Issue34

R. Brighenti et alii, Frattura ed Integrità Strutturale, 34 (2015) 59-68; DOI: 10.3221/IGF-ESIS.34.05 62 0 2 4 6 8 10 Dimensionless time, t / T -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless cyclic stresses,  ' r ,  ' z  ' r,a  ' z,a  ' r  ' z (a) Figure 2 : (a) Radial and axial cyclic dimensionless stresses vs time: definition of the effective stress amplitudes. (b) Scheme of the radial and axial matrix stresses near a cylindrical fibre. Figure 3 : (a) z r    fatigue domains that identifies conventional fatigue life for a biaxial normal stress state. (b) The Wöhler curve for a uniaxial cyclic stress history. A generic mechanical parameter can be reduced by using the above damage variable as follows: ,0 , ( ) 1 ( ) m m f n P N P D N       (6) where ,0 m P is the initial value of the generic parameter, and ( ) m P N is its fatigue affected counterpart. A suitable choice for modeling the matrix material under fatigue is to impose 0 0 m m P E  , where 0 m E is the undamaged Young modulus, whereas its damaged counterpart is equal to the modulus ( ) m E N , with * * 0 ( ) 1 ( , , ) m m cm E N E D R N        , where * * ( , , ) cm D R N  is the damage parameter obtained according to Eq. (5) evaluated by assuming 1, , , max( , ) n a r a z a S      , i.e. the equivalent uniaxial cyclic stress is identified by the maximum principal stress amplitude at the point under consideration. F RACTURE MECHANICS APPROACH TO EXAMINE THE FIBRE DETACHMENT he problem of the fibre-matrix detachment can be solved through a fracture mechanics approach. As a matter of fact, a partially debonded cylindrical fibre can be represented by a three-dimensional crack lying between two different materials [21, 22]. Such a problem is the spatial counterpart of the case related to an elastic bi-material T (a) (b) (b) (a)