Issue 41

M.F. Funari et alii, Frattura ed Integrità Strutturale, 41 (2017) 524-535; DOI: 10.3221/IGF-ESIS.41.63 527 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: ( ) ( ) ( ) 1 1 1 2 2 1 r r i i I II i i f IC IIC G X G X g X G G æ ö æ ö ÷ ÷ ç ç ÷ ÷ ç ç ÷ ÷ = + - ç ç ÷ ÷ ç ç ÷ ÷ ÷ ÷ ç ç è ø è ø (3) 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 individual energy release rates calculated as ( ) 0 c n I n n n G T d D = D D ò and ( ) 0 c t II t t t G T d D = D D ò . For each mode components, the Traction Separation Law (TSL) is assumed to be described by the critical cohesive stresses, ( ) , c c t n T T , the critical and initial opening or transverse relative displacements, namely ( ) 0 , c n n D D and ( ) 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. 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) . (a) (b) (c)