13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- • The presented procedure results in a simple two parameter description of the effective fracture resistance of quasibrittle materials. • The procedure describes the effect of initial crack length on the maximum load values. • The procedure enables the construction of the load-displacement dependence up to maximum load. • The procedure enables a simple classification of the materials fracture process zone evolution. • The procedure can be used in the context of the so called double-K criterion to describe the effective initiation toughness value. • The procedure can be used to examine constraint effects on the materials fracture process zone evolution. • In the future, the procedure may be used to assist damage mechanics type modeling of the failure of quasi-brittle materials. Acknowledgements This work has been part of the FAR project belonging to the SAFIR 2014 research program funded by VTT and by the State Nuclear Waste Management Fund (VYR), as well as other key organizations. The present work is connected to the quantification of constraint effects in brittle and quasi-brittle materials. References [1] C. Le Bellégo, J.F. Dubé, G. Pijaudier-Cabot, B. Gérard, Calibration of nonlocal damage model from size effect tests. European Journal of Mechanics A/Solids, 22 (2003) 33–46. [2] S. Kumar, S.V. Barai, Concrete fracture models and applications, Springer-Verlag, Berlin Heidelberg, 2011. [3] G.R. Irwin, Plastic zone near a crack and fracture toughness. Sagamore Research Conference Proceedings, Vol. 4, 1961. [4] S. Xu, H.W. Reinhardt, Determination of double-K criterion for crack propagation in quasibrittle materials, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams. Int. J. Fract., 98 (1999) 151–77. [5] ASTM E561–10, Standard Test Method for K-R Curve Determination. Annual book of standards, Volume 03.01. ASTM International West Conshohocken, PA, 2011. [6] Z.P. Bažant, J. Planas, Fracture and size effect in concrete and other quasibrittle materials, CRC Press, Florida, 1998. [7] Z.P. Bažant, P.A. Pfeiffer, Determination of fracture energy from size effect and brittleness number. ACI Materials Journal, 84 (1987) 463–80. [8] K.R.W. Wallin, Critical assessment of the standard ASTM E 399. J. ASTM Int., 2, (2005). [9] K.R.W. Wallin, Fracture toughness of engineering materials - estimation and application, EMAS Publishing, Warrington UK, 2011. [10] B.L. Karihaloo, P. Nallathambi, Fracture toughness of plain concrete from three-point bend specimens. Materials and Structures/Matériaux et Constructions, 22, (1989). 85–93. [11] T.M.E. Refai, S.E. Swartz, Fracture behavior of concrete beams in three-point bending considering the influence of size effects, Report No. 190, Engineering Experiment Station, Kansas State University; 1987. [12] C.G. Go, S.E. Swartz, Energy methods for fracture-toughness determination in concrete. Exp. Mech., 26, (1986), 292–6. [13] Z.P. Bažant, R. Gettu, M.T. Kazemi, Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 28, (1991) 43–51. [14] Z. Wu, S. Yang, X. Hu, J. Zheng, An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams, Engng. Frac. Mech., 73, (2006),
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