Issue 33

C. Bagni et alii, Frattura ed Integrità Strutturale, 33 (2015) 105-110; DOI: 10.3221/IGF-ESIS.33.14 110 inter-aggregate distance resulted in highly accurate estimates. Owing to the fact that the two batches of concrete were characterised by the same morphology, this remarkable accuracy strongly supports the idea that length scale parameter l in constitutive law (1) is capable of directly incorporating into the stress analysis the underlying material microstructural features. C ONCLUSIONS  GE applied along with the TCD was seen to result in conservative estimates with the level of conservatism decreasing as the sharpness of the notch decreases.  The use of GE with length scale parameter l equal to the average inter-aggregate distance resulted in highly accurate estimates for the fatigue strength. R EFERENCES [1] Von Ornum, J.L., Fatigue of cement products, ASCE Trans., 51 (1903) 443-451. [2] Von Ornum, J.L., Fatigue of concrete, ASCE Trans., 58 (1907) 294-320. [3] Ohlsson, U., Daerga, P.A., Elfgren, L., Fracture energy and fatigue strength of unreinforced concrete beams at normal and low temperatures, Engng Frac. Mech., 35 l/2/3 (1990) 195-203. [4] Plizzari, G.A., Cangiano, S., Alleruzzo, S., The fatigue behaviour of cracked concrete, Fatigue Fract. Engng Mater. Struct., 20 8 (1997) 1195-1206. [5] Thun, H., Ohlsson, U., Elfgren, L., A deformation criterion for fatigue of concrete in tension, Structural Concrete, 12 3 (2011) 187-197. [6] Mindlin, R.D., Micro-structure in linear elasticity. Arch. Rat. Mech. Analysis, 16 (1964) 52–78. [7] Aifantis, E.C., On the role of gradients in the localization of deformation and fracture, Int. J. Engng. Sci., 30 (1992) 1279–1299. [8] Altan, S.B., Aifantis, E.C., On the structure of the mode III crack-tip in gradient elasticity, Scripta Metall. Mater. 26 (1992) 319–324. [9] Ru, C.Q., Aifantis, E.C., A simple approach to solve boundary-value problems in gradient elasticity, Acta Mech. 101 (1993) 59–68. [10] Askes, H., Gutiérrez, M.A., Implicit gradient elasticity, Int J Numer Meth Engng, 67 (2006) 400-416. [11] Askes, H., Morata I., Aifantis E.C., Finite element analysis with staggered gradient elasticity, Comput Struct, 86 (2008) 1266-1279. [12] Askes, H., Gitman, I.M., Non-Singular Stresses in Gradient Elasticity at Bi-Material Interface with Transverse Crack, Int J Fract, 156 (2009) 217-222. [13] Askes, H., Aifantis, E.C., Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, Int. J. Solids Struct., 48 (2011) 1962–1990. [14] Dixon, W.J., The up-and-down method for small samples. Journal of the American Statistical Association, 60 (1965) 967-978. [15] Susmel, L., A unifying methodology to design un-notched plain and short-fibre/particle reinforced concretes against fatigue, Int. J. Fatigue, 61 (2014) 226–243. [16] Taylor, D., Geometrical effects in fatigue: a unifying theoretical model, Int J Fatigue, 21 (1999) 413-420. [17] Taylor, D., The Theory of Critical Distances: A new perspective in fracture mechanics, Elsevier, Oxford, UK (2007). [18] Susmel, L., Askes, H., Bennett, T., Taylor, D., Theory of Critical Distances vs. Gradient Mechanics in modelling the transition from the short- to long-crack regime at the fatigue limit, Fatigue Fract Engng Mater Struct., 36 9 (2013) 861- 869. [19] Susmel, L., Taylor, D., A novel formulation of the Theory of Critical Distances to estimate Lifetime of Notched Components in the Medium-Cycle Fatigue Regime, Fatigue Fract. Engng. Mater. Struct., 30 7 (2007) 567-581. [20] Susmel, L., Multiaxial Notch Fatigue: from nominal to local stress-strain quantities, Woodhead & CRC, Cambridge, UK, (2009). [21] Askes, H., Susmel, L., Understanding cracked materials: is Linear Elastic Fracture Mechanics obsolete?, Fatigue Fract. Engng. Mater. Struct., 38 (2015) 154–160.