Issue 49

M. Tashkinov et alii, Frattura ed Integrità Strutturale, 49 (2019) 396-411; DOI: 10.3221/IGF-ESIS.49.39

    A

    B

    C

    D

11 D f 

11 D f 

22 D f 

22 D f 

The variables

,

,

and

change instantly when the criterion is

triggered:

min f  

if f

0   

  f

  



(10)

else D

max

1 min f  ,



D

0,99

where

.

max

    E

12 D f 

The variable

changes according to the power damage evolution law:

 



if f

f

0    

;

min







f

f

max    D

  f

min



f  

if f

f

 ;

(11)

min

max







f

f

  

max

min

else

D

final

Here  , according to [32]. The Hashin fracture criterion for a composite ply includes four indicators representing a combination of strength constants and the components of the stress tensor in the ply: 1 min f  , 4, 35 max f  , 0,13   , 0, 484 max D  , 1 final D

2 X S  2

2



11  

12 2 2





f

,

0;

(12)

A

11

t

1

X 

11



 



f

(13)

,

0;

B

11

c





2







2

2

2







 









22

33

12

13

23

22 33



33   







f

, 

0;

(14)

С

22

2

2

2

Y

S

S

t

12

23

   

   

2





2







2

2

2

  

  













 





Y





22

33

c

12

13

23

22 33

22

33



33   











,

(15)

f

1

, 

0

D

22

2

2

2

S

Y

2

S

S

S

4

c

23

i

12

23

t X is tensile strength in direction 1; c

X is compressive strength in direction 1; t

Y is tensile strength in direction 2;

where

c Y is compressive strength in direction 2;

12 S is shear strength in the plane (1,2),

23 S is shear strength in the plane (2,3).

f is the tension failure indicator and B

f is the compression failure indicator for the ply fabric; С

f is the indicator

Here, A

f is indicator of matrix fracture under compression or shear

of matrix fracture under tension or shear in two directions, D

in the plane in two directions. Failure occurs if at least one of these criteria reaches or exceeds 1. It is accepted that variables     11 , A D f      11 B D f  ,     22 C D f  and     22 D D f 

vary according to the

instantaneous evolution law:

min f  

if f

0   

  f



  

(16)

else D

max

400