Issue34

R. Brighenti et alii, Frattura ed Integrità Strutturale, 34 (2015) 59-68; DOI: 10.3221/IGF-ESIS.34.05

0.0 0.2 0.4 0.6 0.8 1.0

(a)

(a)

 ' r

(b)

Dimensionless cyclic stresses,  ' r ,  ' z

 ' r,a

 ' z

 ' z,a

-0.4 -0.2

0

2

4

6

8

10

Dimensionless time, t / T

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.

(b)

(a)

z 

r 

 fatigue domains that identifies conventional fatigue life for a biaxial normal stress state. (b) The Wöhler curve

Figure 3 : (a)

for a uniaxial cyclic stress history.

A generic mechanical parameter can be reduced by using the above damage variable as follows:

   

 

( ) P N P

, f n D N

(6)

1

( )

m

m

,0

( ) m P N is its fatigue affected counterpart.

,0 m P is the initial value of the generic parameter, and

where

A suitable choice for modeling the matrix material under fatigue is to impose 0 0 m m P E  , where 0 m Young modulus, whereas its damaged counterpart is equal to the modulus

E is the undamaged

( ) m E N , with

* * 1 ( , , ) cm E N E D R N       0 ( ) m m

* * ( , , ) cm D R N  is the damage parameter obtained according to Eq. (5) , i.e. the equivalent uniaxial cyclic stress is identified by the maximum ) 

 , where

  



S

evaluated by assuming

max(

,

n

a

, r a z a ,

1,

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

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