Issue 49

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

nodal displacements behind the delamination front [18]:

1 2





I I E X u Z w      ,

(1)

where I X and I Z are shear and opening forces in the node I , u  and w  are displacements corresponding to the shear and opening in the node L (Fig. 1).

Figure 1: Schematic implementation of the VCCT for finite elements

The energy release rate is then calculated as:

ΔE G ΔA ,



(2)

where ∆ is a crack surface. In real materials, the debonding crack usually grows simultaneously in all three modes of deformation (opening, in-plane shear and out-of-plane shear). In order to take this into account, the energy release rates are calculated for each mode ( , ,  ) I II III G G G and the subsequently summed:

T I III G G G G    . II

(3)

G . In this case, the beginning of the opening of two nodes and growth of

The latter is compared with the critical value C the crack occurs when the following condition is met:

G

T c

1  .

(4)

G

c G depends on all three modes of deformation and is defined using the mixed criterion. One of the

The critical value

most used criterion in three-dimension space is the Benzeggah and Kenane (BK) criterion [21]:

G G G  

I

II

III





f

1

,

(5)



 

  

II G G    G G G III





  

IC IIC IC G G G

I

II

III

Ic G , IIc G are determined experimentally for each laminated composite material.

where the constants

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