Issue34

R. Brighenti et alii, Frattura ed Integrità Strutturale, 34 (2015) 59-68; DOI: 10.3221/IGF-ESIS.34.05 67 In the case of fibres aligned with the loading direction ( 0º   ), the sliding parameter stabilises after a certain number of loading cycles, and the maximum strain in the matrix appears to increase very slightly with N . C ONCLUSIONS n the present paper, a micromechanical model for the evaluation of the unixial or multiaxial fatigue behaviour of fibre-reinforced structural elements having equi-oriented or randomly distributed fibres has been presented. The effective spatial arrangement of the fibres is statistically taken into account by adopting a Gaussian-like distribution function, whereas the mechanical effect of the fibre on the composite is accounted for by a homogenization approach aimed at obtaining the macroscopic elastic constants of the material. The fatigue fibre-matrix debonding is evaluated by using a fracture mechanics approach. Matrix damage under fatigue is determined by considering the local anisotropy of the material due to the fibres, i.e. a multiaxial fatigue criterion for constant amplitude loading is proposed. Finally, the micromechanical model is employed to assess the fatigue behaviour of a representative unidirectional-reinforced polymeric samples, providing results in line with the experimental data. R EFERENCES [1] Jones, RMA., Mechanics of Composite Materials, second ed., Taylor & Francis Group, (1999). [2] Cheng, QG., Fiber Reinforced Composites. Nova Science Publishers, Inc., Hauppauge, NY, (2012). ISBN: 978-1- 62081-559-5. [3] Brighenti, R., Numerical modelling of the fatigue behaviour of fiber reinforced composites. Comp Part B, 35(3) (2004) 197–210. DOI: 10.1016/j.compositesb.2003.10.003 [4] Guo, LP., Carpinteri, A., Spagnoli, A., Sun W., Experimental and numerical investigations on fatigue damage propagation and life prediction of high-performance concrete containing reactive mineral admixtures. J Fat., 32 (2010) 227–37. DOI: 10.1016/j.ijfatigue.2009.05.009 [5] Pook, LP., The Role of Crack Growth in Metal Fatigue, Metals Society, London, UK, (1983). [6] Carpinteri, A., (Ed.) Handbook of Fatigue Crack Propagation in Metallic Structures, Elsevier Science BV, Amsterdam, (1994). [7] Pook, LP., Crack Paths, WIT Press, Southampton, UK (2002). [8] Wöhler, A., Versucheüber die festiykeit eisenbahnwagenuchsen, Z Bauwesen, 10 (1860). [9] Basquin, OH., The exponential law of endurance tests, Proc ASTM, 10 (1910) 625–630. [10] Paris, P., Erdogan, F., A critical analysis of crack propagation laws, J. Basic Engng, Trans Am Soc Mech Eng, 85 (1963) 528–534. DOI: 10.1115/1.3656900 [11] Brown, MW., Miller, KJ., A theory for fatigue failure under multiaxial stress-strain condition, Proc Inst Mech Engrs, 187 (1973) 745–755. DOI: 10.1243/PIME_PROC_1973_187_161_02 [12] Carpinteri, A., Macha, E., Brighenti, R., Spagnoli, A., Expected principal stress directions for multiaxial random loading - Part I: Theoretical aspects of the weight function method, Int. J. Fat., 21 (1999) 83–88. DOI: 10.1016/S0142-1123(98)00046-2 [13] Carpinteri, A., Spagnoli, A., Multiaxial high-cycle fatigue criterion for hard metals, Int. J. Fat., 23 (2001) 135–145. DOI: 10.1016/S0142-1123(00)00075-X [14] Sines, G., Failure of materials under combined repeated stresses with superimposed static stresses, Tech. Rep. Technical note 3495, Nat. Adv. Coun. Aeronaut., Washington D.C., USA (1955). [15] Cristofori, A., Susmel, L., Tovo, R., A stress invariant based criterion to estimate fatigue damage under multiaxial loading, Int. J. Fat., 30 (2007) 1646–1658. DOI: 10.1016/j.ijfatigue.2007.11.006 [16] Smith, K.N., Watson, P., Topper, TH., A stress-strain function for the fatigue of metals, J. Mater JMLSA, 5 (1970) 767–778. [17] Macha, E., Sonsino, CM., Energy criteria of multiaxial fatigue failure, Fat. Fract. Engng Mater. Struct., 22 (1999) 1053–1070. DOI: 10.1046/j.1460-2695.1999.00220.x [18] Ottosen, N.S., Stenstrom, R., Ristinmaa, M., Continuum approach to high-cycle fatigue modelling, Int. J. Fat., 30 (2008) 996–1006. DOI: 10.1016/j.ijfatigue.2007.08.009 [19] Brighenti, R., Carpinteri, A., A notch multiaxial-fatigue approach based on damage mechanics, Int. J. Fat., 39 (2012) 122-133. DOI: 10.1016/j.ijfatigue.2011.02.003 I