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A. Spagnoli et alii, Frattura ed Integrità Strutturale, 25 (2013) 94-101; DOI: 10.3221/IGF-ESIS.25.14 101 fatigue crack growth in the Paris regime for concrete seem to be in favour of the present model, in the range of the crack sizes being considered. A CKNOWLEDGEMENTS he authors gratefully acknowledge the financial support of the Italian Ministry of Education, University and Research (MIUR) under the project PRIN 2009 No. 2009Z55NWC_003. R EFERENCES [1] Suresh, S., Fatigue of materials, 2 nd edition, Cambridge University Press, Cambridge, (1998). [2] Kitagawa, H., Yuuki, R., Ohira, T., Crack-morphological aspects in fracture mechanics, Engng Fract. Mech. 7, (1975) 515-529. [3] Bilby, B.A., Cardew, G.E., Howard, I.C., Stress intensity factors at the tips of kinked and forked cracks, In: D.M.R. Taplin (Ed), Fracture 3, Pergamon Press, New York, (1977) 197-200. [4] Lo, K.K., Analysis of branched cracks, J. App. Mech., 45 (1978) 797-802. [5] Cotterell, B., Rice, J.R., Slightly curved or kinked cracks, Int. J. Fract., 16 (1980) 155-169. [6] Suresh, S., Shih, C.F., Plastic near-tip fields for branched cracks, Int. J. Fract., 30 (1986) 237-259. [7] Chen, Y.Z., Stress intensity factors for curved and kinked cracks in plane extension, Theor. and Appl. Fract. Mech., 31 (1999) 223-232. [8] Suresh, S., Crack deflection: implications for the growth of long and short fatigue cracks, Metallurgical Transactions, 14A (1983) 2375-2385. [9] Carpinteri, Al., Scaling laws and renormalization groups for strength and toughness of disordered materials, Int. J. Sol. and Struct., 31 (1994) 291-302. [10] Carpinteri, An., Spagnoli A., Vantadori, S., An approach to size effect in fatigue of metals using fractal theories, Fat. & Fract. Engng Mat. & Struct., 25 (2002) 619-627. [11] Carpinteri, An., Spagnoli, A., A fractal analysis of size effect on fatigue crack growth, Int. J. Fat., 26 (2004) 125-133. [12] Spagnoli, A., Fractality in the threshold condition of fatigue crack growth: an interpretation of the Kitagawa diagram, Chaos, Sol. and Fract., 22 (2004) 589-598. [13] Spagnoli, A., Self-similarity and fractals in the Paris range of fatigue crack growth, Mech. Mat., 37 (2005) 519-529. [14] Carpinteri, An., Spagnoli, A., Vantadori, S., Viappiani, D., Influence of the crack morphology on the fatigue crack growth rate: a continuously-kinked crack model based on fractals, Engng Fract. Mech., 75 (2008) 579-589. [15] Carpinteri An., Spagnoli A., Vantadori S., Size effect in S-N curves: a fractal approach to finite-life fatigue strength, Int. J. Fat. , 31 (2009) 927-933. [16] Carpinteri, An., Spagnoli, A., Vantadori, S., A multifractal analysis of fatigue crack growth and its application to concrete, Engng Fract. Mech., 77 (2010) 974-984. [17] Carpinteri, An., Spagnoli, A., Vantadori, S., Correlating the fractal dimension of a continuously-kinked fatigue crack with some material microstructural features, In: Proceedings of The 13 th International Congress on Mesomechanics Vicenza, Italy, (2011). [18] Barenblatt, G. I., On a model of small fatigue cracks, Engng Fract. Mech., 28 (1987) 623-626. [19] Brighenti, R., Carpinteri, A., Spagnoli, A., Scorza, D., Crack path dependence on inhomogeneities of material microstructure, Frattura ed Integrità Strutturale, 20 (2012) 6-16. [20] Erdogan, F., Sih, G.C., On the crack extension in plates under plane loading and transverse shear, J. Basic Engng., 85 (1963) 519–527. [21] Sih, G.C., Strain-energy-density factor applied to mixed mode crack problems, Int. J. Fract., 10 (1974) 305-321. [22] Tanaka, K, Nakai, Y, Yamashita, M., Fatigue growth threshold of small cracks, Int. J. Fat., 17 (1981) 519–33. [23] Bazant, Z.P., Xu, K., Size effect in fatigue fracture of concrete, ACI Mat. J., 88 (1991) 390-399. [24] Bazant, Z.P., Shell, W.F., Fatigue fracture of high-strength concrete and size effect, ACI Mat. J., 90 (1993) 472-478. T

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