Issue 38

D. Carrella-Payan et alii, Frattura ed Integrità Strutturale, 38 (2016) 184-190; DOI: 10.3221/IGF-ESIS.38.25

was implemented for woven is removed for UD: in woven fabrics, matrix de-cohesion clearly affects the stiffness in longitudinal and transverse directions, whereas in unidirectional plies, the effect of matrix degradation on longitudinal behavior can be neglected. However, the coupling between D 22 and D 12 remains mandatory and has been maintained. Finally, the deletion of this coupling imposes the addition of a propagation term in the formulation of D 12 , so that a pure shear load in a ply remains able to lead to its collapse. With these assumptions applied to the formulations taken from [2], the evolution laws for the damage variables become:   d d d c exp c c d exp c c 2 11 11 1,11 11 2,11 3,11 11 11 5,11 11 4,11 ( )                 

 

 

dN





11

3

   

   



   

11 ( ) 



c

  

  

d d

d

5,11

c exp c     1,11 11 

c d 3,11 11 11   

  

2

11



exp

c

2,11

11 4,11

 

dN

3





11

    

    



22 ( ) 



 f 2 D   12

f d

d d







d 3,22 22 22   



2

22

exp c 



c 5,22 22 4,22  



c

c

exp c

1





1,22

22

2,22

dN



2





D

1

22

12

(3)

3

    

    

    

    

22 ( ) 



c





  

  

d d

d

5,22

f



d 3,22 22 22   



2

2

22



D exp c   



 

c

c

exp

c

1





1,22

22

2,22

22 4,22

12

dN

3

f



2





D

1

22

12

         

         

12 ( ) 



d d

d









d    exp c 2   12 12

d 3,12 12 12   

  

2

12





c

c

exp c

c

1





1,12

2,12

5,12

12 4,12

dN





2





d

2 1

12

12

12 ( ) 



d d

d









d    exp c 2   12 12

d 3,12 12 12   



2

12





c 5,12 12 4,12  

c

c

exp c

1





1,12

2,12

dN





2





d

2 1

12

12

where c i,jk

are the 15 fatigue material coefficients that must be identified, the fatigue failure indices Σ ij

are the ratio between

the effective stress and the ultimate strength of the material in the ij component, and

   

   

   

 

 



ij

ij

ij 

ij 

 

 



 



max

max

;

cycle

ij

cycle

ij



ij      0 0

ij

(4)



0,  

ij



where

ij

,    



ij

ij



0     0

0,  

ij



where

ij

,    



ij

ij

Accumulated permanent strain In addition to these damage evolution laws, the model takes into account the permanent strain which appears in the ply due to a cyclic shear loading. Some matrix debris formed by the shear stress is accumulated in the opening matrix cracks during tension stress [2], which leads to a non-reversible deformation of the ply. The c 9 parameter drives the fatigue permanent strain accumulation following the formulation:

p







d

dd

dd

12

12

12











c max 9

c max 9

.

.

(5)

t

t

12

12

dN

dN

dN

186