PSI - Issue 2_A

Stefano Bennati et al. / Procedia Structural Integrity 2 (2016) 072–079 S. Bennati, P. Fisicaro, P.S. Valvo / Structural Integrity Procedia 00 (2016) 000–000

75

4

Fig. 1. MMB test: (a) loading lever; (b) laminated specimen; (c) detail of the crack tip region and elastic interface.

Since C DCB depends on k z (through  1 and  2 ) and C ENF depends on k x (through  5 ), the elastic interface constants can be evaluated experimentally from DCB and ENF tests (Bennati and Valvo 2014). Alternatively, their values may be estimated by establishing an energy equivalence (Valvo et al. 2015), obtaining

G

E

35

15

, and

.

k

k





(4)

zx h

z

z

x

13 2

2 2

h

2.3. Energy release rate Under I/II mixed-mode fracture conditions, the energy release rate can be written as G = G I + G II , where G I and G II are the contributions related to fracture modes I and II, respectively. For the MMB test specimen,

2

2

dC

dC

I P

P

and

,

G

G

(5)

DCB

ENF





II

I

II

2

2

B da

B da

where

3

c

c









(6)

and

I P

P

P

P





II

4





are the loads responsible for fracture modes I and II, respectively. By substituting Eqs. (2) into (5), we obtain

2

2

2

I P

P

h

A









2

2

and

,

G

I  a h 

G

 a h 

(7)





II

1

I

II

II

2

2 B h

2 1 1 D A D 1 4 

16

B

D

1

where

1 1 1 

  

2 D D

 

  

1 h

1 1 1

2

h

(8)

d

2 1  x k

an





 

 



I 



1

1

 

II

4

h

h

k

h

A

D

 

5 

C

1

1

1

2

1

z

are crack length correction parameters (Bennati et al. 2013b). Eqs. (8) can be regarded as a generalisation for multidirectional laminates of the formulas given by the ASTM (2013) for unidirectional specimens.