Issue34

R. Brighenti et alii, Frattura ed Integrità Strutturale, 34 (2015) 59-68; DOI: 10.3221/IGF-ESIS.34.05 66 (a) 1E+003 1E+004 1E+005 1E+006 1E+007 Number of cycles to failure, N f 25 30 35 40 45 50 55 60 65 70 Stress amplitude,  * (MPa) (b)  f =13%  Exp. res. [28] FEM, present res. 0º 30º Figure 6 : (a) Geometrical dimensions, expressed in (mm), and FEM model of the specimen; (b) the Wöhler curves of the glass fibre- reinforced polyamide specimen: experimental [28] and present results. 1E+003 1E+004 1E+005 1E+006 1E+007 Number of cycles to failure, N f 0.0 0.2 0.4 0.6 0.8 1.0 Matrix damage parameter, D E (-) 0.000 0.010 0.020 Matrix strain,  m (-) (a)  * = 45 MPa  0º 30º D E  m 1E+003 1E+004 1E+005 1E+006 1E+007 Number of cycles to failure, N f 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless debonded length,  (-) 0.0 0.2 0.4 0.6 0.8 1.0 Sliding function, s (-) (b)  * = 45 MPa  0º 30º  s Figure 7 : (a) Damage and strain evolution in the matrix (at point P) vs the number of stress cycles; (b) dimensionless fibre debonded length  , and sliding parameter s , (at point P) vs the number of stress cycles. The fatigue failure of the material is assumed to occur when the maximum matrix strain reaches a given admissible value that has been assumed equal to 10% in the present case. In Figure 6, the experimental S-N curves for the two considered fibre arrangements are reported. It can be observed that the fibres aligned with the fatigue loading direction are most effective and, for a given stress amplitude, a greater number of loading cycles can be reached before the material failure for such fibre arrangement. The numerical evaluation of the number of loading cycles to failure is in accordance with the above observation, providing results that are in acceptable agreement with the experimental outcomes [28]. In Figure 7a, the damage parameter E D , applied to the Young modulus of the matrix, is plotted together with the matrix strain against the number of loading cycles. In Figure 7b, the dimensionless fibre debonded length and the sliding function are plotted against the number of loading cycles N : the function ( ) s N decreases with N , indicating a decreasing of the fibre capability to carry the applied load transferred from the matrix as the number of cycles increases. As a consequence, the stress fraction sustained by the matrix increases with N (being constant the maximum applied stress during fatigue), and the damage in the bulk material increases. (b) (a) (b)