Issue 41

M.F. Funari et alii, Frattura ed Integrità Strutturale, 41 (2017) 524-535; DOI: 10.3221/IGF-ESIS.41.63

The cohesive interfaces The cohesive interfaces are introduced between the sublayers in which the crack initiation could be potentially activated. The crack onset definition is described by means of a mixed crack growth, which is a function of the fracture variables, coinciding with the ratio between ERR mode components and corresponding critical values, as follows:

r

r

( ) 1 i

( ) 1 i

æ ç ç ç ç ç è

2 ö æ

ö ÷ ÷ ÷ ÷ ÷ ÷ ø

G X

II G X

2

÷ ÷

G ç ÷ ç ç ÷ ç ÷ ç ÷

( ) 1 i

I

i g X

1

=

+

-

(3)

f

G

ø è

IC

IIC

where i represents the generic i -th interface in which debonding phenomena may occur, r is the constant utilized to describe fracture in different material and ( ) , IC IIC G G are the total area under the traction separation law, whereas ( ) , I II G G are the

c n

c t

( ) n G T d D I

( ) t G T d D = D D ò . For each mode components, II t t

n = D D ò and n

individual energy release rates calculated as

0

0

the Traction Separation Law (TSL) is assumed to be described by the critical cohesive stresses, ( ) , c c t n 0 , c t t D D . It is worth nothing that the proposed model is quite general to include other existing cohesive formulation on a different TSL or stress based initiation criteria, just by modifying the analytical expression defined in Eq. 3. T T , the critical and initial opening or transverse relative displacements, namely ( ) 0 , c n n D D and ( )

(a)

(b)

(c)

Figure 2 : Representation of the coordinate systems employed: Before crack initiation (a) , After crack initiation, material and moving coordinates systems are coincident (b) , ALE formulation: referential and moving configuration introduced to described debonding phenomena (c) .

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