of energy dissipation in the FPZ H f , are determined based on records of the fracture tests, i.e. from the recorded loading curves, and are regarded as material properties. The model is (partially) validated here by data from experimental campaigns published in the literature, concerning SEN- TPB tests on specimens of different sizes and relative notch lengths. The model parameters were determined in a more or less heuristic way in this study. Thus, a closer connection with methods of evaluation of the FPZ extent using direct experimental imaging techniques (AE, X-ray and similar) is necessary. Own experimental works in this regard are ongoing/in preparation at present. Alternatively, indirect analytical stress-based methods can be applied, which must be connected to test results on material strength. Application of soft-computing optimization methods for this task is also considered for future studies. A CKNOWLEDGEMENT inancial support from the Czech Science Foundation (project No. 15-07210S) and Brno University of Technology, Specific Research programme (project No. FAST-S-16-3475) is gratefully acknowledged. R EFERENCES [1] Karihaloo, B.L., Fracture mechanics and structural concrete, Longman Sci. & Techn., New York (1995). [2] Bažant, Z.P., Planas, J., Fracture and size effect of concrete and other quasi-brittle materials, CRC Press, Boca Raton (1998). [3] Shah, S.P., Swartz, S.E., Ouyang, C., Fracture Mechanics of Concrete: Applications of Fracture Mechanics to Concrete, Rock and Other Quasi-Brittle Materials, Wiley (1995). [4] van Mier, J.G.M., Fracture processes of concrete, CRC Press (1997). [5] Bažant, Z.P., Kazemi, M.T., Size dependence of concrete fracture energy determined by RILEM work-of-fracture method, Int. J. Fract., 51(2) (1991) 121–138. [6] Elices, M., Guinea, G. V., Planas, J., Measurement of the fracture energy using three-point bend tests: part 3– Influence of cutting the P–δ tail, Mater. Struct., 25(6) (1992) 327–334. [7] Hu, X.-Z., Wittmann, F.H., Size effect on toughness induced by crack close to free surface. Engng. Fract. Mech., 65 (2000) 209–221. [8] Trunk, B., Wittmann, F.H., Influence of size on fracture energy of concrete, Mater. Struct, 36 (2001) 260–265. [9] Karihaloo, B.L., Abdalla, H.M., Imjai, T., A simple method for determining the true fracture energy of concrete. Mag. Concr. Res., 55 (2003) 471–481. [10] Duan, K., Hu, X.-Z., Wittmann, F.H., Boundary effect on concrete fracture and non-constant fracture energy distribution, Engng. Fract. Mech., 70 (2003) 2257–2268. [11] Bažant, Z.P., Yu, Q., Size effect in fracture of concrete specimens and structures: new problems and progress, in Li V.C. et al. (eds.), Proc. of the 5th international conference on fracture mechanics of concrete and concrete structures, Vail Colorado, USA, 12–16 April, 2004, 153–162. [12] Hu, X.-Z., Duan, K., Size effect: Influence of proximity of fracture process zone to specimen boundary, Engng. Fract. Mech., 74 (2007) 1093–1100. [13] Yu, Q., Le, J., Hoover, C., Bažant, Z., Problems with Hu-Duan Boundary Effect Model and its comparison to Size- Shape Effect Law for quasi-brittle fracture, J. Eng. Mech., 89 (2010) 40–50. DOI: 10.1061/(ASCE)EM.1943-7889. [14] Cifuentes, H., Alcalde, M., Medina, F., Measuring the size-independent fracture energy of concrete, Strain, 49(1) (2013) 54–59. DOI: 10.1111/str.12012. T F