Issue 29

R. Dimitri et alii, Frattura ed Integrità Strutturale, 29 (2014) 266-283; DOI: 10.3221/IGF-ESIS.29.23

not derived from a potential and is characterized by a mixed-mode relative displacement g m

expressed as

2

2

N T g g  

g

(13)

m

and a mode mixity ratio  =g T

/g N . Single-mode loading conditions are again given by Fig. 2 and defined as

g g 

(1 ) 0 i i i K g

for

  

i

i

max

 

p

i i d K g for g

g g

(14)

  

i

i

i

iu

max

g g 

for

i

iu

with

( g g g  iu i

) ,

i

max max



, ; i N T d 



d

[0,1]

(15)

i

i



( g g

g

)

i

iu

i

and K i as the initial stiffnesses in modes I or II, used to hold the top and bottom faces of the debonding interfaces together in the linear elastic range. In order to avoid interpenetration of the crack surfaces, the following condition is also considered in mode I under compression , 0 N N N N p K g g   (16) The mixed-mode relative displacement corresponding to the onset of softening is computed as

    

2





1



g

g

for g

0

N T

N

max max



g

(17)

2

2 2





g

g

m

,max

N

T

max

max



g

for g

0

T

N

max

according to a quadratic failure criterion of the type

2

2

  

      

  

p

p

N

T



(18)

1

p

p

N

T

max

max

while the debonding propagation under mixed-mode loading is predicted by applying the power law (PL) criterion [13] or the Benzeggagh and Kenane (BK) criterion [14] defined in terms of the mode-I and mode-II work of separation W N , and W T , and fracture energies  N and  T . The expressions for the two criteria are given respectively as follows

W W 



  

T           T 

N



1

(19)



N

for the first criterion, with  as a constant material-dependent parameter, and



T       W W





N T N     



N T W W W  



with

(20)

for the second criterion, with  as the mixed-mode fracture energy, and  as a parameter obtained experimentally for varying materials and mixed-mode ratios. Based on Eq. (19) or (20), the ultimate value of the mixed-mode relative displacement is expressed as





1/



   







  

2     K

2

2(1 ) 



K

N N        

T



g

(21)

. m u

T 

g

 

m

,max

270